News Tag: Research Reflection

Research Reflection: Navigating Uncertainty

Navigating Uncertainty

March 11, 2022

Uncertainty is pervasive and impacts many economic decisions that participants in the macroeconomy frequently make. How should individuals and enterprises navigate this uncertainty? How does this uncertainty spill over to financial markets? How should we incorporate uncertainty, broadly conceived, into policymaking? I have some recent contributions that wrestle with these questions, with some at a much more conceptual level and others directed at enhancing our understanding of markets and policy.

Two of the more conceptual papers mentioned below show how to formalize “ambiguity aversion” in models that are posed in continuous time.  Both papers are co-authored with Jianjun Miao, Boston University. To place this work into context, imagine an environment in which a decision-maker uses historical data to update beliefs about a family of models. Learning can occur with Bayesian updating, but only with the caveat that the updating rule requires a prior distribution. Indeed, when it comes to subjective inputs into decision-making, the Italian probabilist statistician, Bruno de Finetti remarked:

“Subjectivists should feel obligated to recognize that any opinion (so much more the initial one) is only vaguely acceptable. . . So, it is important not only to know the exact answer for an exactly specified initial problem, but what happens changing in a reasonable neighborhood the assumed opinion.”

Robust Bayesian methods seek to address this challenge. In a dynamic setting, ambiguity about the initial subjective prior implies over to the posterior distribution conditioned on a data history. In effect, “yesterday’s posterior is today’s prior.” We adopt a robust Bayesian approach to decision-making and produce tractable continuous-time, recursive formulations by making a novel limiting argument. By design, the outcome is a recursive, smooth ambiguity adjustment.1 This derivation of ambiguity aversion with a well-defined continuous-time limit is provided in the PNAS paper entitled, “Aversion to Ambiguity and Model Misspecification in Dynamic Economic Environments.” Our more recent paper entitled, “Asset Pricing under Smooth Ambiguity in Continuous Time” takes this formulation “out for a spin” by deducing some novel asset pricing implications and exploring consequences for portfolio choice in the face of both Brownian motion risk and ambiguity over alternative models of state dynamics.

The other two conceptual papers discuss challenges that arise when potential model misspecification is entertained at a formal level. It has long been appreciated that we use models that are necessarily misspecified to guide our understanding. One of the more famous quotes in this regard is by George Box (1979):

“Now it would be very remarkable if any system existing in the real world could be exactly represented by asimple model. However, cunningly chosen parsimonious models often do provide remarkably useful approximations.”

When econometricians devise formal tests of models, unfortunately, this insight is often lost. However, a lot is loaded into the term “useful” in Box’s quote. In my view, potential model misspecification is an important component to uncertainty worthy of analysis in its own right.

How is a concern for model misspecification best formalized in practice, and how is the accompanying “aversion” distinct from ambiguity aversion? Two of the recent papers explore this theme building on earlier work by my co-authors and me and by others. One working paper, entitled, “Making Decisions Under Model Misspecification” takes an “axiomatic” approach by formalizing the aversion to potential model misspecification concerns in contrast to aversion to ambiguity over alternative models.

The other paper, “Structured Ambiguity and Model Misspecification” (published in the Journal of Economic Theory) is explicitly dynamic, building connections between statistical measures of divergence and model misspecification concerns. In misspecification analysis, there needs to be some way of limiting the ways in which the dynamic statistical model could be flawed. In our past work, as well as that of many others, we found value in using what are referred to as statistical divergences to restrict the range of possible alternative models under consideration. By design, a statistical divergence is small for models that are hard to distinguish when using historical evidence. As Tom Sargent and I show in the paper, some commonly used approaches to ambiguity aversion are incompatible with our use of statistical divergences to limit the type of potential model misspecification. The paper with Sargent also explores the tension between the well-known statistical construct of admissibility and dynamic consistency.

Importantly, the smooth ambiguity preferences derived in the Hansen-Miao PNAS paper also allow for misspecification concerns. Similarly, Hansen and Sargent in their recent Journal of Economic Theory paper show how to extend previous continuous-time specifications of ambiguity aversion to incorporate explorations of potential model misspecification.2

I also have some applied papers that explore the implications of these decision theory formulations in practice.  I think of them as more than just “illustrations of methods,” as they provide novel substantive insights. My paper with Tom Sargent “Macroeconomic Uncertainty Prices When Beliefs are Tenuous” published in July 2021 in the Journal of Econometrics shows how ambiguity aversion induces fluctuations in asset prices as the perspective investors have on alternative models shifts depending upon the state of the macroeconomy. The research reflection “Acknowledging and Pricing Macroeconomic Uncertainties” VOX EU/CEPR provides a broader perspective and a nontechnical discussion of this research. The two papers with Barnett and Brock explore the implications for the social cost of carbon when ambiguity and model misspecification concerns are incorporated into the modeling.  The decision-maker in these papers is a hypothetical “social planner,” and the social cost of carbon is deduced as the shadow price. The paper entitled, “Uncertainty Spillovers for Markets and Policy” published in August 2021 in the Annual Review of Economics provides an overview of these and related contributions in economics and finance.

