The Cumulative Unanticipated Change in Interest Rates: Evidence on the Misintermediation Hypothesis

The term structure of interest rates is carefully analyzed over the period 1947-77 in order to construct a monthly series on cumulative unanticipated changes in long-term interest rates. This series is a sort of synthetic interest rate, changes in which over several months or years represent entirely unanticipated changes in interest rates. The behavior of this series is examined over recognized business fluctuations, and it is found to be actually more reliably pro-cyclic than the raw long-term interest rate, in spite of Kessel's finding that the market tends to correctly predict the direction of change of interest rates over phases. That the series is pro-cyclic supports the hypothesis we have put forward in another paper, that business fluctuations may be caused by "misintermediation", by which we mean the traditional mis-matching of asset and liability maturities on the part of financial intermediaries.

The Kalman Foundations of Adaptive Least Squares: Applications to Unemployment and Inflation

Adaptive Least Squares (ALS), i.e. recursive regression with asymptotically constant gain, as proposed by Ljung (1992), Sargent (1993, 1999), and Evans and Honkapohja (2001), is an increasingly widely-used method of estimating time-varying relationships and of proxying agents’ time-evolving expectations. This paper provides theoretical foundations for ALS as a special case of the generalized Kalman solution of a Time Varying Parameter (TVP) model. This approach is in the spirit of that proposed by Ljung (1992) and Sargent (1999), but unlike theirs, nests the rigorous Kalman solution of the elementary Local Level Model, and employs a very simple, yet rigorous, initialization. Unlike other approaches, the proposed method allows the asymptotic gain to be estimated by maximum likelihood (ML). The ALS algorithm is illustrated with univariate time series models of U.S. unemployment and inflation. Because the null hypothesis that the coefficients are in fact constant lies on the boundary of the permissible parameter space, the usual regularity conditions for the chi-square limiting distribution of likelihood-based test statistics are not met. Consequently, critical values of the Likelihood Ratio test statistics are established by Monte Carlo means and used to test the constancy of the parameters in the estimated models.Kalman Filter, Adaptive Learning, Adaptive Least Squares, Time Varying Parameter Model, Natural Unemployment Rate, Inflation Forecasting

The Pricing of Short-Lived Options When Price Uncertainty Is Log-Symmetric Stable

The well-known option pricing formula of Black and Scholes depends upon the assumption that price fluctuations are log-normal. However, this formula greatly underestimates the value of options with a low probability of being exercised if, as appears to be more nearly the case in most markets, price fluctuations are in fact symmetrics table or log-symmetric stable. This paper derives a general formula for the value of a put or call option in a general equilibrium, expected utility maximization context. This general formula is found to yield the Black-Scholes formula for a wide variety of underlying processes generating log-normal price uncertainty. It is then used to derive the value of a short-lived option for certain processes that generate log-symmetric stable price uncertainty. Our analysis is restricted to short-lived options for reasons of mathematical tractability. Nevertheless, the formula is useful for evaluating many types of risk.

The Effect of Minimum Wage Legislation on Income Equality: A TheoreticalAnalysis

Minimum wage legislation is frequently advocated in the belief that itcreates a more nearly equal distribution of income. A one-sector model of general equilibrium is used to analyze a universally applicable minimum wage, and a two-sector model is used to analyze a minimum wage that is only applied to certain industries. In both cases we find that a minimum wage may well lower equality (as computed by the Gini index) if we consider reasonable values for the parameters of these two models. In the absence of unemployment compensation, equality can increase only if the elasticity of substitution in production is quite low. In the one-sector case, however, equality necessarily rises if unemployment compensation is present and sufficiently generous.

News or Noise? Signal Extraction Can Generate Volatility Clusters From IID Shocks

We develop a framework in which information about firm value is noisily observed. Investors are then faced with a signal extraction problem. Solving this would enable them to probabilistically infer the fundamental value of the firm and, hence, price its stocks. If the innovations driving the fundamental value of the firm and the noise that obscures this fundamental value in observed data come from non-Gaussian thick-tailed probability distributions, then the implied stock returns could exhibit volatility clustering. We demonstrate the validity of this effect with a simulation study.stock returns, volatility clusters, GARCH processes, signal extraction, thick-tailed distributions, simulations

The Term Structure of Interest Rates

This paper consolidates and interprets the literature on the term structure, as it stands today. Definitions of rates of return, forward rates and holding returns for all time intervals are treated here in a uniform manner and their interrelations, exact or approximate, delineated. The concept of duration is used throughout to simplify mathematical expressions. Continuous compounding is used where possible, to avoid arbitrary distinctions based on compounding assumptions. Both the theoretical and the empirical literature are treated. The attached tables by J. Huston McCulloch give term structure data for U. S. government securities 1946-1987. The tables give discount bond yields, forward rates and par bond yields as defined in the paper. The data relate to the concepts in the paper more precisely than does any previously published data series.

Signal Extraction can Generate Volatility Clusters

volatility clusters; GARCH processes; signal extraction; heavy-tailed distributions