**Research & Projects**

# Thomas Coleman

## Harris School of Public Policy, University of Chicago

### tscoleman@uchicago.edu

## Selected papers and research projects

Below are some of my projects, publications, and working papers
covering various topics:

I am undertaking an examination of two of Snow's publications on the 1854 London
cholera outbreak.
I view Snow's study of cholera as a roadmap or template for current
social science researchers in combining theory and evidence to demonstrate
a causal effect.
Although I discuss the well-known Broad Street outbreak and Snow's mapping,
I focus more attention on the South London "Grand Experiment" which
provides early (possibly the earliest) examples of using tools such
as difference-in-differences and quasi-randomized experiments.
I will be posting
Snow's original data and extending his analysis using modern statistical tools and
techniques.

### Recent Talks, Presentations, Papers

"Lower Bounds for COVID-19 Mortality Based on Towns in Northern Italy":
Working paper at MedRxiv and
short summary note.
Using data from 612 towns in northern Italy hard-hit by the coronavirus in spring 2020, we can estimate
lower bounds for the Infection Fatality Rate. Mortality for men 65-74 is 2.1%, 3.6-times higher than
younger men and 2.6-times higher than women.

Thoughts on Financial Crises and Coronavirus
(or as pdf)
Financial markets have been roiled with bad news about the spread of coronavirus. Many are concerned that
this is a repeat of Ωthe 2008 global crisis, but the causes are fundamentally different - unlike
the 2008 crisis this is not a banking liquidity crisis.

John Snow and Cholera - presentation to the
Spatial Study Group and University of Chicago and the City of Chicago Public Health Department.

Three Popular Narratives on Inequality
and Why They are Wrong Presented in Xi Song's "Social Stratification"
class at University of Pennsylvania. (
Notes and references )

*"The rich (top 1%) have captured most of the income. The middle class is disappearing.
The rich get richer and the poor get poorer."
*

*
* Three narratives about American growth and inequality. We hear them again and again.
And yet they are all wrong. Or at least only half-right. Inequality has increased,
but less than commonly thought. The rich have got richer, but so have the poor.
And the middle class, when properly measured, have done OK over the past 20 or 30 or 40 years.

The answers matter - appropriate policy requires understanding the causes and sources of
inequality and growth, and understanding the causes requires knowing the facts. I critically
examine the evidence on inequality and some of the likely causes.

### Economic Research

"Causality in the
Time of Cholera: John Snow as a Prototype for Causal Inference" and see
John Snow Project.
The story of John Snow's 1855 treatise on cholera is a rollicking good tale
- full of heroism, death, and statistics. Snow's data and analysis provide a template for how to
convincingly demonstrate a causal effect. I consider the Broad Street outbreak and the
south London "Grand Experiment" as
pedagogical examples of using non-experimental data to support a causal effect. I discuss
extensions to Snow's analysis using modern techniques and tools:
difference-in-differences regression and count (Poisson) regression for error analysis in
quasi-randomized control experiments.

"Probability, Expected Utility,
and the Ellsberg Paradox" on SSRN, updated
May 2011 (pdf, 16p). The Ellsberg paradox is often cited as evidence for unknowable
"ambiguity" versus computable "risk", and a refutation of expected utility
maximization and "subjective" or "belief-type" probabilities.
I have concluded the paradox is not convincing.
The results can be explained by differences in distributions that show up
in repeated "games." The distributions behind Ellsberg's thought
experiments are different and economic agents should
be expected to respond to these differences.

Avalanche Risk and Our Behavioral Response to Safety Improvements
- March 2018.
Combining my interest in skiing with teaching microeconomics and studying risk management,
I examine the behavioral
response to improvements in avalanche safety equipment.
When safety technology improves, individuals may take on *more* risk.
This may sound perverse, and people invoke theories about risk compensation and
risk homeostasis to explain why. But I argue that
standard microeconomics provides a more useful approach, by considering not only the
avalanche risk but also the rewards of skiing and being in the mountains.

