DSICE: Dynamic Stochastic Integration of Climate and Economy

I started working on climate change policy modeling in 2008, and it has been a major focus of my efforts since then. In 2010, Yongyang Cai, Thomas Lontzek and I created the DSICE model, extending Nordhaus’ DICE to include productivity shocks as well as stochastic elements of the climate system. While we had earlier published some applications of DSICE, the most complete exposition and application appeared in the Journal of Political Economy in December, 2019. I must first clarify a detail. As the paper says, I was a coauthor in all substantive aspects, even after I removed my name as an official author. This was not due to any dispute with my coauthors or any dissatisfaction with the paper as published. JPE made it clear that the presence of my name as an author reduced the chances of it being accepted. I wanted the paper to appear in JPE and help my coauthors’ career progress. Therefore, I removed my name.

The economic question explored was “What is the social cost of carbon, and how does it depend on parameter assumptions?” Even though we examined a wide range of parameter specifications for Epstein-Zin preferences and the stochastic productivity process advocated by the macroeconomics literature, the range for the current social cost of capital (also, the optimal carbon tax from a world policy perspective) was $40-$100 per ton of carbon. This range includes the results of other models but contains a larger upper region due to our including economic uncertainty. The key intuition is that the loss function is convex, and increasing the variance of future temperatures will increase the social cost of carbon.

We also analyzed the impact of a stochastic tipping process, such as glacier melting leading to rising sea levels. Damages from tipping processes are different from damages related to business cycle fluctuations because, for example, the melting of glaciers is irreversible from the perspective of economic planning. Those damages are only moderately correlated with consumption. Therefore, the stochastic asset pricing kernel that DSICE implicitly computes will discount tipping point damages at a lower rate, magnifying their contribution to the SCC. More generally, we show that there is no one discount rate for climate change damages and that consumption CAPM considerations will affect the SCC.

Our analysis is a major advance in IAM models. We used the full, five-dimensional, climate model developed by Nordhaus, whereas many authors use far simpler climate models. Some assume that CO2 emissions immediately heat the atmosphere, ignoring the heating process in the atmosphere and the presence of the ocean as a heat sink. Climate scientists can use the simplified approach because they think in terms of millennia. Economists cannot ignore events at annual, or even quarterly, frequencies. We solve the dynamic programming model with one-year time periods and have checked that results are unchanged by reducing the time period. A few others have added economic risk to their models but they assume far less variance than standard macroeconomic estimates. Some have included tipping point phenomena in their models but using less realistic specifications.

Twenty-five years ago, I wrote in my book that if meteorologists used the same approach to research as economists, “they would ignore complex models … and instead study evaporation, or convection, or solar heating, or the effects of the earth’s rotation. Both the weather and the economy are phenomena greater than the sum of their parts, and any analysis that does not recognize that is inviting failure.” Our DSICE analysis shows that we now can solve models with realistic economic shocks, realistic specifications for tipping points, and the full Nordhaus climate model. Furthermore, it shows that this kind of multidimensional modeling can be done in many areas of economics.

This paper goes back several years. The code was developed by early 2012, applied to a simpler specification and deployed on a small supercomputer. Thomas Lontzek presented the first version at the 2012 Conference on Climate and the Economy organized by the Institute for International Economic Studies. Yongyang Cai presented this paper at the conference “Developing the Next Generation of Economic Models of Climate Change Conference” at University of Minnesota, September 2014. Earlier versions include Hoover economic working paper 18113 (2017)(https://www.hoover.org/research/social-cost-carbon-economic-and-climate-risk), arXiv:1504.06909 (2015) (https://arxiv.org/abs/1504.06909), NBER working paper 18704 (“The social cost of stochastic and irreversible climate change”), “DSICE: A dynamic stochastic integrated model of climate and economy” (2012) (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1992674), and “Tipping points in a dynamic stochastic IAM” (2012) (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1992660).

