Chickens, Eggs, and Causality, or Which Came First?

*American Journal of Agricultural Economics*, 70 (1988), 237-238.

Long-run neutrality and superneutrality in an ARIMA framework

(with John Seater)

*American Economic Review*, 83 (1993), 402-415.

Around and around: The expectations hypothesis

(with Christian Gilles)

*Journal of Finance*, 53 (1998), 365-383.

Abstract

Forces That Shape the Yield Curve

Federal Reserve Bank of Atlanta *Economic Review* 86(1), 1-15, 2001.

Special Repo Rates: An Introduction

Federal Reserve Bank of Atlanta *Economic Review* 87(2), 27-43, 2002.

Modeling the Term Structure of Interest Rates: An Introduction

Federal Reserve Bank of Atlanta *Economic Review* 89(3), 41-62, 2004.

Happy Hour Economics, or How an Increase in Demand Can Produce a Decrease in Price

Federal Reserve Bank of Atlanta *Economic Review* 90(2), 25-34, 2005.

Inflation and Monetary Regimes

(with Gerald P. Dwyer)

*Journal of International Money and Finance* 28, 1221-1241, 2009.

Bayesian inference and prediction of a multiple-change-point panel model with
nonparametric priors

(with Mark Jensen)

*Journal of Econometrics*, 210 (2019), 187-202.

Bayesian Methods Presentation

An introduction that is intended as more of a rocket ride than an intuition builder.

October 2017

Long-Term Bond Yields: A No-Arbitrage Perspective

Derives and presents a number of useful expressions.

February 2018

The power function and the "File drawer problem"

The "file drawer problem" arises when reports of experiments with insignificant results are "left in a file drawer" and the associated datasets remain unobserved. [The phrase was coined by Rosenthal (1979).] This behavior constitutes a selection process that truncates the sample space for datasets. The sampling distribution for observed datasets is restricted to a truncation set implied by the critical region for the test statistic. The truncated sampling distribution is normalized by the probability of the truncation set, and this probability is given by the power function. Because the normalization involves model parameters, the likelihood is affected. Such changes in the likelihood can have dramatic effects on inference regarding the parameters when sample sizes are not sufficiently large.

November 2017

Tent pole model of the future Eurodollar rate

This paper describes a simple model of the future Eurodollar rate that can be used to extract the probability of future FOMC target-rate ranges from the prices of Eurodollar futures and options. I call it the tent-pole model. Each future target-rate range has its own "tent" supported by a "pole" located at the expected future average overnight rate (conditioned on that target-rate range and adjusted to allow for the expected future term premium). The height of the pole is determined by the probability of the target-rate range. The tent itself is the continuous distribution of the future term premium around its expectation. The implied distribution for the future Eurodollar spot rate is a mixture of these tents. For near-term contracts, the tents will be narrow in width (since the uncertainty about the future term premium will be small) and consequently the mixture distribution will display distinct multi-modality. For longer-term contracts, the multi-modality will be obscured by blurring produced as a result of the greater uncertainty about the future term premium.

The approach to estimation is Bayesian. The locations, heights, and widths of the tents are all unobserved. A prior is used to associate expected future rates with their target-rate ranges. The empirical results are consistent with those based on a less parsimonious (and less interpretable) Bayesian nonparametric model.

May 2017

Real exchange rates and unit roots: Learning about the distribution

The goal of this paper is to learn about the distribution of the autoregression coefficient for real exchange rates, including the probability of a unit root. The paper is an exercise in Bayesian statistics. The approach we take allows us to learn not only about the distribution for each specific case for which we have data, but also the generic case for which we have no data as yet. The posterior distribution for the generic case constitutes a well-informed prior distribution for a new case when such data becomes available. The estimation of the distribution for the generic case amounts to indirect density estimation for a latent variables. With this in mind, we adopt a nonparametric Bayesian prior that embodies great flexibility and allows for a unit root as a special case.

July 2017

To answer or not to answer: That is the question

In the first part of the paper I present a simple structural model of supply and demand, pose a policy question, and answer it in terms of the structural parameters. Then, given some data, I show how to provide a realistic assessment of the uncertainty in that answer. In the second part of the paper I present common modifications of the structural system (in particular, scaling and renormalization) that turn out to make answering the policy question more difficult or impossible.

