Comparing Sunspot Equilibrium And Lottery Equilibrium Allocations: The Finite Case*

Sunspot equilibrium and lottery equilibrium are two stochastic solution concepts for nonstochastic economies. We compare these concepts in a class of completely finite, (possibly) nonconvex exchange economies with perfect markets, which requires extending the lottery model to the finite case. Every equilibrium allocation of our lottery model is also a sunspot equilibrium allocation. The converse is almost always true. There are exceptions, however: For some economies, there exist sunspot equilibrium allocations with no lottery equilibrium counterpart.     

The intraday liquidity management game

We use a game theoretical framework to analyze the intraday behavior of banks with respect to settlement of interbank claims in a real-time gross settlement setting. The game played by banks depends upon the intraday credit policy of the central bank and it encompasses two well-known game theoretical paradigms: the prisoner's dilemma and the stag hunt. The former arises in a collateralized credit regime where banks have an incentive to postpone payments when daylight liquidity is costly, an outcome that is socially inefficient. The latter arises in a priced credit regime where the postponement of payments can be socially efficient. Banks are risk neutral, but we show that most of the results are unaffected by risk aversion.     

Equity Risk, Conversion Risk, and the Demand for Insurance

Existing insurance theory fails when applied to real property because it does not account for variations in the economic environment. The article studies optimal property insurance in the presence of two sources of variation: equity risk and conversion risk. Equity risk is randomness of the value of a property. It tends to raise demand for conventional insurance. In contrast, conversion risk is randomness in the value the property would have if, after severe damage, it were converted to the highest‐valued use. It is distinct from equity risk because the highest‐valued use is typically not the current one. Under independent conversion risk, the optimum upper limit is a compromise among underlying conversion thresholds. Absent independence, the optimum can be quite different. Conversion risk can raise or lower the demand for property insurance. Insurance contracts that fail to address conversion tend to undermine the orderly disposition of obligations and reduce the gains from reallocation of risks through insurance.     

Real‐time forecast combinations for the oil price

Baumeister and Kilian (Journal of Business and Economic Statistics, 2015, 33(3), 338–351) combine forecasts from six empirical models to predict real oil prices. In this paper, we broadly reproduce their main economic findings, employing their preferred measures of the real oil price and other real‐time variables. Mindful of the importance of Brent crude oil as a global price benchmark, we extend consideration to the North Sea‐based measure and update the evaluation sample to 2017:12. We model the oil price futures curve using a factor‐based Nelson–Siegel specification estimated in real time to fill in missing values for oil price futures in the raw data. We find that the combined forecasts for Brent are as effective as for other oil price measures. The extended sample using the oil price measures adopted by Baumeister and Kilian yields similar results to those reported in their paper. Also, the futures‐based model improves forecast accuracy at longer horizons.     

Decentralizing lottery allocations in markets with indivisible commodities

Summary In economies with indivisible commodities, consumers tend to prefer lotteries in commodities. A potential mechanism for satisying these preferences is unrestricted purchasing and selling of lotteries in decentralized markets, as suggested in Prescott and Townsend [Int. Econ. Rev.25, 1–20]. However, this paper shows in several examples that such lottery equilibria do not always exist for economies with finitely many consumers. Other conditions are needed. In the examples, equilibrium and the associated welfare gains are realized if consumptions are bounded or if lotteries are based upon a common sunspot device as defined by Shell [mimeo, 1977] and Cass and Shell [J. Pol. Econ.91, 193–227]. The paper shows that any lottery equilibrium is either a Walrasian equilibrium or a sunspot equilibrium, but there are Walrasian and sunspot equilibria that are not lottery equilibria.This paper is based on Chapter 3 of my doctoral dissertation, written while I was a student at Cornell University. I thank Larry Blume, Yue Yun Chen, David Easley, Aditya Goenka, John Marshall, Bruce Smith, John Wooders and an anonymous referee. I am particularly grateful to Karl Shell and Cheng-Zhong Qin. I thank the Academic Senate at UCSB for financial support.     

Investing under model uncertainty: Decision based evaluation of exchange rate forecasts in the US,UK and Japan

We evaluate the forecast performance of a range of theory-based and atheoretical models explaining exchange rates in the US, UK and Japan. A decision-making environment is fully described for an investor who optimally allocates portfolio shares to domestic and foreign assets. Methods necessary to compute and use forecasts in this context are proposed, including the means of combining density forecasts to deal with model uncertainty. An out-of-sample forecast evaluation exercise is described using both statistical criteria and decision-based criteria. The theory-based models are found to perform relatively well when their forecasts are judged by their economic value.     

Measuring underlying economic activity

Recently, interest in the methodology of constructing coincident economic indicators has been revived by the work of Stock and Watson (1989b). They adopt the framework of the state space form and Kalman filter in which to construct an optimal estimate of an unobserved component. This is interpreted as corresponding to underlying economic activity derived from a set of observed indicator variables. In this paper we apply the Stock and Watson approach to the UK where the observed indicator variables are those that make up the Central Statistical Office (CSO) coincident indicator. The time series properties of the indicator variables are examined and three of the five variables are first difference stationary and are cointegrated, the remaining two are stationary in levels. We then construct two alternative measures of economic activity, each of which deals with the different orders of stationarity of the variables. The first uses the levels of the observed component variables that allows for the cointegrating relationship. The second imposes stationarity on the I(1) variables before the estimation by taking first differences. The levels index is viewed as the preferred specification as it allows for the long-run relationships between the variables and has a superior statistical fit. ©1996 John Wiley & Sons, Ltd.     

Does judgment improve macroeconomic density forecasts?

This paper presents empirical evidence on how judgmental adjustments affect the accuracy of macroeconomic density forecasts. Judgment is defined as the difference between professional forecasters’ densities and the forecast densities from statistical models. Using entropic tilting, we evaluate whether judgments about the mean, variance and skew improve the accuracy of density forecasts for UK output growth and inflation. We find that not all judgmental adjustments help. Judgments about point forecasts tend to improve density forecast accuracy at short horizons and at times of heightened macroeconomic uncertainty. Judgments about the variance hinder at short horizons, but can improve tail risk forecasts at longer horizons. Judgments about skew in general take value away, with gains seen only for longer horizon output growth forecasts when statistical models took longer to learn that downside risks had reduced with the end of the Great Recession. Overall, density forecasts from statistical models prove hard to beat.     

A Free Entry and Exit Experiment

Fels reports on the writing of student papers in a macroeconomic seminar for undergraduates majoring in economics. In addition to obvious benefits to students, there were high ratings from the participants for the instructor.