Many tests have rejected the implications of the consumption CAPM fordata on U.S. asset returns. All of the tests, though, assume that thepricing errors satisfy the Central Limit Theorem. I provide empiricalevidence that the marginal distributions of the pricing errors are so heavy-tailed that they do not satisfy the Central Limit Theorem. Usingrecent work on jackknifing, I construct a method of testing asset pricing models with heavy-tailed errors. Using this procedure, I find that theconsumption CAPM is not rejected by annual U.S. data.

We present a new simple and short proof of the existence ofequilibria in the classical single-sector growth model.

We develop and apply bootstrap methods for diffusion models whenfitted to the long run as characterized by the stationarydistribution of the data. To obtain bootstrap refinements tostatistical inference, we simulate candidate diffusion processes. Weuse these bootstrap methods to assess measurements of local meanreversion or “pull” to the center of the distribution for short-terminterest rates. We also use them to evaluate the fit of the model to the empirical density.

Macroeconomics is at a crossroads. The call of real science isdrawing it forward to a degree that is without precedent in thehistory of the field. But the field's origins are related to theexceptional policy relevance of macroeconomics, and the fieldcontinues to be pressed for answers to difficult policy problems thatsometimes are beyond the current capabilities of the field.Continuing tensions exist between policy demands and the constraintsof systematic, rigorous scientific development. A commonly mentionedexample is the increasing size of structural macroeconometric models.While highly regarded in many governments, those massive models aregreeted with skepticism by the best economics journals.

Models of the exchange process based on search theory can be used toanalyze the features of objects that make them more or less likely toemerge as money in equilibrium. These models illustrate thetrade-off between endogenous acceptability (an equilibrium property)and intrinsic characteristics of goods, such as storability or recognizability. We look at how the relativesupply and demand for various goods affect their likelihood ofbecoming money. Intuitively, goods in high demand and/or low supplyare more likely to appear as commodity money, subject to thequalification that which object ends up circulating as a medium ofexchange depends at least partly on convention. Welfare propertiesand fiat money are discussed.

We study learning in Bayesian games (or games with differentialinformation) with an arbitrary number of bounded rational players,i.e., players who choose approximate best response strategies[approximate Bayesian Nash Equilibrium (BNE) strategies] and who alsoare allowed to be completely irrational in some states of the world.We show that bounded rational players by repetition can reach a limitfull information BNE outcome. We also prove the converse, i.e., givena limit full information BNE outcome, we can construct a sequence ofbounded rational plays that converges to the limit full informationBNE outcome.

We use a general equilibrium model to study the impact offully funding social security on the distribution of consumptionacross cohorts and over time. In an initial stationary equilibriumwith an unfunded social security system, the capital/output ratio,debt/output ratio, and rate of return to capital are 3.2, 0.6, and6.8%, respectively. In our first experiment, we suddenly terminatesocial security payments but compensate entitled generations by amassive one-time increase in government debt. Eventually, theaggregate physical capital stock rises by 40%, the return on capitalfalls to 4.4%, and the labor income tax rate falls from 33.9 to14%. We estimate the size of the entitlement debt to be 2.7 timesreal GDP, which is paid off by levying a 38% labor income tax rateduring the first 40 years of the transition. In our secondexperiment, we leave social security benefits untouched but force thegovernment temporarily to increase the tax on labor income so asgradually to accumulate private physical capital, from the proceedsof which it eventually finances social security payments. Thisparticular government-run funding scheme delivers larger efficiencygains (in both the exogenous and endogenous price cases) thanprivatization, an outcome stemming from the scheme's public provisionof insurance both against life-span risk and labor income volatility.

We examine asset prices and returns in the context of a pureexchange economy. Our purpose is to identify the key channels by which changes in preferences affect the equity premium and the risk-free rate and to develop intuition that is useful for understanding asset pricing in more complicatedeconomies. Our analysis suggests that capital gains play a crucial role ingenerating empirically plausible mean equity premia.

