Causal Analytics for Applied Risk Analysis Louis Anthony Cox, Jr

Discussion: Principles for Applying the Frameworks to Improve Decisions and Policies
How might an engineer, planner, or policy maker apply insights from the preceding frameworks to improve practical disaster protection and mitigation decisions, such as how high to build a costly levee or sea wall, or how large (and rare) a tsunami, earthquake, flood, or hurricane to plan for in the design of nuclear power plants or other facilities, or how much to invest in a proposed community resilience or civil defense program? The following suggested principles seek to distil from the fameworks implications to help guide practical decision-making when current choices have long-lasting consequences that may affect risks and benefits to future generations.

1. 
   Use wide framing. Consider a wide range of alternatives to optimize benefits produced for resources spent, taking into account opportunity costs. Exploit different ways to reduce risk. The optimal economic growth framework implies that each method for maximizing a social objective function – whether by investing in economic growth, in reducing potential disaster-related losses, in less costly and more rapid and resilient recovery following disasters, or in other improvements that reduce risk or increase wellbeing – should be funded optimally in each period in competition and combination with the other approaches. In simple settings with diminishing marginal returns, for example, this typically requires funding each alternative up to the point where a different one starts to yield larger marginal returns in improving the objective function. Thus, a planner wondering whether to invest in a higher sea wall or barrier against flooding should ask not only “Is the extra cost of a taller barrier justified by the extra benefit from reduced risk?” but also “Could a larger reduction in risk (or, more generally increase in objective function) be achieved by not making it taller, and instead applying the resulting cost savings to other opportunities, such as relocating people or improving local early warning and transportation systems?” More generally, optimal provision of safety and other good requires considering opportunity costs and optimizing economic trade-offs, while avoiding narrow framing (Kahneman, 2011) that considers only one approach at a time (e.g., investment in levees, but not change in zoning or land use). The optimization problems to be solved can be viewed as allocating each period’s limited resources to a portfolio of alternative ways to increase the objective function, with one of those ways being to bequeath more to the next generation, which may have different opportunities.
   
2. 
   Follow golden-rule consumption and investment principles. Do not over-invest (or under-invest) in protecting or benefitting future generations compared to the present one. Biases such as the affect heuristic (Kahneman, 2011) can encourage simplistic thinking that equates current consumption with selfishness and greed (bad affect) and equates current investment to protect or benefit future generations with benevolence, virtuous self-restraint, and generosity (good affect). Optimal growth models, including ones with ethical and justice constraints, tell a more nuanced story. Under-consumption and over-accumulation of capital stocks to pass on to the future violate the golden-rule maxim of doing in each generation what one would want other generations to do to maximize sustainable utility (Phelps, 1961). From this perspective, increasing saving and investment on behalf of the future is not necessarily always better. Instead saving and investing at the golden-rule rate, and not more, maximizes the wellbeing of present and future generations. Thus, optimal economic growth theory weans us from a multi-generation zero-sum perspective, in which increased current consumption necessarily comes at a cost to future generations. Instead, it encourage a cooperative perspective in which members of different generations collaborate in maximizing the sustainable level of wellbeing.
   
3. 
   Use simple rules to help optimize current decisions. Exploit qualitative properties of optimal policies to simplify practical decisions. The economic growth perspective can be implemented in detail if trustworthy mathematical or computational models are available representing the causal relation between choices and the probabilities of their consequences (immediate and delayed). Techniques such as stochastic dynamic programming can then be used to decide what to do in each period to maximize a social objective function. Mathematical and computational techniques and resulting solutions can become quite sophisticated and complex, but, in many settings, the optimal solutions have qualitative properties that can inform and improve practical decision-making with simple rules that take into account future effects, even when detailed models and numerical optimization results are not available. For example, both optimal growth and Rawslian justice might require first boosting economic productivity as quickly as possible to a level where desirable institutions can be sustained and passed on from one generation to the next. Once there, optimal growth policies often have simple characteristics, such as saving and investing just enough so that the marginal productivity of additional capital stock offsets (equals) its effective depreciation rate due to aging, population growth (which dilutes the capital-per-worker), and other causes, including occasional disasters or catastrophes (Phelps, 1961). Risk management to jointly optimize consumption and investments in growth, disaster prevention and mitigation to maximize average utility of consumption per capita per period might require keeping capital stocks of renewable resources at or above certain threshold levels to avoid risk of collapse, which could reduce or eliminate their availability to subsequent generations (Olson, 2005). Such simple characterizations of optimal growth and risk management policies can help to focus practical policy-making analysis and deliberation on a few key questions, such as whether the current savings and investment rate is clearly above or below the socially optimal rate (e.g., the golden rule rate, in a Solow growth model (Phelps, 1961)); or whether stocks of renewable resources are currently above or below safety-stock thresholds. The answers then suggest directions for remedial actions, such as increasing or reducing investment, respectively. Pragmatic constraints may limit how much adjustment can be made how quickly. In short, knowledge of the qualitative properties of optimal policies, such as the existence of thresholds or of optimal rates of capital accumulation or investment, can produce simple decision rules (e.g., take action to increase investment or stock of a renewable resource if we are below the optimal level, or to decrease it if we are above the optimal level, where the optimal level is estimated from data on depreciation rates or renewal rates, respectively). Such simple rules can often help to answer the practical policy question of what to do next, even without explicit formulation, estimation, and solution of sophisticated multi-period optimization models.
   
