Some Lessons from the Yield Curve

This paper reviews the literature on the relation between short- and long-term interest rates. It summarizes the mixed evidence on the expectations hypothesis of the term structure: when long rates are high relative to short rates, short rates tend to rise as implied by the expectations hypothesis, but long rates tend to fall which is contrary to the expectations hypothesis. The paper discusses the response of the U.S. bond market to shifts in monetary policy in the spring of 1994, and reviews the debate over the optimal maturity structure of the U.S. government debt.

Estimating the Equity Premium

To estimate the equity premium, it is helpful to use finance theory: not the old-fashioned theory that efficient markets imply a constant equity premium, but theory that restricts the time-series behavior of valuation ratios, and that links the cross-section of stock prices to the level of the equity premium. Under plausible conditions, valuation ratios such as the dividend-price ratio should not have trends or explosive behavior. This fact can be used to strengthen the evidence for predictability in stock returns. Steady-state valuation models are also useful predictors of stock returns given the high degree of persistence in valuation ratios and the difficulty of estimating free parameters in regression models for stock returns. A steady-state approach suggests that the world geometric average equity premium was almost 4% at the end of March 2007, implying a world arithmetic average equity premium somewhat above 5%. Both valuation ratios and the cross-section of stock prices imply that the equity premium fell considerably in the late 20th Century, but has risen modestly in the early years of the 21st Century.

Does Saving Anticipate Declining Labor Income? An Alternative Test of the Permanent Income Hypothesis

The permanent income hypothesis implies that people save because they rationally expect their labor income to decline; they save "for a rainy day". It follows that saving should be at least as good a predictor of declines in labor income as any other forecast that can be constructed from publicly available information.The paper tests this hitherto ignored implication of the permanent income hypothesis, using quarterly aggregate data for the period 1953-84 in the U.S. A vector autoregression for saving and changes in labor income is used to generate an unrestricted forecast of declines in labor income. In the VAR, saving Granger causes labor income changes as one would expect if the PIH is true. The mean of the unrestricted forecast is far from the mean of saving, but the dynamics of the two series are quite similar.The paper presents both formal test statistics and an informal evaluation of the "fit" of the permanent income hypothesis. By contrast with most of the recent literature, the results here are valid when income is nonstationary.

Intertemporal Asset Pricing Without Consumption Data

This paper proposes a new way to generalize the insights of static asset pricing theory to a multi-period setting. The paper uses a loglinear approximation to the budget constraint to substitute out consumption from a standard intertemporal asset pricing model. In a homoskedastic lognormal selling, the consumption-wealth ratio is shown to depend on the elasticity of intertemporal substitution in consumption, while asset risk premia are determined by the coefficient of relative risk aversion. Risk premia are related to the covariances of asset returns with the market return and with news about the discounted value of all future market returns.

Stock Returns and the Term Structure

It is well known that in the postwar period stockreturns have tended to be low when the short term nominal interest rate is high. In this paper I show that more generally the state of the term structure of interest rates predicts stock returns. Risk premia on stocks appear to move closely together with those on 20-year Treasury bonds, while risk premia on Treasury bills move somewhat independently. Average returns on 20-year bonds have been very low relative to average returns on stocks. I use these observations to test some simple asset pricing models. First I consider latent variable models in which betas are constant and risk premia vary with expected returns on a small number of unobservable hedge portfolios. The data strongly reject a single-latent-variable model.The last part of the paper examines the relationship between conditional means and variances of returns on bills, bonds and stocks. Bill returns tend to be high when their conditional variance is high, but there is a perverse negative relationship between stock returns and their conditional variance. A model is estimated which assumes that asset returns are determined by their time-varying betas with a fixed-weight "benchmark" portfolio of bills, bonds and stocks, whose return is proportional to its conditional variance. This portfolio is estimated to place almost all its weight on bills, indicating that uncertainty about nominal interest rates is important in pricing both short- and long-term assets.

Money Announcements, the Demand for Bank Reserves and the Behavior of the Federal Funds Rate Within the Statement Week

The effect of money stock announcements on the Federal funds rate has been attributed informally to the information conveyed by the announcements about aggregate reserve demand. This "Aggregate Information Hypothesis" explains the effect without reference to Federal Reserve intervention in the funds market. In this paper I provide a formal model of the Aggregate Information Hypothesis under lagged reserve accounting.The model relies on imperfect information in the funds market, and on imperfect bank arbitrage of reserve demand between days of the week. Some stylized facts are presented about funds rate behavior in the period 1980-1983.

Is Consumption Too Smooth?

For thirty years, it has been accepted that consumption is smooth because permanent income is smoother than measured income. This paper considers the evidence for the contrary position, that permanent income is in fact less smooth than measured income, so that the smoothness of consumption cannot be straightforwardly explained by permanent income theory. Quarterly first differences of labor income in the United States are well described by an AR(1) with a positive autoregressive parameter. Innovations to such a process are "more than permanent;" there is no deterministic trend to which the series must eventually return, and good or bad fortune in one period can be expected to be at least partially repeated in the next. Changes to permanent income should therefore be greater than the innovations to measured income, and changes in consumption should be more variable than innovations to measured income. In fact, changes in consumption are much less variable than are income innovations. We consider two possible explanations for this paradox, first, that innovations to labor income are in reality much less persistent than appears from an AR(l), and second, that consumers have more information than do econometricians, so that only a fraction of the estimated innovations are actually unexpected by consumers. The univariate time series results are less than decisive, but the balance of the evidence, whether from fitting ARMA models or from examining the spectral density, is more favorable to the view that innovations are persistent than to the opposite view, that there is slow reversion to trend. The information question is taken up within a bivariate model of income and savings that can accommodate the feedback from saving to income that is predicted by the permanent income theory if consumers have superior information. Nevertheless, our results are the same; changes in consumption are typically smaller than those warranted by the change in permanent income. We show that our finding of "excess smoothness" is consistent with the earlier findings of "excess sensitivity" of consumption to income. Our analysis is conducted within a "logarithmic" version of the permanent income hypothesis, a formulation that recognizes that rates of growth of income and saving ratios have greater claim to stationarity than do changes in income and saving flows.