We show that absence of arbitrage in frictionless markets implies a lower bound on the average of the logarithm of the reciprocal of the stochastic discount factor implicit in asset pricing models. The greatest lower boundfor a given asset menu is the average continuously compounded return on itsgrowth-optimal portfolio. We use this bound to evaluate the plausibility ofvarious parametric asset pricing models to characterize financial marketpuzzles such as the equity premium puzzle and the risk-free ratepuzzle. We show that the insights offered by the growth-optimal boundsdiffer substantially from those obtained by other nonparametric bounds.

Futures-market exchanges guarantee the performance of all contractsto encourage active trading between anonymous partners. Traders buyfrom or sell to the clearinghouse. The exchanges rely primarily on amargin system — traders post a performance bond that they forfeit ifthey default — to manage their risk exposure. The marketvalue of the performance guarantee is the amount a trader would have to pay toinsure his performance if there were no exchange guarantee.Anunderpriced guarantee subsidizes high-risk traders and ultimatelyundermines the credibility of the exchange's commitment to perform.An adequate margin policy fairly prices the exchange performanceguarantee within an (economically insignificant) varepsilonneighborhood. I show that the value of a call (put) option with astrike price equal to the futures price minus (plus) the margin is anupper bound to the market value of the exchange's performanceguarantee. The probability that the futures price change exceeds themargin is the probability that the option expires “in the money.” Iestimate the value of the option on the December S&P 500 futurescontract during the market crash in October 1987 to illustrate thetechnique. For the first half of the month the value of theperformance guarantee was fairly priced. On the day of the crash itwas underpriced by as much as 10% of the value of the futurescontract. Futures-market margin committees moved quickly; by the endof the month the value of the performance guarantee was fairly priced.

This paper develops a dynamic model of seigniorage in whicheconomies' equilibrium paths reflect the ongoing strategicinteraction between an optimizing government and a rational public.The model extends existing positive models of monetary policy andinflation by explicitly incorporating the intertemporal linkagesamong budget deficits, debt, and inflation. A central finding is thatthe public's rational responses to government policies may wellcreate incentives for the government to reduce inflation and thepublic debt over time. A sufficiently myopic government may, however,provoke a rising equilibrium path of inflation and public debt.

We explore alternative approaches to numerical solutions oflarge rational-expectations models. We discuss and compare severalcurrent alternatives, focusing on the trade-offs in accuracy, space,and speed. The models range from representative-agent models withmany goods and capital stocks, to models of heterogeneous agents withcomplete or incomplete asset markets. The methods includeperturbation and projection methods. We show that these methods arecapable of analyzing moderately large models even when we use onlyelementary, general-purpose numerical methods.

We examine a decision theoretic model of portfoliochoice in which investors face income risk that is not directlyinsurable.We consider the sensitivity of savings and portfolioallocation rules to different assumptions about utility, thestochastic process for income and asset returns, and market frictions(transactions costs and short-sale constraints).Under CRRA timeadditive utility, habit persistence utility, and for a broad range ofparameterizations, the model predicts that investors wish to borrowand invest all of their savings in stocks. This qualitativeimplication is robust to the introduction of significant transactioncosts in the stock market, and contrasts sharply with portfolioallocation models in which there is no labor income.

Public capital subject to congestion is introduced into an endogenousgrowth model and the transitional dynamic paths under alternativefiscal policies are characterized. Several new insights are obtainedfrom this more general framework. During the transition, the twocapital stocks always approach their common equilibrium growth ratefrom opposite directions. Government policy induces the more volatileresponse in the capital stock upon which it impinges most directly:private capital in the case of a tax, public capital in the case ofexpenditure. Finally, we characterize a time-varying income tax thatenables the decentralized economy to replicate both the first-besttransitional dynamics and steady-state equilibrium of a centrallyplanned economy. The steady-state component corrects forexternalities that arise when government expenditure deviates fromits social optimum, and the effects of congestion. The transitionalcomponent corrects for myopic behavior by the representative agentalong the adjustment path.