Finally, I joined a set of scholars across alternative disciplines in writing a perspectives issue on lessons from decision theory for designing public policy responses to pandemics entitled, “Rational Policymaking During a Pandemic” published in January 2021 in PNAS.

 

1 The notion of “smooth ambiguity” was introduced by Klibanoff, Marinacci, Mukerji (2005, Econometrica), but with the explicit link to robust Bayesian methods.
2 See Chen and Epstein, 2002, Econometrica for a continuous-time formulation of ambiguity aversion.

Papers:

Applications:

 

Hansen on Global Pandemic and Using Quantitative Models to Guide Policy Amid COVID-19

Professor Lars Peter Hansen recently published a working paper titled, “Using Quantitative Models to Guide Policy Amid COVID-19 Uncertainty,” that looks at how economic models may help us better understand the COVID-19 outbreak.

Reflection: Working Paper on Pricing Uncertainty Induced by Climate Change

I have repeatedly asked myself, “Why did you write this paper?”

It is hard to dispute the social importance of environmental questions. As I, and others, have argued elsewhere, purely evidence-based policy is a misnomer in general, and most certainly for this particular problem. Theory and evidence have to be equal dance partners.

Quantitative storytelling is a credible way to conduct policy analysis in dynamic settings. It combines so-called “stylized modeling” with empirical evidence. We purposefully consider multiple stories, with carefully worked-out narratives that are formally captured as models, which have different ramifications for the environment and the economy. For dynamic problems such as this one, multiple “stories” are virtually impossible to dismiss on either theoretical or empirical grounds. I have little doubt that this multiplicity is germane to many policy problems. So, perhaps the answer to my own question should be obvious.

This analysis has attracted much more attention than most of my recent papers. For me, it has been both challenging and rewarding. My co-authors, Mike Barnett, William “Buz” Brock and I pushed ourselves to bring together tools from decision theory, asset valuation and control theory to confront uncertainty outside of the usual confines of risk analysis typically focused on in economics and finance.

So why did I pose the question at the outset? In part, perhaps in large part, this contribution is a “proof-in-concept” paper for informing policy in the face of uncertainty. Thus, we designed the framework to be a template for future research, including by ourselves and other researchers. But we also deliberately chose climate economics as our featured example. Because our specific analysis is both novel and novelistic, I feel it needs some explanation. While we use the social cost of carbon to explore the impact of uncertainty, our reported numbers are merely our first step for this type of analysis. These numbers are not ready to be posted on the Environmental Protection Agency (EPA) website, which is mechanically embraced by “green books” for policy analyses. We did not write this to provide soundbites for media coverage.

In our quantitative application, we show that the social cost of carbon could become very large without additional forms of mitigation, technological change, adaptation and/or policy intervention. We abstract from regional and developmental heterogeneity, which should be part of a more full accounting. Of course, these limitations should be explored and they will alter the implied social cost of carbon. We are actively engaged in revealing extensions that will allow us to confront some of these shortcomings along with more ambitious climate inputs. In summary, this paper is not meant as the answer, but as our initial step in incorporating broad notions of uncertainty in a formal policy analysis while avoiding overstated claims of our current knowledge base.

I am continually haunted by the warning in Hayek’s Nobel address:

“Even if true scientists should recognize the limits of studying human behavior, as long as the public has expectations, there will be people who pretend or believe that they can do more to meet popular demand than what is really in their power.”

While those social scientists interested in quantitative policy analysis should not just throw in the towel, they should remain cognizant of the limits to their knowledge and understanding.

For more on “Pricing Uncertainty Induced by Climate Change,” watch Lars Peter Hansen in conversation with co-author Michael Barnett or read the full paper.

Lars Peter Hansen is the Director of BFI’s Macro Finance Research Program and the David Rockefeller Distinguished Service Professor in Economics and Statistics and the Booth School of Business.

This reflection was originally posted on the Becker Friedman Institute website.

Chicago Booth Review: Purely Evidence-based Policy Doesn’t Exist by Lars Peter Hansen

Reflection on MFR’s conference on Cryptocurrencies and Blockchains

The Macro Finance Research Program (MFR) co-hosted a conference on, “Cryptocurrencies and Blockchains” with conference architects Eric Budish, Zhiguo He, Jacob Leshno and Harald Uhlig. While the topics covered at the conference have received major public attention, the aim of it was to explore what new special modeling challenges are posed by the introduction of cryptocurrencies and what economic and social consequences to expect with the technological advances associated with distributed ledgers for reducing transactions costs and enhancing social welfare. To address these issues, the conference brought together experts in asset pricing, monetary economics, market design and computer science to engage in productive exchanges.

