Frank Ackerman found another outlet for his tired and wrong claims. Here's my response.

Ackerman and Munitz (2016) offer a critique of estimates of the economic impact of climate change and the social cost of carbon in general, and the FUND model in particular. I am grateful for the opportunity to reply. In this response, I note that (i) their concerns are not new; (ii) they highlight strengths of FUND rather than its weaknesses; and (iii) they revisit their old mistakes. I conclude with a few improvements to FUND prompted by Messrs Ackerman and Munitz.

Incremental contribution
There is little if anything new in Ackerman and Munitz (2016). They note that FUND’s estimates of the social cost of carbon are highly sensitive to assumptions about (i) carbon dioxide fertilization and (ii) vulnerability to climate change. Anthoff, Tol, and Yohe (2009) and Waldhoff et al. (2014) previously report a strong sensitivity to carbon dioxide fertilization. Tol (1996) and Anthoff and Tol (2012b) previously highlight the importance of development and vulnerability. It is unfortunate that these papers were not referred to by Messrs Ackerman and Munitz.

Highlighting FUND’s strengths
That said, I am grateful to Messrs Ackerman and Munitz for highlighting two of FUND’s main strengths. Other integrated assessment models attribute all impacts of climate change to global warming. FUND, on the other hand, separates climate change, sea level rise, ocean acidification, and carbon dioxide fertilization. This is key because the dynamics of these processes are quite distinct.

Although it is generally acknowledged that poorer countries are more vulnerable to climate change, other integrated assessment models assume that growing richer leaves vulnerability unaffected. Instead, FUND assumes that societies will become less vulnerable in the future if they grow richer.

Repeating past mistakes
A third concern is that Ackerman and Munitz (2016) revisit an earlier paper (Ackerman and Munitz 2012a) but omit key details. Having downloaded the source code, Messrs Ackerman and Munitz altered the code, and claimed there was an error and that this error was due to Anthoff and Tol. Ackerman and Munitz (2012b) withdraws some of the more egregious claims by Ackerman and Munitz (2012a), particularly that the alleged error was made by Anthoff and Tol. Stern (2012) notes that Ackerman and Munitz had suppressed evidence that contradicts their claim of an error. Anthoff and Tol (2012a) show that the Ackerman and Munitz test for errors is inconclusive. In other words, Ackerman and Munitz (i) claimed an error had been made without evidence, (ii) ignored evidence that there was no error, and (iii) blamed the error-that-wasn’t on the wrong people.

Improvements to FUND
Upon reflection, we changed access to the model code. FUND can still be freely downloaded and used by anybody, but changes in code or data are now attributed to specific users. This prevents a repetition of Ackerman and Munitz (2012a): Any alteration is tied to a particular programmer and therefore no one can blame someone else for an error they themselves made.

We also changed the model specification. Reading the agricultural impact function as a univariate probability distribution, a reader may conclude that, in FUND3.6 and prior, there is a risk of dividing by zero. There is not. The probability distribution is bivariate, not univariate, so that the risk is minimal – and indeed unobserved in the many Monte Carlo experiments run with the model. Furthermore, the code has safeguards at three levels against numerical errors. (These issues were pointed out to Mr Ackerman before Ackerman and Munitz (2012a) was submitted for publication.) Nevertheless, in order to avoid further misinterpretation, we reformulated these equations.

At the end of the day, I am grateful to Messrs Ackerman and Munitz for prompting these improvements, although I would wish for more nuanced and rigorous analysis in the future. At code school, we learned that a user interface has to be robust to anything. Our software engineering lecturer used the metaphor of a chimp typing random keys. That metaphor does not apply here. When putting FUND in the public domain, I overlooked that I created a new interface, one prone to interpretation and reinterpretation. Messrs Ackerman and Munitz usefully remind us that interfaces have to be robust to the unexpected.

References
Ackerman, Frank, and Charles Munitz. 2012a. "Climate damages in the FUND model: A disaggregated analysis." Ecological Economics 77 (0):219-224.
Ackerman, Frank, and Charles Munitz. 2012b. "Reply to Anthoff and Tol." Ecological Economics 81:43. doi: 10.1016/j.ecolecon.2012.06.023.
Ackerman, Frank, and Charles Munitz. 2016. "A Critique of Climate Damage Modeling: Carbon fertilization, adaptation, and the limits of FUND." Energy Research and Social Science.
Anthoff, David, and Richard S. J. Tol. 2012a. "Climate damages in the FUND model: A comment." Ecological Economics 81:42. doi: 10.1016/j.ecolecon.2012.06.012.
Anthoff, David, and Richard S. J. Tol. 2012b. "Schelling's Conjecture on Climate and Development: A Test." In Climate Change and Common Sense -- Essays in Honour of Tom Schelling, edited by Robert W. Hahn and Alistair M. Ulph, 260-274. Oxford: Oxford University Press.
Anthoff, David, Richard S. J. Tol, and Gary W. Yohe. 2009. "Risk Aversion, Time Preference, and the Social Cost of Carbon." Environmental Research Letters 4 (2-2):1-7.
Stern, David I. 2012. "Letter from the Associate Editor concerning the comments from Anthoff and Tol and Ackerman and Munitz." Ecological Economics 81:41. doi: 10.1016/j.ecolecon.2012.06.007.
Tol, Richard S. J. 1996. "The Damage Costs of Climate Change Towards a Dynamic Representation." Ecological Economics 19:67-90.
Waldhoff, Stephanie, David Anthoff, Steven K. Rose, and Richard S. J. Tol. 2014. "The marginal damage costs of different greenhouse gases: An application of FUND." Economics 8. doi: 10.5018/economics-ejournal.ja.2014-31.