Employment and Unemployment Flows
- July/August 2010,
based on the dynamic models of labor force states discussed below.
Unemployment in the U.S. rose dramatically from 2007 to 2011
going from about 6.8 million people in May 2007 to over 14.6
million in June 2010.
This is often spoken of as "losing 7.8 million jobs," but the reality
is that something closer to 4-to-6 million jobs were
lost *each month*, with a comparable (but just slightly lower)
number found each month. Employment and unemployment
are dynamic with large monthly flows,
and to understand them we need to look at these flows.
The BLS recently started publishing flow data. This note examines those flows,
with some interesting conclusions.

Complete paper at SSRN
with detailed figures and tables (pdf)

"Unemployment Behavior: Evidence
from the CPS Work Experience Survey", T. Coleman, *The
Journal of Human Resources*, vol. 24, no. 1 (winter 1989): 1-38.
(Large scanned pdf - 9MB)
This describes the general statistical process generating retrospective
data for "weeks unemployed during the year"
and then assumes a specific, tractable, stochastic process
for empirical application. The conclusion is
that entry rates into unemployment and differences
across people are important, more important than spell exit
rates for explaining levels of unemployment and weeks during the
year.

"A Dynamic Model
of Labor Supply Under Uncertainty 1985", T. Coleman,
Research Paper No. 272, State University of New York at Stony Brook,
July 1985 (on SSRN, pdf, 190k). Lays out the model as in 1981 paper but also
discusses estimation and identification in some detail. Simplifies to
a stationary environment with a single wage and then fits gross flow
data. Includes empirical results showing interesting differences
across demographic groups in fitted parameters and resulting
behavior.

"A Dynamic
Model of Labor Supply Under Uncertainty 1981" T. Coleman and
J. Heckman 1981 (pdf, 220k). Lays out the theory of a three-state
model of labor supply (job, unemployed, and out of the labor force)
in full detail - stationary and non-stationary, discrete and
continuous time. Proves existence and uniqueness of the value
function. Not much on estimation or identification.

### Risk Management

*Quantitative Risk Management* (Wiley) and
*A Practical Guide to Risk Management* (RF of the CFA)
are books that deliver
a synthesis of common-sense management together with the cutting-edge
tools of modern theory. Most provocatively they challenge
the conventional wisdom that "risk management" is or ever
should be delegated to a separate department. Good managers
have always known that managing risk is central to a financial
firm and must be the responsibility of anyone who contributes
to the profit of the firm.
*Quantitative Risk Management* was published by Wiley (2012).
*A Practical Guide to Risk Management*
was published by the Research Foundation of the CFA Institute (2011).
See summary page for a little more detail.

"A Guide to Duration, DV01, and Yield Curve Risk Transformations"
Yield curve risk and sensitivities (DV01s) can be
measured with respect to different variables:
forward rates, par rates, zero yields, or others. This paper describes
a simple method for transforming sensitivities between alternate
representations and provides examples. The benefit of this transformation
method is that it only requires calculating the risk of a small
set of alternate instrument and does not require re-calculating the
original portfolio risk. The paper is also available in a
digitally enhanced version
in .cdf/.nbp format with dynamic interactivity enabled
(requires free Wolfram Player).

"How Precision of the Sharpe Ratio
Improves with Monthly Data"
I provide small-sample and
large-sample formulae for the distribution of the Sharpe, highlighting the distinction between using
annual data versus annualized monthly data. When using more than two years of monthly data the
large-sample
generally provides a good approximation, simplifying the calculation of confidence intervals.

"Financial Risk Measurement and Joint
Extreme Events: The Normal, Student-t, and Mixture of Normals"
The normal distribution often does a poor job of representing the tails
for financial returns or P&L in the univariate case. What
receives less attention is that for a joint normal distribution events in the tails look as if they are
independent: Extreme events will not occur together, whatever the correlation (except for the boundary
cases of ±1).

### Finance, Asset Valuation, and Modeling

"Swap Valuation with Dual Curves -
Approximations"
For the case of single-curve (libor) valuation it is well-known that receiving fixed on a swap is
equivalent to long a fixed coupon bond and short a floating bond. In the past few years,
however, markets have moved to dual-curve valuation - cash flows are projected with the libor curve but discounted off the OIS (Fed Funds)
curve. The usual valuation approximations no longer apply. I develop an alternative
approximation for valuation and risk (DV01) that is useful in practice and provides valuable
insights into single-curve versus dual-curve valuation and risk.