This paper introduces two features that help document the validity of our computational results. As many know, I do not trust anyone’s computational results, even my own. My lectures frequently use the phrase “Trust, but verify” taken from the Russian Doveryáy, no proveryáy. The JPE paper’s results relied on trillions of small optimization problems and billions of regressions. The sheer scale of the problem justifiably raises reliability questions. DSICE uses value function iteration over centuries, necessary because of the non-stationary nature of the problem. Each iteration takes the time t value function and computes the time t-1 value function at a set of points efficient for approximation and then applies regression to approximate the time t-1 value function. At each iteration, we check the quality of this approximation by computing the difference between the approximation and the true value at a random set of points in the state space. Our verification tests tell us that we have three- to four-digit accuracy for most of the important functions. This approach to verifying computational results can be applied to any computational work in economics, and help deal with the replication problems in economics. We are not aware of any other serious work which performs demanding verification tests, but strongly advocate its adoption by authors, editors, referees, and journals.

Many journals encourage authors to share their code, but our code contains copyrighted material and cannot be publicly posted. Readers need to be assured of accuracy of computations behind a paper’s results. To that end, we created Mathematica notebooks for a few examples which contained the solutions and code that would allow the reader to check first-order conditions.

The kind of modeling in DSICE has often been called, and is still being called, impossible to do. Many authors indicate that they would like to examine more general models (which would still be far simpler than DSICE) but assert that it is intractable. We were able to solve the models in the JPE paper for several reasons: we used high quality numerical methods for integration and optimization, we developed basis functions that were suited to the problem, and we were able to use massive parallelization. The key novelty in this paper was using supercomputing at a scale far beyond other economics work (as far as we know).

Massive parallelism is natural for solving dynamic programming problems. We got our first experience by working with Miron Livny (developer of HTCondor), Stephen Wright and Greg Thain, all at the University of Wisconsin. Livny gave us access to a UW cluster — “unlimited access with zero priority” — which worked fine for Yongyang’s 2008 PhD thesis. When, in 2010, we began developing DSICE, we had to move to supercomputers. In November, 2012, we applied to the Blue Waters supercomputer supported by the NSF, and had access to it nearly continuously until NSF ended the project last year. Access to Blue Waters made it possible to solve the most complex example in our JPE paper with about 80,000 cores for over four hours. We owe a lot to the University of Wisconsin people who got us started and to the Blue Waters project for giving us what we needed for the applications of DSICE used in our JPE paper.

This paper proves that regular economists at any university can get access to substantial supercomputing time. Many of you will be skeptical about this claim because I am a Stanford employee in the heart of Silicon Valley and Yongyang was supported by a NSF grant administered by Argonne National Labs and the University of Chicago. Stanford may have access to high-power computers, but those resources are controlled by individual University units. The Hoover Institution does not (nor should it) have a supercomputer for research. At one time, Yongyang and I thought we would have access to computers at Argonne and/or Chicago, but the co-PIs of that grant at Argonne and UC denied our request for access to any UC or Argonne computer. We instead, at the suggestion of Bob Rosner, applied for allocations on Blue Waters. Yongyang and I wrote the proposals, wrote the end-of-year reports, and made the required appearances at the annual Blue Waters Symposium. Yongyang did the coding without major support from Blue Waters staff; in fact, he found a bug in their compiler. From 2013 to 2019, we received over one million node hours, where each node had between 16 and 32 cores, adding up to over 25 million core hours.

I emphasize these facts for two reasons: to show that social scientists do not need major institutional support to get supercomputer time, and to recognize Yongyang for his hard work and determination in getting the job done with little help.

I have long advocated the use of modern computing hardware and algorithms in economics. Our JPE paper is just one demonstration of what economists can do on their own. This blog will discuss other such demonstrations. I also hope that the computational science community will see that economists can be worthy research partners.

Here we go again

Last Friday, Karl Schmedders (IMD University and University of Zurich) and I placed an op-ed in The Hill: https://thehill.com/opinion/international/509991-the-real-view-from-europe-on-coronavirus-relief-in-america. We made the point that the US Government has again failed to fix obvious problems with the unemployment insurance systems, forcing another costly and inefficient stimulus package. We also pointed to the absence of an endgame to deal with rising personal debt arising from the rent moratorium. Europe has not had these problems because they learned from past crises. Why can’t American lawmakers learn?