This paper considers a nonborrowed-monetary-base VAR and a targetsand instrument framework favored by the monetarists to resolve thepuzzles thrown up by monetary VAR studies.The results show thatnonborrowed-monetary-base shocks produce responses consistent with apriori expectations about the effects of monetary policy on interestrates, prices, and output.

I develop an algorithm for solving dynamic models in which individualdecision rules and the cross-sectional distribution of agents'characteristics influence each other. To illustrate the algorithm, Isolve an endowment economy with incomplete markets, a continuum ofheterogeneous agents, and aggregate shocks. The key innovation of thealgorithm is to parameterize the (cross-sectional) density with aflexible functional form, which makes it possible to avoid simulationtechniques. The paper shows how to check for accuracy and establisheslinks between the properties of the incomplete-markets economy andthe aspects involved in obtaining a numerical solution.

We derive asset-pricing and portfolio-choice implicationsof a dynamic incomplete-markets model in which consumers areheterogeneous in several respects: labor income, asset wealth, andpreferences. In contrast to earlier papers, we insist on at leastroughly matching the model's implications forheterogeneity — notably, the equilibrium distributions of income andwealth — with those in U.S. data. This approach seems natural:Models that rely critically on heterogeneity for explaining assetprices are not convincing unless the heterogeneity is quantitativelyreasonable. We find that the class of models we consider here isvery far from success in explaining the equity premium whenparameters are restricted to produce reasonable equilibriumheterogeneity. We express the equity premium as a product of twofactors: the standard deviation of the excess return and the marketprice of risk. The first factor, as expected, is much too low in the model. The size of the market price of risk depends crucially on theconstraints on borrowing. If substantial borrowing is allowed, themarket price of risk is about one one-hundredth of what it is in the data(and about 15% higher than in the representative-agent model).However, under the most severe borrowing constraints that we consider, the market price of risk is quite close to the observedvalue.

There exist a variety of reasons for the failure to find a uniquecointegrating relationship between economic time series where onewould normally be expected on the basis of economic theory. Amongthese are the testing procedure, the span of the data set, the choiceof lag length in generating the test statistic, the presence ofstructural breaks, and the presence of cointegration only beyond somethreshold. We propose the concept of regime-sensitive cointegrationwhereby the underlying series need not be cointegrated at all times.We show that cointegration can be switched off when a commonstochastic trend is added. Alternatively, cointegration can beswitched on or off because series normally believed to contain a unitactually do not. This implies that a linear combination of suchvariables need not be cointegrated. To illustrate the conceptempirically, we test the hypothesis of interest-rate parity, andrelated hypotheses, using daily Eurorates for the United States andCanada.

We construct portfolios of stocks and bonds that are maximallypredictable with respect to a set of ex-ante observable economicvariables, and show that these levels of predictability arestatistically significant, even after controlling for data-snoopingbiases.We disaggregate the sources of predictability by usingseveral asset groups — sector portfolios, market-capitalizationportfolios, and stock/bond/utility portfolios — and find that thesources of maximal predictability shift considerably across assetclasses and sectors as the return horizon changes.Using threeout-of-sample measures of predictability — forecast errors, Merton'smarket-timing measure, and the profitability of asset-allocationstrategies based on maximizing predictability — we show that thepredictability of the maximally predictable portfolio is genuine andeconomically significant.

We demonstrate that multiple stationary rational-expectationsequilibria exist in a version of Lucas's island economy. Theexistence of these equilibria follows from the fact that there is an indeterminate set of monetary equilibria in the two-period overlapping-generations model. We show how to construct stationaryrational-expectations equilibria by randomizing over the set ofnonstationary monetary equilibria.In some of our equilibria, apositively sloped Phillips curve exists even though our economycontains no signal-extraction problem as in the original Lucas paper.Our equilibria are indexed by beliefs and are examples of theexistence of sunspot equilibria in which allocations may differacross states of nature for which preferences, technology, andendowments are identical.Our technique for constructing stationarysunspot equilibria should prove useful in a wide class of models inwhich an indeterminate stationary equilibrium exists.