Thresholds, tipping points, and random events in dynamic economic systems
Charles Sims ([email protected]) is a Faculty Fellow at the Howard H. Baker Jr. Center for Public Policy and an assistant professor in the Department of Economics at the University of Tennessee, 1640 Cumberland Ave, Knoxville, TN 37920.
David Finnoff ([email protected]) is an associate professor in the Department of Economics and Finance, 1000 E. University Avenue, University of Wyoming, Laramie, WY 82071.
Charles F. Mason ([email protected]) is the H. A. "Dave" True, Jr. Chair in Petroleum and Natural Gas Economics in the Department of Economics and Finance, 1000 E. University Avenue, University of Wyoming, Laramie, WY 82071.
In economics, threshold behavior is most commonly observed in the literature related to dynamic economic systems with multiple equilibria (Dasgupta and Mäler, 2003; Deissenberg et al., 2004). In these systems, tipping point phenomena arise when variables cross a threshold in the state space that represents the boundary of two different basins of attraction. Crossing this boundary triggers a shift from one long run outcome to another. Thresholds of this type have been investigated in growth theory (Skiba, 1978), development (Azariadis and Drazen, 1990), labor (Diamond, 1982), trade
(Krugman, 1991), environmental (Tahvonen and Salo, 1996), and natural resources (Lewis and Schmalensee, 1977). Initial conditions and economic shocks take on increased importance in such systems as initial conditions may determine the optimality of a given equilibrium and random events can cause a system to unexpectedly tip causing lock-in to undesirable long run outcomes. Multiple equilibria most commonly arise due to convex production technologies but may also arise in concave systems (Wirl and Feichtinger, 2005). The thresholds in the multiple equilibria systems are usually called Skiba thresholds or points though all thresholds in these models are not Skiba thresholds.
In 2005, a special issue of the Journal of Economic Behavior & Organization (JEBO) was devoted to thresholds and multiple equilibria (Semmler, 2005). Since that time, economic research in this area has extended in five main areas:
2. Development of coupled human-natural models that more fully mesh social and natural science perspectives on thresholds and tipping points (see Sims, Finnoff, and O’Regan in this volume). Economic decisions are often made in the context of natural systems that have a history of or are thought to exhibit thresholds and tipping points. For example, epidemiologists have long known disease dynamics are governed by prevalence thresholds above which the disease outbreaks and below which eradication is achieved (Allen and Lahodny Jr, 2012). Ecologists are aware of regime shifts in natural systems whereby ecological processes flip as seen in the eutrophication of shallow lakes (Carpenter et al., 1999). Climatologists are increasingly concerned about potentially
irreversible climate tipping points (Lenton et al., 2008). This integration has caused economists to more carefully differentiate between thresholds and regime shifts. A threshold is a boundary in the state space that causes a discontinuous change in economic outcomes but leaves the dynamic economic system unchanged. The dynamic systems models with multiple equilibria discussed above are all examples. In contrast, a regime shift is an event that triggers a discrete change in the
dynamics of the system (see Baggio and Fackler in this volume). This integration has also led to a greater focus on whether thresholds and tipping point phenomena have economic or ecological origins (see Fenichel and Horan in this volume).
3. Use of agent based and network models to investigate how individual- or firm-level behavior manifests as tipping point phenomena at an aggregate level (see Wood, Mason and Finnoff in this volume). Agent-based models allow for the study of macro phenomena without making
2015). Agent-based models have also been used to investigate the factors that trigger cooperation in a common pool resource problem (Janssen and Rollins, 2012).
4. Adoption of recent advances in the econometrics literature on the well-known identification problem to differentiate systems with thresholds and tipping points from those that simply produce identical empirical patterns (see Chavas, Grainger and Hudson in this volume). Many dynamical processes that have little to do with tipping points produce identical empirical patterns (Brock, 2006). The recent popularity of identification techniques have allowed economists to separate true tipping point dynamics that produce punctuated equilibria from exogenous dynamics of unobserved variables (Durlauf and Young, 2004).