"A Primer on Credit Default Swaps
(CDS)" - 21 October 2008 (revised October 2010).
What is a CDS? How does
a CDS behave in response to changes in the markets? How does one
value a CDS? What is the risk? This primer aims to answer these
questions for plain-vanilla single-name CDS, showing that a CDS is
equivalent to a leveraged floating-rate corporate bond (a floating
rate note or FRN).

"Convexity
Adjustment for Constant Maturity Swaps" *Derivatives
Quarterly*, Winter 1995 (pdf, 60k). Both CMS (Constant
Maturity Swap) and LIBOR-in-arrears swaps have payments that are
linear with respect to an index while the offsetting hedges are
convex. The linearity of the payment (relative to the convex hedges)
imposes a cost that requires a "convexity adjustment"
applied to the linear payment. This note lays out a practical
method for calculating the value of the convexity adjustment.

"Adjusting Constant
Maturity Swaps for Convexity" *Derivatives Week*,
August 28, 1995 (pdf, 20k). Outlines the "convexity
adjustment" applied to constant maturity swaps.

"A Practical Guide To Bonds
And Swaps" February 1998, updated 2005 (pdf, 52p., 180k)
This manual
provides a practical introduction to the fixed income capital
markets. It is intended to provide the practical, institutional
aspects of the markets together with the fundamental concepts used in
today's capital markets. In line with their ubiquity throughout the
markets, derivatives (swaps and options) are introduced early.

"Fitting Forward Rates To Market
Data" 1998.
This paper has two purposes. First, to outline a general framework or
methodology for fitting the forward curve to market data. Second, to
report on and compare results from fitting forward curves using three
particular functional forms: piece-wise constant forward rates,
piece-wise linear zero rates, and piece-wise linear forward rates.
The third is particularly interesting because it retains much of the
simplicity and ease of use from the first two while solving a problem
(large jumps in the instantaneous forward rates) exhibited by them.
Results are reported for US dollar swap curves for October 1994 and
June 1997.

"Accurately Estimating
and Building the Yield Curve" 1999 (34 slides, pdf, 90k)
Presentation for *Risk Magazine* Yield Curve Course, October
1999. Using methodology from "Fitting Forward Rates to Market
Data," discusses the general approach to fitting the yield
curve, mathematics of yield and forward curves, a simple example, use
of and criteria for curves, choice of input data, and various
functional forms.

"Convexity And Correlation
Effects in Swap Pricing; 1997 (30 slides, pdf, 100k)
Presentation for *Risk Magazine* Swap Course, September
1997. Discusses some simple approaches to modeling products that
incorporate correlation, such as yield curve spread options.
Focus on using the simplest model which solves the problem
and on hedging and managing risks.

### Miscellaneous

"Managing a Sovereign Wealth Fund: A View from Practitioners",
co-authored with D. Darcet and M. du Jeu, in
*Economics of Sovereign Wealth Funds: Issues for Policymakers*,
ed. U. S. Das, A. Mazarei, H. van der Hoorn, published by the IMF.

"Compensating Fund
Managers for Risk-Adjusted Performance," Thomas S. Coleman
and Laurence B. Siegel, *Journal of Alternative Investments*,
volume 2, number 3, winter 1999 (pdf, 40k). Explores a
risk-adjusted performance fee structure for hedge funds that
addresses incentive compatibility and helps reduce asymmetry, while
at the same time being feasible and easy to implement.

"Estimating The
Correlation Of Non-Contemporaneous Time-Series" on SSRN,
December 2007 draft (pdf, 280k), or abridged
version. Examines the problem of estimating the correlation of
non-contemporaneous time-series observations such as daily returns
for the FTSE and S&P500 stock indexes.

"Effective
degrees of freedom during the radiation era," Thomas S.
Coleman and Matts Roos, *Physical Review D ***68***
027702 (2003)*, e-print at http://arxiv.org/abs/astro-ph/0304281.
This paper updates the curves of the effective degrees of freedom for
the energy density g_{*}(T) and for the entropy density
g_{*S}(T) during the era of radiation domination in the
Universe. We find that a plain count of effective degrees of freedom
sets an upper limit to the temperature of the quark-hadron transition
at T_{QCD}< 235 MeV for the energy density and T_{QCD}<
245 MeV for the entropy density.