4. 
   Do not discount the utility from future benefits. Count lives saved in different generations equally and count increases in utility received in different generations equally. In particular, do not discount future lives saved or future utility from benefits received simply because they are in the future. This follows from Rawlsian justice models that treat the interests of future participants in an extended multi-generational social contract symmetrically with present ones. It implies that benefits such as improvements in quality-of-life per person per year due to increased resilience and reduced anxiety, or greater consumption utility per capita-year, should not be discounted. In making cost-benefit comparisons, lives saved or life-years improved that accrue over the lifetime of a facility should all be counted equally according to such models of justice over time. The practical effect of this recommendation is to increase the present evaluation of benefits that flow from current decisions into the future, such as the benefits from risk reductions obtained via current investments in levees or in other protective or resilient infrastructure. Although multi-period optimization methods such as stochastic dynamic programming can still be used to decide what to do in detail, if credible models are available to support the required calculations, concern for intergenerational justice will modify the usual objective function of expected discounted social utility to give equal weights to life-saving or other intrinsically valued benefits received at different times.
   
5. 
   Consider the value of waiting. Do not commit prematurely to expensive present actions with long-lasting or irreversible consequences. Trust future generations to help decide what is best. This principle requires current decision-makers to consider the potential value of seeking and using better information to improve decisions before committing resources or foreclosing other options. For example, it may be worthwhile for Federal regulators to let individual states experiment with new measures first, and to learn from the consequences, before deciding on a Federal policy that all states must follow. This cautious principle, of seeking to learn more before betting large-scale investment decisions with lasting consequences on what currently seems to be the best choice, follows from studies of fundamental trade-offs in making protective investments under uncertainty, such as the trade-off between investing in proposed measures to protect future generations against possible future harms vs. investing in other ways that, in retrospect, all members of all generations might prefer (Krysiak and Collado, 2009; Hoberg and Baumgartner 2011). Acknowledging realistic uncertainties about future costs, benefits, risk attitudes, preferences, technology alternatives, and opportunity costs highlights the potential value of seeking more information before committing to decisions with long-lasting or irreversible consequences, such as about the height of a levee, enactment of enduring regulation of carbon dioxide emissions, diminishment of economic growth rates in order to invest in protective measures, or consumption of non-renewable resources.
   

Our first principle above, wide framing, encourages planners confronted with a proposed costly measure to reduce risks to future generations to ask not only “Is it worthwhile?” in the sense that the proposed measure’s benefits exceed its costs, but also “Is there a cheaper way to achieve the same benefits?” The latter question is typically a matter for engineers and economists. The answer is often that no one knows yet. If further research can reduce current uncertainties, then value-of-information (VOI) calculations from decision analysis can address the question of whether the benefits of that research, in terms of improving decisions and their probable outcomes, exceed the costs of doing it, including potential costs from delay. (Indeed, such VOI considerations are automatically included in stochastic dynamic programming whenever acquiring more information is a possible choice.) Thus, the planner should also ask a third question: “Is it worthwhile to pay for better information before deciding whether to approve the proposed risk-reducing measure?” When decisions have long-lasting consequences that affect future generations, the value of information acquired to help make the best decision – the decision that will be preferred in retrospect when future information becomes available – may be especially great.