5. Quantifying the economic impacts of thresholds and tipping points (see Heutel, Moreno-Cruz, and Shayegh in this volume). Traditionally, economic models are developed to explain observed threshold behavior and tipping point phenomena and suggest possible avenues to avoid them. As computable general equilibrium models have advanced, greater attention has been devoted to linking dynamic models with models of the larger economy to more carefully articulate the implications of crossing a threshold or tipping point. This is particularly evident in the growth of integrated assessment models in climate change economics (Lenton and Ciscar, 2013).
economic considerations in the designation of critical habitat. Since its establishment in 2003, the Baker Center has developed a research and policy outreach agenda focused on global security, energy, and the environment. The workshop attracted papers that provide policy-relevant insights consistent with this agenda. We thank Matthew Murray, the Director of the Baker Center, along with the Baker Center staff, for their help in making the workshop such a success.
Several studies focus on climate change and two of them utilize integrated assessment models (IAM). Dereck Lemoine and Christian Trager show how aversion to Knightian uncertainty about a climate tipping point affects the optimal tax on carbon emissions. Knightian uncertainty is thought to be key to formulating climate policy since climate tipping points have rarely been observed in history. Using a numeric application based on a reformulation of the DICE IAM as an infinite-horizon dynamic programming problem, they show that aversion to Knightian uncertainty about climate tipping points does increase the optimal tax on carbon emissions but only by a small amount. Garth Heutel, Juan Moreno-Cruz, and Soheil Shayegh also use a variant of DICE to study the effect of climate tipping points on the optimal usage of CO2 emission reduction policies and solar geoengineering. They compare
dynamics. Determining when climate tipping points have been crossed in the past can help current policy makers better understand when the costs and benefits of climate policies my abruptly shift. Unfortunately, identifying the presence of climate tipping points from CO2 data is an enormous
empirical challenge because lag effects in CO2 concentrations can vary with previous concentration
levels. This can undermine the usage of more traditional quantile autoregressive models. They find evidence of reversible tipping points but not irreversible tipping points.
Two studies focus on energy. The first uses evolutionary game theory and agent-based modeling to investigate a regime shift from one cartel to another in world oil markets. Aaron Wood, Charles Mason, and David Finnoff consider the historical interval where world oil market dominance shifted from seven major oil firms to OPEC. They are particularly interested in the learning and adaptation that characterize the 13 year delay between OPEC’s founding and its ascent to the leading force in global oil markets. They find two factors are critical to the ability of OPEC countries to learn to operate as a collusive cartel: market share advantage and discontent over comparatively low payoffs. The second energy paper takes an empirical approach. Charles Mason and Neil Wilmot study the economic impacts of one potential manifestation of reversible thresholds and tipping points in the larger macroeconomy – price
discontinuities. Utilizing an application to the market for Renewable Information Numbers, they show that both time-varying volatility and price jumps contribute to the fat tails in the distribution of price returns and ultimately investments in capital projects linked to renewables.
a risk-based inspection process recently proposed by the US Department of Agriculture’s Animal and Plant Health Inspection Service (APHIS). They find that heterogeneity among exporters is essential for arriving at a plausible and optimal threshold for compliance group designation. David Finnoff, Rick Horan, Jason Shogren, Carson Reeling, and Kevin Berry make the point that decisions about the best risk reduction mix between human and natural sources of risk reduction matter most for systems vulnerable to ex post multi-stability. If a managed natural resource system has the potential to begin in one of multiple, locally optimal basins of attraction, ex ante decisions of risk reduction can affect the initial conditions for the ex post system, thereby determining the ex post basin of attraction and the optimal ex post state. In the case of a managed natural resource at risk of invasion, an ex ante system that is convex and uniquely stable without risk may become non-convex and multi-stable in the presence of endogenous risks and ex post multi-stability.
valuable predator but no ability to control an unmarketable prey species. The implication of this work is that thresholds in ecological systems may disappear as managers are given increased flexibility to manage the system. Eric Naevdal focuses on optimal resource management when the resource is at risk of catastrophic collapse. The paper provides results that qualify Weitzman’s well-known “dismal
theorem” and question commonly held views about the importance of the marginal value of a resource after a catastrophe: even if the marginal value function with respect to the initial level of the state variable may approach infinity as the state variable goes to zero it need not be optimal to avoid this point in finite time at almost any cost.