October 2016

Nonparametric density estimation using a mixture of order-statistic distributions

This paper presents a Bayesian nonparameteric model for predictive density estimation that incorporates order-statistic distributions into a Dirichlet Process Mixture (DPM) model. In particular, the kernel is the density of the j-th order statistic given a sample size of k from a pre-specified continuous distribution. By requiring the prior distribution for j to be uniform conditional on k, the prior predictive distribution is made to equal the pre-specified distribution. The model is completed by specifying a prior distribution for k, which plays the role of a precision parameter, and a prior distribution for the concentration parameter, which affects amount of clustering through the distribution of the stick-breaking weights. The model presented in this paper can be interpreted as a more flexible version of that in Petrone (1999) "Bayesian density estimation using Bernstein polynomials."

June 2017

Nonparametric Bayesian density estimation on a circle

This note describes nonparametric Bayesian density estimation for circular data using a Dirichlet Process Mixture model with the von Mises distribution as the kernel. A natural prior for the parameters produces a prior predictive distribution for the mean vector that is uniformly distributed on the unit disk.

August 2017

Simplex regression

This note characterizes a class of regression models where the set of coefficients is restricted to the simplex (i.e., the coefficients are nonnegative and sum to one). This structure arises in the context of fitting a functional form nonparametrically where the functional form is subject to shape constraints of a particular sort. Two examples are given. The approach to inference is Bayesian, using a Dirichlet-based sparsity prior. A variety of approaches to sampling from the posterior distribution are presented.

May 2016

Fitting a distribution to survey data for the half-life of deviations from PPP

This note presents a nonparametric Bayesian approach to fitting a distribution to the survey data provided in Kilian and Zha (2002) regarding the prior for the half-life of deviations from purchasing power parity (PPP). A point mass at infinity is included. The unknown density is represented as an average of shape-restricted Bernstein polynomials, each of which has been skewed according to a preliminary parametric fit. A sparsity prior is adopted for regularization.

December 2015

Maximum entropy on a simplex: An expository note

March 2006

*Note:* A companion *Mathematica* package is available.

Apparent arbitrage

February 2010 (with Christian Gilles)

Abstract

Forces that shape the yield curve: Parts I and II

March 2001

*Note:* This paper is intended as an introduction for advanced undergraduate and beginning graduate students. For the most part, it uses only high-school algebra. The paper is divided into two parts. Part 1 presents material that was largely incorporated into a *Review* article. Part 2 completes the analysis, providing material beyond the scope of the *Review* article.

Abstract

Modeling the state-price deflator and the term structure of interest rates

February 2000 (with Christian Gilles)

Abstract

Modeling negative autoregression in continuous time

February 2000

*Status:* Preliminary

Abstract

Consumption and asset prices with homothetic recursive preferences

June 1999 (with Christian Gilles)

Abstract

Consumption and asset prices with recursive preferences: Continuous-time approximations to discrete-time models

June 1999

Abstract

Deflated gains and numeraire invariance: A simple exposition

August 1999

*Status:* Preliminary and incomplete

A simple model of the failure of the expectations hypothesis

June 1998

Abstract

The essence of asset pricing

January 1998

*Status:*Preliminary and incomplete

*Notes:* This is an introductory paper, presenting a number of topics in a simple one-period, binomial model.

The absence of arbitrage and general equilibrium in continuous time: An overview

October 1997 (with Christian Gilles )

*Status:* Preliminary and incomplete

Abstract

Risk-neutral pricing and risk neutrality: A tale of two equivalent martingale measures

October 1996 (with Christian Gilles)

*Status:* Preliminary and incomplete

Abstract

Estimating exponential-affine models of the term structure

September 1996 (with Christian Gilles)

*Status:* Preliminary and incomplete

Abstract

The term structure of repo spreads

July 1996 (with Christian Gilles)

*Status:* Preliminary and incomplete.

Abstract

Term premia in exponential-affine models of the term structure

April 1996 (with Christian Gilles )

*Status:* Preliminary and incomplete

Abstract

The term structure of tax-exempt spreads: The effect of convexity

January 1995

*Status:* Preliminary and incomplete

Abstract

Fitting the term structure of interest rates with smoothing splines

September 1994 (with Douglas Nychka and David Zervos)

*Status:* Appeared as FEDS 95-1, Federal Reserve Board, Washington DC.

*Notes:* The figures are missing from this version.

Abstract

Happy-hour economics

June 1991

Abstract

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