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

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

We develop and apply bootstrap methods for diffusion models when fitted to the long run as characterized by the stationary distribution of the data. To obtain bootstrap refinements to statistical inference, we simulate candidate diffusion processes. We use these bootstrap methods to assess measurements of local mean reversion or “pull” to the center of the distribution for short-term interest 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 is drawing it forward to a degree that is without precedent in the history of the field. But the field's origins are related to the exceptional policy relevance of macroeconomics, and the field continues to be pressed for answers to difficult policy problems that sometimes are beyond the current capabilities of the field. Continuing tensions exist between policy demands and the constraints of systematic, rigorous scientific development. A commonly mentioned example is the increasing size of structural macroeconometric models. While highly regarded in many governments, those massive models are greeted with skepticism by the best economics journals.

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

We use a general equilibrium model to study the impact of fully funding social security on the distribution of consumption across cohorts and over time. In an initial stationary equilibrium with an unfunded social security system, the capital/output ratio, debt/output ratio, and rate of return to capital are 3.2, 0.6, and 6.8%, respectively. In our first experiment, we suddenly terminate social security payments but compensate entitled generations by a massive one-time increase in government debt. Eventually, the aggregate physical capital stock rises by 40%, the return on capital falls to 4.4%, and the labor income tax rate falls from 33.9 to 14%. We estimate the size of the entitlement debt to be 2.7 times real GDP, which is paid off by levying a 38% labor income tax rate during the first 40 years of the transition. In our second experiment, we leave social security benefits untouched but force the government temporarily to increase the tax on labor income so as gradually to accumulate private physical capital, from the proceeds of which it eventually finances social security payments. This particular government-run funding scheme delivers larger efficiency gains (in both the exogenous and endogenous price cases) than privatization, an outcome stemming from the scheme's public provision of insurance both against life-span risk and labor income volatility.

We study learning in Bayesian games (or games with differential information) 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 also are allowed to be completely irrational in some states of the world. We show that bounded rational players by repetition can reach a limit full information BNE outcome. We also prove the converse, i.e., given a limit full information BNE outcome, we can construct a sequence of bounded rational plays that converges to the limit full information BNE outcome.

We examine asset prices and returns in the context of a pure exchange 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 complicated economies. Our analysis suggests that capital gains play a crucial role in generating 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 bound for a given asset menu is the average continuously compounded return on its growth-optimal portfolio. We use this bound to evaluate the plausibility of various parametric asset pricing models to characterize financial market puzzles such as the equity premium puzzle and the risk-free rate puzzle. We show that the insights offered by the growth-optimal bounds differ substantially from those obtained by other nonparametric bounds.

Futures-market exchanges guarantee the performance of all contracts to encourage active trading between anonymous partners. Traders buy from or sell to the clearinghouse. The exchanges rely primarily on a margin system — traders post a performance bond that they forfeit if they default — to manage their risk exposure. The market value of the performance guarantee is the amount a trader would have to pay to insure his performance if there were no exchange guarantee. An underpriced guarantee subsidizes high-risk traders and ultimately undermines the credibility of the exchange's commitment to perform. An adequate margin policy fairly prices the exchange performance guarantee within an (economically insignificant) varepsilon neighborhood. I show that the value of a call (put) option with a strike price equal to the futures price minus (plus) the margin is an upper bound to the market value of the exchange's performance guarantee. The probability that the futures price change exceeds the margin is the probability that the option expires “in the money.” I estimate the value of the option on the December S&P 500 futures contract during the market crash in October 1987 to illustrate the technique. For the first half of the month the value of the performance guarantee was fairly priced. On the day of the crash it was underpriced by as much as 10% of the value of the futures contract. Futures-market margin committees moved quickly; by the end of the month the value of the performance guarantee was fairly priced.

This paper develops a dynamic model of seigniorage in which economies' equilibrium paths reflect the ongoing strategic interaction between an optimizing government and a rational public. The model extends existing positive models of monetary policy and inflation by explicitly incorporating the intertemporal linkages among budget deficits, debt, and inflation. A central finding is that the public's rational responses to government policies may well create incentives for the government to reduce inflation and the public 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 of large rational-expectations models. We discuss and compare several current alternatives, focusing on the trade-offs in accuracy, space, and speed. The models range from representative-agent models with many goods and capital stocks, to models of heterogeneous agents with complete or incomplete asset markets. The methods include perturbation and projection methods. We show that these methods are capable of analyzing moderately large models even when we use only elementary, general-purpose numerical methods.