Two studies focus on public health responses to infectious disease. Charles Sims, David Finnoff, and Suzanne O’Regan couple a stochastic epidemiological model of disease spread with an optimal stopping model to show how efforts to improve disease forecasting influence cost-effective public health
responses to infectious disease. First moment improvements in disease forecasts (adjustments to the expected prevalence of the disease in the future) can hasten or delay cost-effective public health responses to infectious disease. But second moment improvements in disease forecasts (lowering the forecast error) will always hasten public health responses. Using a gonorrhea and pneumococcus outbreak as illustrative examples, they illustrate how the relationship between disease forecasting and public health responses depends on the forecast error, private prevention by individuals and the location of epidemiological thresholds. Kevin Berry and David Finnoff take on the challenge of investment in prevention and adaptation capital stocks in the face of increasing global risk from
pandemic disease leading to an uncertain regime shift. A differentiation is made between investment in prevention, which can be in remote regions where the risk of pandemic disease builds, and investment in domestic adaptation in an attempt to protect one’s own country. Results demonstrate that
prevention effort is not 100% effective. Furthermore, in the face of risk that is rising over time due to changing environmental conditions, stocks of both capital ought be built up with large initial
investments, and then continually invested in over time. Investments and the mixture of strategies in the portfolio of risk reduction capital depend on how the underlying risk of a pandemic changes over time as well as the marginal returns to each capital stock, and how these adjust as the risk changes.
Much of the existing literature assumes a threshold or regime shift in environmental damages but exogenous and fixed environmental preferences. In the final paper, Bruno Nkuiya and Christopher Costello consider whether the possibility of a future shift in environmental preferences may affect optimal current emissions of a pollutant. They model the regime shift using a hazard function and convert the stochastic regime shift model into a deterministic optimal control problem. This approach allows them to identify a direct effect in which the uncertainty about the regime shift raises the incentive to pollute and an indirect effect where the uncertainty about the regime shift lowers the incentive to pollute. Only in a special case where the pollutant causes no environmental damage will the possibility of a shift in environmental preferences unambiguously lead to lower current emissions.
This special issue was made possible due to the support of many. We in particular are grateful for the support provided by Elsevier, JEBO and especially JEBO Editor William Neilson. We thank all authors for their valuable contributions to both the workshop and this special issue. We also thank paper discussants that provided valuable comments that improved the papers in this volume and aided in the journal review process. These individuals are Florian Diekert, Jacob LaRiviere, Eili Klein, Jacob Hochard, Ben Meiselman, Max Melstrom, Scott Farrow, David Kling, Zhi Li, Shana McDermott, Rolf Groeneveld, and Michael Taylor.
References
Allen, L.J., Lahodny Jr, G.E., 2012. Extinction thresholds in deterministic and stochastic epidemic models. Journal of Biological Dynamics 6, 590-611.
Azariadis, C., Drazen, A., 1990. Threshold externalities in economic development. The Quarterly Journal of Economics, 501-526.
Boettiger, C., Mangel, M., Munch, S., 2015. Avoiding tipping points in fisheries management through Gaussian process dynamic programming. Proceedings of the Royal Society of London B: Biological Sciences 282, 20141631.
Brock, W.A., 2006. Tipping points, abrupt opinion changes, and punctuated policy change, in: Repetto, R. (Ed.), Punctuated Equilibrium and the Dynamics of US Environmental Policy. Yale Univeristy Press, pp. 47-77.
Carpenter, S.R., Ludwig, D., Brock, W.A., 1999. Management of eutrophication for lakes subject to potentially irreversible change. Ecological Applications 9, 751-771.
Crépin, A.-S., Biggs, R., Polasky, S., Troell, M., de Zeeuw, A., 2012. Regime shifts and management. Ecological Economics 84, 15-22.