During the conference I was reminded of the commonly used slogan: “evidence-based policy.” Except for pure marketing purposes, I find this terminology to be a misnomer, a misleading portrayal of academic discourse and the advancement of understanding. While we want to embrace evidence, this evidence seldom speaks for itself and typically requires a modeling or conceptual framework for interpretation. Of course, observed phenomena, including say the behavior of cryptocurrencies, motivate and influence how we structure alternative modeling frameworks. But our interpretations of the data and its implications are through the lens’ of models. Essential to this conference and to this new area of research are the modeling challenges for this exciting new area of research. At the conference, formal models were continually featured throughout the presentations and discussions as a way to enhance our understanding of the crypto-blockchain phenomenon and to guide our thinking about the potential for socially productive outcomes. The models were sometimes used to frame empirical measurement, but they also played preeminent roles in the presentations and captured much of the discussion.

Research presented at this conference, including papers by the four co-organizers, provided formal modeling efforts that addressed central questions pertaining to cryptocurrency and distributed ledgers including:

    • What underlies the potential fragile cryptocurrency valuation?
    • Under what circumstances could a cryptocurrency such as bitcoin be exposed to broad-based attacks or be vulnerable for crashes in valuation?
    • How do we better understand the current blockchain constructions, and what institutional changes might lead to better outcomes?
    • How do features of centralized and decentralized distributed ledgers impact the outcomes of competition?

View the conference schedule and posted slides here.

As this is a relatively new literature, the “output” of the conference did not include final and settled answers to these questions but instead productive starts to producing such answers. Progress was evident both in terms of the actual papers, but just as importantly, in terms of the informal conversations that occurred between sessions, at coffee breaks and over dinner. It was fascinating to see how earlier insights from monetary economics, asset pricing and market design were used and modified to shed light on the adoption of distributed ledgers and the behavior of cryptocurrencies.

In alternative contexts, Don Wilson, University of Chicago alumnus of University of Chicago and founder and CEO of the highly successful DRW, Robert Townsend, MIT and Richard Sandor, chairman and CEO of the American Financial Exchange, reminded us of the varied and intriguing uses of blockchains and, more generally, distributed ledgers. After listening to Don Wilson, I was led to consider more fully the possibility that blockchain-type distributed ledgers could in the future engender private sector trust and reduce the overall fragility of the financial system. This point was reinforced later in remarks by Richard Sandor.

Rob Townsend was a long-time colleague, first at Carnegie-Mellon and then at the University of Chicago and is an old friend of mine. He has done innovate work in monetary economics, contract theory and development. He gave a thought-provoking dinner discussion that suggested ways to use some of the existing tools of economic analysis to understand the economic value of distributed ledgers. Along with others, he gave an optimistic assessment, but from the vantage point of an “applied theorist” suggesting formalisms that we could draw upon to understand better an economic rationale for this optimism.

I had the opportunity to structure a lunch-time conversation related to the conference theme. I used it to engage two very thoughtful people, Richard Sandor and Neil Wallace, with substantively different backgrounds and perspectives. Richard has been a pioneer in the creation of financial markets and recently completed a book entitled, “Electronic Trading and Blockchain: Yesterday, Today and Tomorrow.” An important lesson from the book was recently captured by J. Christopher Giancarlo, the current head of the CFTC:

What I found fascinating in Dr. Sandor’s recounting of this five-decade long evolution from trading pits to electronic trading of futures was the absence of any grand plan behind the transformation. … Market evolution happened because a good idea was coupled with capable technology and mutual commercial interest with enough time to catch on and gain traction.

It is good to be reminded of this past dynamism in the creation and evolution of financial markets and the adoption of innovative financial technologies.

I have known Neil Wallace since I was a graduate student at the University of Minnesota. He even served on my dissertation committee. Neil emerged as a young scholar in the 1960s after receiving his PhD from the University of Chicago to become an intellectual leader in monetary economics. Although Neil was undoubtedly exposed to Friedman’s well-known monetarism as a graduate student, he pushed the economics community to probe much more deeply by opening the hood of money demand and exploring the productive role of money in more fundamental terms. Throughout the conference, there were repeated references to some of Neil’s important contributions and insights.

Together, Neil and Richard provided a fascinating dialogue as they offered valuable back-and-forth perspectives of technological and modeling advances and challenges for the future. Richard reminded us of the long history of the blockchain and distributed ledgers and of their promise to reduce substantially financial transactions costs. Throughout the conference, Neil gave his perspective on conference papers discussing connections to previous research as well as new challenges for future advances. The dialogue really set the stage nicely for this blossoming area of academic endeavor.

Interestingly, the program included a financial forensic paper entitled, “Is Bitcoin Really Un-Tethered?” by Griffin and Shams. The authors looked across multiple blockchains to detect potential price manipulation in observed trading patterns. As an academic, I view the value of such detections less in terms of pinpointing the specific bad behavior and more as a way to detect flaws in existing trading protocols. We should not be surprised that market participants push the boundaries of trading opportunities. In other contexts, I am sometimes confused as to how “bad behavior” on the part of traders is even defined, and when it justifiably results in formal accusations. Instead, for me, this forensic work is vital as a way to reassess the existing rules in place that traders confront that could engender the suspicious market outcomes.