Last April, Karl and I wrote an op-ed on the best approach to helping corporations in the current crisis. Our point was that Federal aid to any publicly traded corporation should require that firm to give the US a proportionate equity interest in the firm, but in a manner that does not interfere with management and is not a form of nationalization. This was hardly a radical idea because in 2008, also a time with a Democratic House, a Republican Senate and a Republican President, assistance to corporations often required substantial equity positions for the Federal government. The CARES Act instead made loans which are unlikely to be repaid. So, I would like someone to show me the math that says the approach in CARES is better than that taken in 2008-9.

Fortune magazine published that op-ed on April 16, 2020: https://fortune.com/2020/04/16/coronavirus-economic-impact-government-bailout-business-loans-preferred-stock/

European governments did use the equity approach this spring in some cases.

Henry Petrovski, author of “To Engineer is Human” and other books on engineering, often writes on how engineers learn from their mistakes. European policymakers have learned some lessons from crises. Why can’t American policymakers and their economics advisors learn from their failures?

An earlier and more detailed piece on the preferred stock approach is available at http://www.igmchicago.org/covid-19/the-preferred-stock-approach-to-help-corporations/. For your convenience, I put that version below.


The preferred stock approach to help corporations

Dr. Kenneth L. Judd, Hoover Institution, Stanford University, judd@stanford.edu

Prof. Karl Schmedders, Department of Business Administration, IMD Lausanne, karl.schmedders@imd.org

March 25, 2020

The good news from Washington is that policymakers are making progress on a plan for the COVID-19 crisis. The bad news is that many details are missing, and there does not seem to be a coherent plan based on sound economic principles. The Federal government does not have unlimited resources and the use of those funds must be transparent and defensible in this already toxic political environment.

One approach under consideration is to lend substantial amounts of money to businesses. Perhaps that is the best way to help some firms, but we don’t like the idea of large-scale lending to corporations at low interest rates. Some corporations do need access to cash, but it will be impossible for the government to determine which ones “deserve” the help. There are not enough government bureaucrats in Washington for sorting through the requests in a rational and fair manner. To insure some rationality to the allocation of these funds, there should be a price paid by borrowers that does not interfere with the immediate policy goals. So, here is a (crazy?) idea. Let’s have the US government (Fed, Treasury, or some other entity) buy newly issued preferred stock of publicly-traded corporations.

Here are our points:

First, many firms need cash to survive the sudden disruption in business. Some are having supplier problems, some have experienced a sharp downturn in demand, and some have had to shut down but must still pay fixed costs such as rent and interest. Some firms will ultimately go through bankruptcy but that should be determined later when the true long-run economic value of a firm can be determined.

Second, lending adds to corporate debt, and obligations to repay that debt may create future liquidity problems. That problem is only aggravated by using high interest rates to steer government aid to corporations that need the cash most. The obligations from issuing preferred stock can be adjusted to available cash as long as the owners of preferred shares are treated at least as well as owners of common stock.

Third, preferred stock has no voting rights. We do not want government bureaucrats in board rooms.

Fourth, we believe that the US government will make substantial profits from this approach. We believe that the collapse in stock markets is partly due to the rush to cash and not related to long-run fundamentals. Who disagrees with this assessment of future equity values? Some corporate leaders have said they prefer cheap credit to any government equity position. It sounds like they share our optimistic view. If the US government thinks that it would lose money on these preferred stock investments then we are in far deeper trouble than we thought.

The key point is to get cash to corporations quickly, but do so in a manner that does not create new financial problems, does not interfere with corporate management decisions, but allows the government to share in the upside potential of the future US economy.

We next expand on these points.


We must minimize the number of bankruptcies. Our court system does not have the capacity to handle the potential tsunami of bankruptcies.  

Many people point to the airlines as examples of where bankruptcies do not disrupt operations. When airlines go through Chapter 11, they can continue operations during bankruptcy through debtor-in-possession (DIP) financing which are loans senior to all other claims. Creditors will participate in DIP financing as long as the cash flow from ongoing business can cover operating costs and DIP obligations and if alternative uses of cash are not better investments.

