Roger Craine

Optimal monetary policy with uncertainty

This paper investigates the effect of uncertainty on the optimal policy response. Uncertainty plays a central role in both monetarist and neo-Keynesian policy prescriptions. Monetarists advocate cautious policy responses to exogenous shocks because they believe there is a long and variable (uncertain) lag between the policy response and its ultimate impact on the economy. Neo-Keynesians on the other hand believe that imperfect information can cause a dynamic disequilibrium in which shocks are multiplied if they are not offset by policy. A simple dynamic random coefficient model is used to approximate this uncertainty. It is shown that when uncertainty about the impact of policy is dominant the optimal policy converges to a fixed money growth rate, but when uncertainty about the transition dynamics is dominant a very active countercyclical policy is optimal. When both sources of uncertainty are present, as they are in general, the optimal policy response depends on the relative uncertainty and the policy may become more aggressive as uncertainty about the impact of policy increases.

Rational Bubbles: A Test

Abstract This paper presents a robust no rational bubbles restriction for equity markets, tests out the restriction, and examines the power of the test. The restriction does not require a constant discount factor or the specification of a particular asset pricing model. A unit root in the price-dividend ratio violates the no rational bubbles restriction. Augmented Dickey-Fuller (1979) tests cannot reject the unit root null, and local to unity confidence intervals [Stock (1991)] include unity. The Dickey-Fuller tests have excellent power against stationary alternatives generated with driving discounted dividend growth factors that have low serial correlation. The results in this paper indicate that either the price-dividend ratio contains a rational bubble, or the discount factor must be stochastic and contain a large predictable component.

Valuing the Futures Market Clearinghouse's Default Exposure During the 1987 Crash

Futures market clearinghouses are intermediaries that make large volume trading between anonymous parties feasible. During the October 1987 market crash rumors spread that a major clearinghouse might fail. This paper presents estimates of three measures of the default exposure on the popular S&P500 futures contract traded on the Chicago Mercantile Exchange. We estimate the traditional summary statistic for risk exposure: the tail probabilities that the change in the futures price exceeds the margin. And we estimate two economic measures of the risk--the expected value of the payoffs in the tails and expected value of the payoffs in the tails conditional on landing in the tail. The economic measures of risk reveal exposure from low probability large payoff events--like a crash--that does not show up tail probabilities. The tail probabilities only capture the likelihood of a crash, not the expected loss. The estimated measures of risk follow directly from estimates of the conditional distribution of futures price changes. We infer a jump-diffusion process and a log-normal rocess from the prices of traded options and we estimate a jump-diffusion process from time-series data on futures prices. After the crash the forward-looking jump-diffusion model inferred from traded options reflects the fears of another crash voiced by market participants. The model indicates another jump is unlikely, but if it occurred it would be big and negative. The tail probabilities are small, less than 2%. But, the day after the crash the model estimates the expected value of payoffs in the tails conditional on landing in the tail equals of 55% of the S&P500 futures price. According to this estimate roughly

Monetary Policy Shocks and Security Market Responses

10.5 billion in liquid reserves would be required to weather another crash. On October 20 the Federal Reserve announced it stood ready to supply the necessary liquidity.

Estimation Analogies in Control

An old and unanswered question is: how does monetary policy work? This paper contributes to a growing recent literature that tries to quantify the first step of the process. These studies use daily data to estimate the response of security prices-bond yields and equity returns - to exogenous monetary policy surprises. We extend the literature in three directions: (1) theory: we specify a general factor model in which security prices respond to multiple sources of systematic risk - monetary policy surprises and other market wide information shocks - and idiosyncratic risk. (2) Empirical: we use all of the daily data while other studies use a small sub-sample of less than 10% of the data. And (3) econometric: we estimate a vector model and impose the over-identifying restrictions. Our empirical results show that efficiently estimating a more general model leads to economically important differences. Our results solve a puzzle and highlight an important neglected short-run channel of monetary policy. Cochrane and Piazzesi (2002), the latest of many, found that long maturity bond yields increase in response to a surprise tightening in monetary policy - a result they properly label a puzzle. Our results eliminate the puzzle. The yield curve response to a monetary surprise displays the classical textbook pattern - short maturity yields rise and long maturity yields do nothing. Common information shocks have a level effect on the yield curve - all yields increase in response to a positive shock. We also find that the equity market, which is ignored in most studies and textbooks, is quantitatively the most important channel for monetary policy in the short run. The wealth effect from a monetary surprise in the equity market dwarfs the wealth effect in debt markets.

Choosing a monetary instrument The case of supply-side shocks

Abstract Least squares estimation and quadratic openloop optimal control share both algebra and intuition; this paper explores the duality to develop the parallels in each. Estimation results suggest control analogs to correlation measures, significance tests, distributed lags and problems of multicollinearity, tests of compatability between restrictions and data, and a version of the Kalman filter that is sometimes computationally expedient. Conversely, the control literature provides methods of incorporating certain types of inequality restrictions and a development of recursive estimation based on the Kalman filter. A by-product is a method of solving control problems using least squares computer programs.

Why Random Walk Models of the Term Structure Are Hard to Reject

Abstract This paper examines the monetary instrument choice problem in models with an explicit supply sector and endogenous prices and price expectations. We use the popular linear-quadratic certainty-equivalence framework to obtain analytic solutions. The results indicate that interest rate policies generally are better able to insulate the real sector from unanticipated supply shocks. We also show that at this level of abstraction the optimal choice of an instrument is independent of the specification of expectations, e.g., rational vs. adaptive price expectations. The paper then reports empirical evidence from two experiments on the large nonlinear MIT-PENN-SSRC econometric model. The evidence is consistent with the hypothesis that interest rate policies are preferable if the supply sector is the major source of uncertainty.

On control with instruments of differing frequency

Tests of random walk models of the term structure generally fail to reject the null hypothesis, whereas direct tests of the fair game-efficient markets (FGEM) hypothesis generally reject the null. Random walk tests can be interpreted as FGEM tests that add measurement errors to the forward-rate revisions used in direct tests. Our empirical application is consistent with the literature; direct tests strongly reject the null, but random walk tests do not, despite using the same data and numbers of observations. The random walk measurement error is shown to reduce local asymptotic test power, which may explain this empirical puzzle.

Valuing the Futures Market Performance Guarantee

Abstract When some instruments are more frequently adjustable than others — the text example is monetary and fiscal policy, but applications extend from agriculture to engineering — the control solutions must be modified to incorporate the implied restrictions. The necessary modifications are developed for two stochastic (and, implicitly, deterministic) control specifications, one a closed-loop random coefficients algorithm based on serially uncorrelated coefficient errors, and the other an open-loop solution based on (single-realization) estimated coefficients. The modifications, while essential, do not fundamentally alter the character of the solutions.

Classical versus bayesian models—on the dangers of a little bit of knowledge

.._W....n il-nan Institute of University of Business and California at Economic Research Berkeley FISHER CENTER FOR REAL ESTATE AND URBAN ECONOMICS WORKING PAPER SERIES These papers are preliminary in nature: their purpose is to stimulate discussion and comment. Therefore, they are not to be cited or quoted in any publication without the ex- press permission of the author. WORKING PAPER NO. 96-243 VALUING THE FUTURES MARKET PERFORMANCE GUARANTEE BY Roger Craine WALTER A. HAAS SCHOOL OF BUSINESS