Unfortunately, I missed the lunchtime address of Hyun Shin who is a distinguished academic and now has a front row seat on policy challenges in his capacity as Head of Research and Economic Adviser at the Bank of International Settlements. His combined academic and policy perspectives were a welcome addition to the conference.

This event offered a terrific opportunity for an external scholar like me to witness a fascinating new area of research, and I was pleased that the Macro Finance Research Program, which I lead, could serve as a co-sponsor of this conference.

– Lars Peter Hansen

Hansen Reflects on the Beginnings of the Becker Friedman Institute for Research in Economics with retrospective essay

In this retrospective essay, Lars Peter Hansen reflects on the beginnings of the Becker Friedman Institute at the University of Chicago. Professor Hansen was the founding director of the Friedman Institute in 2008, guiding the Institute through its evolution into the Becker Friedman Institute for Research in Economics in 2011, and to its new home in the Saieh Hall for Economics in 2014. Through his service and vision, BFI has become world renowned as a hub for economic research.

Reflection on the 2018 MFM Summer Session for Young Scholars at Cape Cod, MA

On June 17- 21, 2018, we held our third summer camp for the Macro Financial Modeling (MFM) project at Wequassett Resort and Golf Club at Cape Cod, MA. We again attracted a high-quality and energetic group of young scholars interested in the connections between macroeconomics and finance.

In 2000, the National Research Council (NRC) published a report on how to nurture linkages between mathematics and the sciences. Lars served on this committee and was intrigued by one of the featured recommendations:

“Increase the number of specialized summer institutes … organized around a core of committed senior scientists and mathematical scientists, and aimed at fostering linkages between the sciences and mathematical sciences. The Geophysical Fluid Dynamics Program at Woods Hole (incidentally Woods Hole is located at Cape Cod and administered by the University of Chicago), … could serve as a model for introducing senior scientists, graduate students, and postdoctoral fellows to cross-disciplinary research and for sustaining their interest in and commitment to such research. … Such institutes (programs) would foster the prolonged interactions necessary to establish meaningful cross-disciplinary collaborations, provide researchers opportunities to network with colleagues from other disciplines, and help a core group of researchers establish a sufficient understanding of each other’s disciplines to recognize promising research opportunities at the disciplines’ interface.”

This idea percolated over the years and was in part a motivator for our summer camps aimed at exploring linkages, not just between mathematics and the sciences, but between the important fields of finance and macroeconomics. With Andy Lo’s complementary vision, Amy Boonstra’s unbounded energy, and the willingness of key elite scholars to attend and participate, the six-year-old MFM project and our community is now a well-established entity with wide ranging participation. This year we had 41 new attendees, 10 previous summer session attendees, 19 posters, 10 lightning talks by student presenters, 3 keynote speeches, 11 scholarly tutorials on a wide range of topics and one interactive panel discussion. In addition, we had two of our earliest MFM Fellowship awardees, Aaron Pancost, University of Texas McCombs School of Business, and BFI Research Fellow, Moritz Lenel, share their experiences with preparing for the job market, allowing our younger scholars to ask questions and seek advice. This is a new component to the summer session that we implemented, and we received great feedback from students reporting that the exchange was valuable in their own preparations for the job market.

MFM poster session participants exchanging feedback

This year fintech, financial innovation and investment, and economic challenges in China were included among subjects that were explored. We were treated to a panel with Beverly Hirtle, Executive Vice President Director of Research at the NY Fed with experience in financial market oversight and stress testing, Tao Wang, Head of China Economic Research, UBS Investment Bank with a particular expertise in macroeconomics and finance in Asia, and Richard Sandor, Chairman and CEO of the American Financial Exchange and Professor at the University of Chicago, who has had vast experience in the creation of financial markets.

Equally important was the more informal networking that took place between sessions, over meals and during a boat tour. Young scholars with overlapping interests got to know one another and engaged in conversations with more senior scholars. Often, it is actually the informal exchanges that spark new ideas, new approaches to problems or new perspectives on important challenges. The casual nature of these exchanges allow students to feel more confident seeking feedback from their peers and from the more senior, elite participants. One of the most fascinating aspects of the summer camp is the relentless dedication these students display to fully take advantage of this time given to them to discuss research with their peers, even as the bus returns from a late night dinner and an exhausting day.

While it is difficult to measure the long-term benefits to such a program, we are confident that they are very high. We believe that the most important aspect of the MFM project is the network and community of exceptional scholars that we have successfully created which will ultimately nurture important advances decades into the future. After the summer camp experience, our “campers” were more than happy to share their perceptions of the summer program benefits. Some of the student testimonials are included within this piece.

This year, we invested more time into recording some of the most substantial highlights from the 2018 MFM Summer Session, and we look forward to sharing videos and other coverage soon!