The past experience with bankrupt airlines is not applicable in these times. The GM situation in December, 2008, is more relevant. GM was about to run out of cash. Private-sector DIP financing at reasonable terms was not available. Chapter 7 — liquidation of all assets — was the likely outcome of any GM bankruptcy. Because of this, the Bush administration lent GM money and took an equity position, giving the Obama administration time to work out the reorganization of GM.

Preferred stock

Equity investment by the government is better than loans for helping firms deal with cash flow problems, but we do not want government officials sitting on corporate boards. Preferred stock fits these requirements. All management decisions are still in the hands of the voting shareholders. No government moral hazard. This is not nationalization.

Preferred shares are uncommon in the US because of various legal details, but given the emergency nature of the situation we are sure that this could be changed quickly. We do not know all the various details of existing types of preferred stock.  There may need to be changes in tax law and regulations but do lawyers have anything better to do at this time?

There is one important detail left to discuss: price. The lack of preferred stock plus the panic condition of the market makes it difficult to rely on market prices for preferred shares. Negotiating the price for each corporation could lead to costly delays. In our opinion, the simplest approach would be to have the firm’s financial obligations to holders of these preferred shares be the same as their obligations to owners of common shares. In essence, make the preferred shares the same as common shares but with no vote. In that case, market prices tell us the right price for a deal.

The preferred equity approach also helps with reaching some political consensus. Substantial aid to corporations will be opposed by many political leaders. Equity participation allows all to share in the upside potential of these investments.


Many of the 2008-2009 bailouts had similar features. The AIG bailout, in particular, was one where the government received substantial equity participation in return for bailout money. The US Treasury claims it made $22.7B on this deal. While some dispute this number, the point remains: equity participation was a feature of TARP and other interventions.

In the Chrysler bailout in the late 1970’s, the government received warrants. Chrysler was saved, Chrysler stock went up and the US made money. However, warrants are not appropriate for the current crisis because price negotiations will cause delays.

These previous bailouts were special deals between the US and the borrower. TARP included equity positions but had many other complicated features. The government was a major player in the GM bankruptcy proceedings and political considerations played a major role in the final settlement. 

The firm-by-firm approach of past bailouts is not possible in the current situation because there are too many borrowers and too few government lawyers. Any plan must avoid discretion that may lead to cronyism and political interference. The current situation demands a simple, transparent program where each firm faces the same offer of government assistance, decides how much help they need, and how much equity dilution they pay for that help, all without ceding any control. If a corporation does go bankrupt in the future, the US government claims are settled on terms standard for preferred stock.

Alternative approaches

There may be some other financial mechanisms that could accomplish the same goal more quickly. Perhaps this requires changes in laws regarding what the Fed and/or the Treasury can buy. Perhaps required changes in regulations and laws make it impossible to immediately get to the target situation.  It may be easier to immediately issue the loans but make them convertible, at the government’s option, to preferred stock when the preferred stock is issued and regulations have been adjusted appropriately. It is obvious that we do not understand all the legal details but we are sure that the army of lawyers sitting at home (or their ski lodges, or their beach houses, or wherever) can find some path that requires minimal changes in laws and regulations and can be quickly implemented.

The big advantage of the preferred stock approach is that each corporation faces the same menu. No special deals for cruise lines, for hotels, or other industries that claim special circumstances. Perhaps we will eventually agree that some industries deserve special treatment but that can wait. The task now is to avoid unnecessary business failures. Later we can decide on burden sharing.


This proposal addresses only the problems faced by publicly traded corporations. There is nothing in this proposal that directly addresses the financial challenges of small businesses or of the millions of workers who are facing substantial loss of income. It is a political fact that government aid to corporations will get high priority. There are two advantages of this proposal: it is simple and transparent, and it will likely produce revenue for the US government to cover the costs of aiding the rest of the economy. 

There are surely many problems with our proposal that we have not considered. We pose a specific question: is there a better way to help publicly traded corporations? 


There will be massive financial aid to businesses. In the case of publicly traded corporations, existing institutions and financial instruments similar to preferred stock can be used to accomplish the key objectives: quickly send funds to the firms with the greatest needs, offer repayment terms that do not cause more liquidity problems in the near term, avoid any kind of nationalization of industry, minimize the long-run drain on increasingly scarce US government resources, and avoid political conflict.