Likewise, there may be a value to keeping options open, recognizing that the best choice based on current information may not still be seen as the best one when evaluated using future information. There can be a “real option” value to keeping options open until better information is available on which to act, even if delay is costly. Again, stochastic dynamic programming considers such real option values as well as VOI, and optimizes information collection and the timing of decisions, including ones with irreversible or long-lasting. However, the guiding principle of stochastic dynamic programming is the Bellman optimality principle: that each generation’s (or period’s) decisions are made optimally, assuming that all future generations’ (or periods’) decisions will likewise be made optimally (Olson, 2005). Practical application of this principle across generations requires decision-makers in different generations to collaborate in implementing it consistently, with each generation acting accordingly, but having to trust other generations to do the same. Behavioral game theory suggests that such cooperation is far more likely than would be expected based on purely rational (System 2) responses, in part because of moral psychology and pro-social impulses (System 1 responses) that make us eager to reciprocate the generosity of earlier generations by being, in our turn, equally generous to our successors. However, System 1 responses are notoriously non-quantitative, and are not designed to identify and optimize quantitative trade-offs (Kahneman, 2011). Thus, deliberate investments in social capital, a culture of trustworthiness and effective cooperation, and building resilient communities, may help generations to collaborate more effectively over time in implementing long-term plans that benefit all of them.

Conclusions
Making decisions well over time is challenging for societies as well as for individuals. Our moral intuitions often deliver altruistic and benign impulses toward others, including strangers separated from us in time or by geography. But they usually do not render finely calculated decisions about how to optimize trade-offs between our benefits and theirs. Nor do they identify the most efficient use of protective and other investments (e.g., in growth of economic prosperity, or in building community resilience) to accomplish desired trade-offs, or to carry out the prescriptions of ethical and justice theories to maximize the average or minimum wellbeing of members of present and future generations. Methods of multi-period optimization that have long been used in optimal economic growth models can accomplish these quantitative trade-off and optimization tasks. They can be adjusted to incorporate principles of intergenerational justice, such as assuring that the lives and utilities of future people are not discounted relative to those of people now living. In simple models, including the multi-generation pie-charting example that we started with and in golden-rule optimal growth models (Phelps, 1961), multi-period optimization leads to simple consumption and investment rules that also satisfy equity and sustainability conditions. In this way, System 2 methods can be used to help identify multi-generation investment plans to achieve ethical goals that System 1 might approve of. The results can often be expressed as simple decision rules that are useful for informing practical policy-making, such as taking actions to adjust levels of investments or of renewable resources toward desired target levels based on estimated marginal rates of return or renewal rates, respectively, perhaps with adjustments for the value of information and of keeping options open.

However, even when clear and simple rules can be identified for maximizing a social objective function, such as the average or minimum utility per capita in present and future generations, it takes cooperation across generations to implement them. In turn, this may require just and effective institutions, high social capital, and community resilience, as prerequisites for effective multi-generational cooperation in managing losses due to natural disasters or other causes. These insights suggest that successful efforts to improve intergenerational justice and efficiency must be rooted in a deep understanding of human social nature and cooperation over time, and of the possibilities for designing and maintaining effective cultures and institutions for promoting and sustaining such cooperation. They also require clear understanding of the goals that we seek to achieve in collaboration with other generations, and of the trade-offs that we want to make when those goals conflict.

The frameworks and principles discussed in this chapter make a start at clarifying possible goals and trade-offs among them, and the implications of technical principles (especially, stochastic dynamic programming distributed over multiple generations) for achieving them. How to develop institutions and cultures that promote effective cooperation over time and across generations, as well as within them, without necessarily assuming that future generations will share our preferences and values, remains a worthy problem for both theoretical and applied investigation.
Epilog: A Vision for Causal Analytics in Risk Analysis
This book has set forth a particular vision of how individuals, organizations, and societies can use analytics to identify choices that make their preferred outcomes more likely and predictably regrettable decisions less likely. It uses causal models to describe how a relevant part of the world works by describing how outcome probabilities change in response to different choices of actions, policies, or interventions. Chapters 1-9 discussed and illustrated technical methods for using data to learn, validate, and document causal models using techniques such as Bayesian networks, structural equations, and probabilistic simulation modeling. Chapters 10-15 discussed various ways in which causal understanding of the relation between current actions and probabilities of future consequences can be used in risk management.