Learn more about the MFM project here.

Lars Peter Hansen and Diana Petrova
Macro Financial Research Initiative

MFM Co-Directors, Lars Peter Hansen and Andy Lo, and our 2018 MFM Summer Session elite speakers

 

“The MFM Summer Camp was a unique and valuable opportunity for young scholars interested in macroeconomics and finance. The diversity of expertise and interests among the faculty and students was useful for getting feedback on both the empirical and theoretical components of my research. It was also helpful for learning about insightful similarities between the policies, markets, and models I study and those better understood by my peers. The panels and talks from policy and industry insiders were also valuable for improving my understanding of how financial markets and regulation function in practice. The participants ran the spectrum of experience from students just beginning independent research, to those just starting careers at a university, to Nobel laureates. Speaking with researchers across such a variety of career stages was useful for not only providing feedback on specific research projects but also helping to shape my research agenda more broadly.” – Sasha Indarte, Northwestern University and 2017 MFM fellowship awardee

“The MFM summer session was just amazing. It gave us a great opportunity to meet with students and junior scholars with similar research interests in macro finance but from very different research backgrounds. Faculty presentations given by top researchers in macro finance were insightful and inspiring. They provided us with an overview of the research frontier in the literature and encouraged us to work on unresolved, big questions in macro finance. Besides, I really enjoyed presenting my paper in front of all participants in the lightning talk session. After my talk, I discussed my paper with Tobias Adrian. He provided me with fresh insights into how to apply my model to study the effectiveness of the Fed’s lending programs during the financial crisis. Last but not the least, talks given by scholars from the financial industry were eye-opening. For instance, Long Chen’s talk about how technology is shaping the finance industry raised many thought-provoking questions that need to be addressed by a generation of future researchers. Overall the MFM summer camp was an excellent experience for me. I would definitely recommend it to any young scholar who has an interest in macro finance. – Yiyao Wang, University of Chicago Booth School of Business and 2018 MFM fellowship awardee

“I am thrilled to have had the opportunity to attend the MFM Summer Session. Lectures given by both professors and industry practitioners covered some of the latest research advances in the field of macro-finance as well as the first-order questions that the field is still struggling to solve. This provided an inspiring starting point for future research. In addition to lectures by faculty, poster sessions and young scholar lectures were a great way to showcase the questions my peers are studying. I also found more informal conversations with my fellow classmates to be very rewarding. Talking about bankruptcy on a bus ride home from dinner, for example, provided the spark I needed to push forward an ongoing household finance project of mine. To put it simply, I’m excited for this group to be my future colleagues! The summer camp was fantastic, and I will be able to immediately apply this unique experience to my ongoing research.” – Peter Maxted, Harvard University

“The MFM Summer Session was the most remarkable experience so far in my PhD life. During MFM I developed my professional network, got feedback on my research, broadened my horizon and got new ideas by both learning about peers’ research and listening to and talking to speakers. First, MFM is an unparalleled chance for developing professional network. The fact that all participants gather together in an intimate environment for 3 days makes it very easy to know each other quickly and in depth. On the bus, during breaks, over meals, at night around the fire pit, participants have plentiful opportunities to talk with each other, and they’re situations that are suitable for talking about both research and personal topics. Second, it’s a super valuable chance to market our own research. MFM participants are extremely diversified in terms of their institutions, interests, and demographics. By presenting or talking about our research with each other during MFM, one not only gets a rare chance to publicize his or her research into a broad research community at once, but also gets very diversified feedback.” – Scarlet (Sijia) Chen, Stanford University

2018 MFM Summer Session for Young Scholars

Reflection on Recent Trip to Shanghai, China

I recently had the opportunity to return to Shanghai for a variety of interesting events. I had previously visited there in January of 2018. While previous visits provided me with some important new perspectives on the fascinating Chinese economy, this one was more oriented to professional conferences. I was the opening act for two conferences, both held at Fudan University. The first conference was the 2018 International Symposium on Financial Engineering and Risk Management (FERM 2018) at which I presented The Price of Macroeconomic Uncertainty with Tenuous Beliefs. While the conference features “risk management” in its title, my talk explored the consequences of taking a broader view toward uncertainty beyond the more narrow confines of risk. The second one was the China Meeting of the Econometric Society where I presented on Valuation Dynamics in Models with Financial Frictions. The Shanghai Advanced Institute of Finance (SAIF) organized a conference at which I presented on Confronting Economic Uncertainty. Finally, Grace and I had a very nice evening with some University of Chicago alumni in Shanghai sharing ideas and perspectives.