We examine a decision theoretic model of portfolio choice in which investors face income risk that is not directly insurable. We consider the sensitivity of savings and portfolio allocation rules to different assumptions about utility, the stochastic process for income and asset returns, and market frictions (transactions costs and short-sale constraints). Under CRRA time additive utility, habit persistence utility, and for a broad range of parameterizations, the model predicts that investors wish to borrow and invest all of their savings in stocks. This qualitative implication is robust to the introduction of significant transaction costs in the stock market, and contrasts sharply with portfolio allocation models in which there is no labor income.

Public capital subject to congestion is introduced into an endogenous growth model and the transitional dynamic paths under alternative fiscal policies are characterized. Several new insights are obtained from this more general framework. During the transition, the two capital stocks always approach their common equilibrium growth rate from opposite directions. Government policy induces the more volatile response in the capital stock upon which it impinges most directly: private capital in the case of a tax, public capital in the case of expenditure. Finally, we characterize a time-varying income tax that enables the decentralized economy to replicate both the first-best transitional dynamics and steady-state equilibrium of a centrally planned economy. The steady-state component corrects for externalities that arise when government expenditure deviates from its social optimum, and the effects of congestion. The transitional component corrects for myopic behavior by the representative agent along the adjustment path.

This paper considers a nonborrowed-monetary-base VAR and a targets and instrument framework favored by the monetarists to resolve the puzzles thrown up by monetary VAR studies. The results show that nonborrowed-monetary-base shocks produce responses consistent with a priori expectations about the effects of monetary policy on interest rates, prices, and output.

I develop an algorithm for solving dynamic models in which individual decision rules and the cross-sectional distribution of agents' characteristics influence each other. To illustrate the algorithm, I solve an endowment economy with incomplete markets, a continuum of heterogeneous agents, and aggregate shocks. The key innovation of the algorithm is to parameterize the (cross-sectional) density with a flexible functional form, which makes it possible to avoid simulation techniques. The paper shows how to check for accuracy and establishes links between the properties of the incomplete-markets economy and the aspects involved in obtaining a numerical solution.

We derive asset-pricing and portfolio-choice implications of a dynamic incomplete-markets model in which consumers are heterogeneous in several respects: labor income, asset wealth, and preferences. In contrast to earlier papers, we insist on at least roughly matching the model's implications for heterogeneity — notably, the equilibrium distributions of income and wealth — with those in U.S. data. This approach seems natural: Models that rely critically on heterogeneity for explaining asset prices are not convincing unless the heterogeneity is quantitatively reasonable. We find that the class of models we consider here is very far from success in explaining the equity premium when parameters are restricted to produce reasonable equilibrium heterogeneity. We express the equity premium as a product of two factors: the standard deviation of the excess return and the market price 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 the constraints on borrowing. If substantial borrowing is allowed, the market 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 observed value.

There exist a variety of reasons for the failure to find a unique cointegrating relationship between economic time series where one would normally be expected on the basis of economic theory. Among these are the testing procedure, the span of the data set, the choice of lag length in generating the test statistic, the presence of structural breaks, and the presence of cointegration only beyond some threshold. We propose the concept of regime-sensitive cointegration whereby the underlying series need not be cointegrated at all times. We show that cointegration can be switched off when a common stochastic trend is added. Alternatively, cointegration can be switched on or off because series normally believed to contain a unit actually do not. This implies that a linear combination of such variables need not be cointegrated. To illustrate the concept empirically, we test the hypothesis of interest-rate parity, and related hypotheses, using daily Eurorates for the United States and Canada.

We construct portfolios of stocks and bonds that are maximally predictable with respect to a set of ex-ante observable economic variables, and show that these levels of predictability are statistically significant, even after controlling for data-snooping biases. We disaggregate the sources of predictability by using several asset groups — sector portfolios, market-capitalization portfolios, and stock/bond/utility portfolios — and find that the sources of maximal predictability shift considerably across asset classes and sectors as the return horizon changes. Using three out-of-sample measures of predictability — forecast errors, Merton's market-timing measure, and the profitability of asset-allocation strategies based on maximizing predictability — we show that the predictability of the maximally predictable portfolio is genuine and economically significant.

We demonstrate that multiple stationary rational-expectations equilibria exist in a version of Lucas's island economy. The existence 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 stationary rational-expectations equilibria by randomizing over the set of nonstationary monetary equilibria. In some of our equilibria, a positively sloped Phillips curve exists even though our economy contains no signal-extraction problem as in the original Lucas paper. Our equilibria are indexed by beliefs and are examples of the existence of sunspot equilibria in which allocations may differ across states of nature for which preferences, technology, and endowments are identical. Our technique for constructing stationary sunspot equilibria should prove useful in a wide class of models in which an indeterminate stationary equilibrium exists.