Causal models, in turn, are used to quantify how probabilities of outcomes change as decision variables or policies are changed. Policies can be be thought of as decision rules that map data or observations – what a decision-maker sees or knows – to choices of actions or controllable inputs to a system or situation. Consequences result. Markov decision processes, influence diagrams, optimal control, reinforcement learning, multi-arm bandit problems, and probabilistic simulation models allow quantitative modeling of the causal relationship between actions or policies and outcome probabilities. Given such a causal model and a utility function or social utility function expressing preferences for outcomes and attitude toward risk, optimization algorithms solve for the best actions or policies – those that maximize expected utility or reward or net present value; or, in some formulations, minimize expected loss or regret. Sensitivity analyses and value of information (VOI) analyses characterize the robustness of recommended decisions to remaining uncertainties and help decide whether to acquire more information before acting, given the potential costs and benefits of delay. For decisions made sequentially over time, dynamic optimization techniques can be used to optimize the timing of interventions. It then remains to implement the recommended decisions or policies, evaluate how well they are working (Chapters 10 and 11), and adjust them over time as conditions change or simply as better information is collected.

Implementing this vision of causal modeling, decision optimization, and ongoing evaluation and adaptive learning requires causal analytics methods to meet the following five technical challenges:

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  Learning: How to infer correct causal models (e.g., causal Bayesian networks or optimal control models or simulation models) from observational data?
  
• 
  Inference: How to use causal models to infer probable values of unobserved variables from values of observed variables? This subsumes diagnosis of observed symptoms in terms of probable underlying causes; prognosis or forecasting of future observations from past ones; detection of anomalies or changes in data-generating processes; and identification of the most probable explanation for observed quantities in terms of the values of unobserved ones.
  
• 
  Causal prediction: How to predict correctly how changing controllable inputs would change outcome probabilities or frequencies, e.g., how reducing exposures would change mortality rates? The answer to this manipulative-causation question is needed to optimize controllable inputs to make preferred outcomes more likely.
  
• 
  Attribution and evaluation: How to use a causal model to attribute effects to their cause(s), meaning quantifying how the effects would have been different had the causes been different? Defining and estimating direct, total, controlled direct, natural direct, natural indirect, and mediated effects of one variable on another are variations on attribution that are enabled by causal graph methods. Evaluation of the effects of an intervention or policy amounts to attributing a change in outcomes or their probabilities to it.
  
• 
  Generalization: How to generalize answers from study populations(s) to other populations?
  
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  Decision optimization: How to find combinations of controllable inputs to maximize the value (e.g., the expected utility) of resulting outcome probabilities? Simulation-optimization, influence diagram algorithms, dynamic optimization algorithms such as stochastic dynamic programming, and reinforcement learning provide constructive methods for answering this question.
  

Chapters 1 and 2 discussed technical methods for meeting each of these challenges for causal Bayesian networks (BNs), dynamic Bayesian networks (DBNs), influence diagrams, and other models equivalent to them. Subsequent chapters applied causal modeling and risk analytics methods, especially probabilistic simulation and Bayesian networks, to several diverse real-world risk analysis and policy challenges. They illustrate how a combination of descriptive, predictive, prescriptive, evaluation, learning, and collaborative analytics principles and methods can be applied to clarify a wide range of public and occupational health risk analysis problems and more general questions of policy analysis for both the short and long runs. Throughout, causal analysis and modeling of risk have played central roles by quantifying the changes in outcome probabilities, frequencies, or expected values caused by changes in controllable inputs.

The central lessons of this book are that (1) Methods of causal analytics are now sufficiently well developed to support both the theory and practice of risk analysis; and (2) It is is important to use them in practice. In particular, causal analytics methods such as structural equation models, causal Bayesian network and directed acyclic graph (DAG) models, and probabilistic simulation models are useful for addressing structural and mechanistic causation, as well as predictive causation. They can be used to model manipulative causation, which is essential to guide effective decision-making. By contrast, currently widely used methods of association-based analytics, such as statistical regression modeling of observational data, are usually much less useful for understanding, predicting, and optimizing the effects of policies and interventions on outcomes of concern, because they do not describe manipulative causation.

Our hope is that the methods for causal analytics explained and illustrated in this book will increasingly be applied by policy analysts, risk analysts, and other analytics practitioners to make data more useful in guiding causally effective decisions – that is, decisions that willbetter accomplish what they are intended to, while more successfully avoiding unintended and unwanted conseqeunces. We believe that better understanding of the causal relation between actions or policies and their probable outcomes is the key to more effective decision recommendations and to more useful evaluations of their effects. Modern causal analytics methods and software for developing such understanding are now much more readily available than ever before. Using them can transform the practice of applied risk analysis, decision analysis, and policy analysis, enabling practitioners to provide more effective and reliable advice on what to do to achieve desired outcomes.