Myself and Peng Shige of Shadong University

A very nice part of this visit was my opportunity talk informally to a variety of scholars. China’s most imminent probabilistic and stochastic control expert, Shige Peng, and I talked for a couple of hours about overlapping research interests. He has done some very innovative research on how to confront uncertainty in dynamic environments, a topic which I continue to work on. I talked at length to Chris Sims (my former advisor), briefly to Tom Sargent (my long-term collaborator), Jianqing Fan (my intellectual host and distinguished statistician), Xiaohong Chen (a former colleague and collaborator), and Jeffrey Lacker (former head of the Richmond Federal Reserve). Enrique Sentana, a longtime friend, give me a very generous introduction at the 2018 China Econometric Society meeting. I had many other productive and stimulating conversations that made this a packed week.

In terms of new perspectives on China, I was informed by a variety of sources about the local public finance challenges. In the past, local governments have faced some perverse incentives for engaging in public investments funded by land sales and sometime dubious financing arrangements through shadow banking. They typically do not have tax authority and rely in part from revenue from the central government. Local public finance challenges and stress for the financial system are some cause for concern. A recent paper that addresses some of these issues is, ”The Financing of Local Government in China: Stimulus Loan Wanes and Shadow Banking Waxes” by my colleague, Zhiguo He, and collaborators.

Reflection on 11th Financial Risks International Forum in Paris – March 26-27, 2018

I was kindly invited to be a featured speaker at the 11th Financial Risks International Forum held at the Chambre de Commerce in Paris on March 26 & 27, 2018 located near the Arc de Triomphe. The forum brought together academics, professionals and regulators.  The aim of this year’s forum was to explore emerging extra-financial risks such as climate risks, demographic risks and cyber risks, have emerged and require new tools and methodologies to evaluate them. The event was hosted by the Institut Louis Bachelier, in cooperation with the Fondation du Risque, and the Europlace Institute of Finance.

I was invited based on research that I have undertaken with William “Buz” Brock related to climate change, uncertainty and economic analysis.  In our current collaboration, we have brought aboard Mike Barnett, a Ph.D. student in the joint program in Economics and Finance at the University of Chicago.

Two aspects of this conference drew my attention in advance of my talk.  First my research features a broader notion of uncertainty that pushes beyond the usual risk modeling and measurement commonly used in economic and financial analysis.  Indeed the term “risk” was prominent in the official aims of the conference. Second, Louis Bachelier, the namesake of a hosting Institute, did fundamental research on the mathematical underpinning of models of efficient financial markets and Brownian motion well ahead of his time.  While Bachelier’s Ph.D thesis entitled Théorie de la Spéculation was completed in 1900, this work was unknown to economists for quite some time. Apparently it was the truly prominent (University of Chicago) statistician “Jimmie” Savage who brought it to the attention of the truly prominent economist (an alumnus of the University of Chicago undergraduate college) Paul Samuelson in the early 1950’s.  Samuelson then featured Bachelier’s work in his own important contribution to the theory of efficient markets.

In my talk at the conference, I used the occasion to develop some interrelated themes around climate change and economic analysis:

 

  1. While much recent research in macro asset pricing has featured the pricing implications of “long-run risk,” the “risk” components pertaining to economic growth can be notoriously hard to quantify.  For this reason, I find it better to conceive of these in terms of broader notions of uncertainty while acknowledging the difficulties in measuring them and the resulting ambiguities.
  2. Climate uncertainty is potential important example of such a long-run uncertainty. Climate change induced by human economic activity could unfold over multiple decades and even longer and could push the environment and the economy into places not well captured by historical evidence.  Meaningful climate policy therefore has to go beyond purely evidence-based approaches often advocated for micro policy analysis.  Formal modeling and consequent model uncertainty is central to understanding the nature of this uncertainty.  Some climate science experts provide insightful and tractable characterizations of divergent predictions across models of the climate system and delineate the difficulties in calibrating “climate sensitivity” based on recent historical evidence.  In fact, dynamic macroeconomic policy assessment can seldom, if ever, be purely evidence based; but climate economics is a dramatic example of how model ambiguity can come into play.  An important challenge going forward is to bring to bear concrete and meaningful assessments of climate model ambiguity into economic analysis.  My co-authors and I are looking to existing climate science research along with inputs from some of my University of Chicago colleagues with expertise in climate dynamics and statistics for assistance in the challenging task. Measurement efforts within the economics community have targeted damages, which is also a key input into the analysis along with the climate science characterizations of the dynamic transmission mechanism for human imprints on the environment.
  3. Asset pricing tools are a valuable tool of policy analysis in the presence of uncertainty. The economics community has treated uncertainty within the realm of climate change in ways that are times convoluted and confusing.  Asset pricing places uncertainty at the forefront in meaningful ways.  An asset pricing perspective, including that associated with Bachelier, is typically used in applications to provide portfolio advice or to offer an enhanced understanding of how financial markets price exposure to macroeconomic uncertainty.  The so called “social cost of carbon,” conceived of as a so-called Pivouvian tax on an externality with bad social consequences, in this case a tax on carbon emission, can be represented as an asset price.  This opens the door to a meaningful incorporation of uncertainty into this cost measure.  Moreover, the tools of asset pricing provide coherent ways to conduct local policy analyses (analyses of small changes) in tractable ways and shed light on the impact of more discrete alterations in policy.   Thus my interest in asset pricing tools goes well beyond motivations given by people who teach investment classes.
  4. Uncertainty in the policy realm is often naively associated with inaction or denial.  My co-authors and I find it fruitful to exploit modern decision theory under uncertainty in formal ways to frame climate policy challenges.  It has long been evident from decision theory that action does not necessary require precise knowledge (of course such knowledge would be desirable).  The possibility of bad environmental outcomes can suffice to justify immediate policy responses.  For a dramatic but truly extreme illustration of this one need only to reconsider Pascal’s famous wager posed in the seventeenth century.  Pascal argues that people should act as if God exists.  Why?  He supposes an extreme cost (actually infinite) to behaving otherwise should God actually exist and modest cost to behaving as if God exists when indeed he does not.  The special cost specification makes this example extreme, but such an illustration reminds us that we should care about more than just probabilities when making decisions.