Dannenberg, A., Löschel, A., Paolacci, G., Reif, C., Tavoni, A., 2015. On the provision of public goods with probabilistic and ambiguous thresholds. Environmental and Resource Economics 61, 365-383.
Dasgupta, P., Mäler, K.-G., 2003. The Economics of Non-Convex Ecosystems: Introduction. Environmental and Resource Economics 26, 499-525.
Deissenberg, C., Feichtinger, G., Semmler, W., Wirl, F., 2004. Multiple equilibria, history dependence, and global dynamics in intertemporal optimization models, in: Barnett, W.A., Deissenberg, C.,
Diamond, P.A., 1982. Aggregate demand management in search equilibrium. The Journal of Political Economy, 881-894.
Durlauf, S.N., Young, H.P., 2004. Social Dynamics. Mit Press.
Gualdi, S., Tarzia, M., Zamponi, F., Bouchaud, J.-P., 2015. Tipping points in macroeconomic agent-based models. Journal of Economic Dynamics and Control 50, 29-61.
Janssen, M.A., Rollins, N.D., 2012. Evolution of cooperation in asymmetric commons dilemmas. Journal of Economic Behavior & Organization 81, 220-229.
Krugman, P., 1991. History versus expectations. The Quarterly Journal of Economics, 651-667.
Leibenstein, H., 1950. Bandwagon, snob, and Veblen effects in the theory of consumers' demand. The Quarterly Journal of Economics, 183-207.
Lengnick, M., 2013. Agent-based macroeconomics: A baseline model. Journal of Economic Behavior & Organization 86, 102-120.
Lenton, T.M., Ciscar, J.-C., 2013. Integrating tipping points into climate impact assessments. Climatic Change 117, 585-597.
Lenton, T.M., Held, H., Kriegler, E., Hall, J.W., Lucht, W., Rahmstorf, S., Schellnhuber, H.J., 2008. Tipping elements in the Earth's climate system. Proceedings of the National Academy of Sciences 105, 1786-1793.
Lewis, T.R., Schmalensee, R., 1977. Nonconvexity and optimal exhaustion of renewable resources. International Economic Review, 535-552.
Pindyck, R.S., 2007. Uncertainty in Environmental Economics. Review of Environmental Economics and Policy 1, 45-65.
Schelling, T.C., 1971. Dynamic models of segregation. Journal of Mathematical Sociology 1, 143-186. Semmler, W., 2005. Introduction. Journal of Economic Behavior & Organization 57, 381-389.
Skiba, A., 1978. Optimal growth with a convex-concave production function. Econometrica: Journal of the Econometric Society, 527-539.
Tahvonen, O., Salo, S., 1996. Nonconvexities in optimal pollution accumulation. Journal of Environmental Economics and Management 31, 160-177.
Order of papers:
1. Ambiguous Tipping Points by Christian Traeger
2. Climate Tipping Points and Solar Geoengineering by Juan Moreno-Cruz 3. Policy tradeoffs under risk of abrupt climate change by Yacov Tsur
4. How Should Economists Model Climate? Tipping Points and Nonlinear Dynamics of Carbon Dioxide Concentrations by Corbett Grainger
5. OPEC, the Seven Sisters, and Oil Market Dominance: An Evolutionary Game Theory and Agent-Based Modeling Approach by Aaron Wood
6. Price Discontinuities in the Market for RINs by Chuck Mason
7. Harnessing enforcement leverage at the border to minimize biological risk from international live species trade by Michael Springborn
8. Natural vs Anthropogenic Risk Reduction: Facing Invasion Risks Involving Multi-Stable Outcomes by David Finnoff
9. Optimal management with reversible regime shifts by Michele Baggio
10. Tinbergen and Tipping points: Could some thresholds be policy-induced? by Eli Fenichel 11. Catastrophes and Ex Post Shadow Prices - How The Value Of The Last Fish In A Lake Is Infinity
And Why We Shouldn't Care (Much) by Eric Naevdal
12. Public control of rational and unpredictable epidemics by Charles Sims
13. Choosing between adaptation and prevention with an increasing probability of a pandemic by Kevin Berry