Term Structure of Macroeconomic Uncertainty – Updated March, 2018

An artist’s depiction of a seminar I gave at Bocconi University on the topic of this reflection

Dynamic economic models typically feature shocks or random impulses as a way to capture uncertainty. These impulses capture surprises or random outcomes, and economic variables respond over time to these surprises. The impulses could be technology shocks, policy shocks or a variety of other impulses that impinge on the macroeconomy. The structure of the dynamic economic model informs us as to how these random impulses propagate over time. For instance, consider a shock that comes as a surprise today. Its impact will persist over many future time periods. Perhaps the shock will have permanent consequences or alternatively its impact might well diminish over time. Part of understanding and analyzing the implications of an economic model entails characterizing which of the random shocks are most potent and how quickly do their impacts dissipate over time. Models typically differ in terms of their implications for these random impulses and their propagation.

Characterizing how a dynamic economic system responds to random impulses has a long history in economic analysis. Indeed, Frisch’s (1933) classic paper, “Propagation Problems and Impulse Problems in Dynamic Economics” includes such calculations. A surprise or random impulse occurs at some point in time and then the dynamic system responds in subsequent time periods giving rise to what economists and others studying dynamical systems call an impulse response function. The resulting characterizations have been pervasive in understanding model implications and empirical evidence. Much effort has been devoted to measuring the importance of alternative economic shocks and how their impacts play over time. A leading example of such research is a seminal paper by Sims (1980) entitled: “Macroeconomics and Reality” whereby a collection of macroeconomic variables is interconnected through their responses to alternative economic shocks. I was lucky enough to see this paper develop when I was a graduate student research assistant on this project at the University of Minnesota. While much of the subsequent applied research features linear models, there are interesting extensions to models that feature nonlinearity.

With co-authors Jose Scheinkman, and more recently, with Jarda Borovicka, I have extended this approach taking an asset pricing perspective. Macroeconomic shocks by their very nature are ones that cannot be diversified or averaged out over a large cross-section. As such, the exposures of the payoffs on these investments, either real or financial, to macroeconomic shocks cannot simply be averaged out across a large population of potential investment opportunities. Basic economic analysis informs us that for people to make investments with payoffs or rewards that are exposed to macroeconomic uncertainty, they must be compensated in terms of the returns they expect to receive. Thus, in well-functioning markets, there are compensations for being exposed to uncertain macroeconomic impulses. This insight is at the heart of asset pricing.

Since the impact of macroeconomic shocks propagates over time, there is a dynamic dimension to the market compensations for investment exposure to these shocks. While impulse response functions trace out consequences of shocks as they impact economic variables over time, my co-authors and I use the investor compensations, represented formally as “shock price elasticities,” to provide pricing counterparts to impulse responses. Since exposure to macroeconomic impulses requires compensation and impulses have consequences in subsequent time periods, the implied market compensations depend on the associated investment horizon. Interpreted more broadly, these compensations provide information about what macroeconomic shocks are most consequential to the people inside the dynamic models as measured by market prices. They allow researchers to make model comparisons because different models may imply distinct compensations.

The following figures serve as an illustration of these methods. We live in a world with uncertainty, which includes the future of macroeconomic growth. Imagine this uncertainty is characterized by shocks and their transmissions. Some macroeconomic shocks, or shocks that alter investment opportunities, change growth rates and thus have permanent consequences for the macroeconomy. For instance, technological advances that come as surprises can have long-lasting impacts in contrast say to policy changes that can be undone in the future.

To understand the implied compensations, we consider two models of investor preferences as to how concerned they are about risk and its structure. To set the stage for this comparison, consider how a decision maker views two distinct lotteries over future consumption: for Lottery A, there is a coin flip every time period. If the coin comes up heads, consumption will be relatively high, and if it comes up tails, it will be relatively low. For the Lottery B, there is a single coin flip applicable to all future time periods. If the flip comes up heads, consumption is relatively high for all future time periods, and if it comes up tails, consumption is relatively low for all time periods. In this example, there is a 50 percent chance of relatively high consumption in any given period for both lotteries. The intertemporal composition of risk differs, however. In the Lottery A, since there is a different draw every time period, there is a sense in which the risk is diversified over time. Under what economists call a ‘time separable power utility’ specification of investor preferences commonly used in macroeconomics, a decision maker views the two lotteries as comparable. In a more general ‘recursive utility’ specification, the intertemporal composition of risk can matter. In particular, an investor can prefer Lottery B to Lottery A. See Kreps and Porteus (1978) for further discussion.

In what follows, I contrast the investor compensations for two such specifications applied to an economy with macroeconomic growth-rate risk. For the recursive utility specification, there is a forward-looking channel that captures investors’ risk concerns as they speculate about the future that is absent in the power utility specification. For the recursive utility specification, I impose what economists call a unitary elasticity of intertemporal substitution, but this is for convenience and for sake of illustration. Otherwise, I follow Bansal and Yaron (2004) in their paper entitled “Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles” by adopting a highly simplified model of the macroeconomy in which there are shocks both to the macroeconomy and to its growth rate. There is a third shock to the overall volatility of the economy that alters the magnitude of the responses of the temporary and permanent shocks.

I plot consumption responses to transitory and permanent shocks in Figure 1. By their very nature shocks to growth rates have a permanent consequence, but in the long-run risk model, their impact builds over time. This is reflected in how a permanent shock impacts the macroeconomy over different horizons. As is seen by Figure 1, the initial response is modest but becomes more prominent over longer time periods and converges as the response time gets longer and longer. In contrast, the impact of the transitory shock is initially higher than that of the permanent shock but it eventually has an impact that decays to zero. The magnitude of the responses depends on the current level of stochastic volatility in the macroeconomy. This dependence is captured by the blue bands.

The pricing counterparts to impulse responses displayed in Figure 2 compare implications for two models of investor preferences. The compensations are expressed, as is often done in finance, as increases in the conditional means of returns per unit of standard deviation, a standard measure of volatility. The price elasticities or compensations for the recursive utility are larger for the permanent shock than for the transitory shock at all horizons. Moreover, the permanent shock compensations have a flat trajectory. As with impulse responses, the magnitude of these compensations depends on the current level of stochastic volatility. The price elasticities for the power utility specification, the one for which investors are not concerned about the intertemporal composition of risk, show the same patterns as the impulses reported in the initial figure. Thus, the compensations for the permanent shock start out small and build over time.

 

Figure 1
Figure 2

For a more detailed discussion and code, click here.

These plots illustrate that the recursive utility specification of investor preferences implies sizable compensations for the permanent shock even at short horizons in contrast to the power utility model, in which the short-run compensations are small. They show in a transparent way how recursive utility specifications of investor preferences change market compensations by featuring shocks with long-term consequences. In particular, their pricing impact can be quantitatively important over even short time horizons and exposit a pricing mechanism in research by Bansal and Yaron and many other scholars.

This is just one illustration of model comparisons. Recently there has been substantial interest in the impact of intermediation on asset prices and real economic activity. The models have explicit roles for financial intermediaries in facilitating real investment opportunities subject to alternative forms of financing constraints. The implications of models feature endogenously determined nonlinear mechanisms by which shocks today impact the investment in current and future times periods. Borovicka and I, in our essay, “Term Structure of Uncertainty in the Macroeconomy’’ provide pricing comparisons across some of the models featuring an explicit role for financial intermediation showing the impact of state dependence and nonlinearity in valuation. The wealth of financial intermediaries relative to households is an important state variable in these economics that fluctuates over time. The analogous computations to those depicted in Figure 2 show how the relative wealth alters the implied market compensations over alternative investment horizons.

References

Bansal, Ravi, and Amir Yaron. “Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles.” The Journal of Finance 59, no. 4 (2004): 1481-509. http://www.jstor.org/stable/3694869.

Borovicka, Jaroslav and Lars Peter Hansen. “Term Structure of Uncertainty in the Macroeconomy.” Handbook of Macroeconomics: Volume 2B (2016) Chapter 20, Elsevier B.V., 1641–1696

Borovicka, Jaroslav, Hansen, Lars Peter. and Sheinkman, Jose A. “Shock Elasticities and Impulse Responses.” Mathematics and Financial Economics. No. 8 (2014): 333-354.

Frisch, Ragnar. “Propagation Problems and Impulse Problems in Dynamic Economics,” in Economic Essays in Honour of Gustav Cassel (London: Allen & Unwin, 1933), 171–205.

Kreps, David M., and Evan L. Porteus. “Temporal Resolution of Uncertainty and Dynamic Choice Theory.” Econometrica 46, no. 1 (1978): 185-200. doi:10.2307/1913656.

Sims, Christopher A. “Macroeconomics and Reality.” Econometrica 48, no. 1 (1980): 1-48. doi:10.2307/1912017.