Research Database

This paper examines several grounds for doubting the value of much of the special attention recently devoted to unit root econometrics. Unit root hypotheses are less well connected to economic theory than is often suggested or assumed; distribution theory for tests of other hypotheses in models containing unit roots are less often affected by the presence of unit roots than has been widely recognized; and the Bayesian inferential theory for dynamic models is largely unaffected by the presence of unit roots. The paper displays an example to show that when Bayesian probability statements and classical marginal significance levels diverge as they do for unit root models, the marginal significance levels are misleading. The paper shows how to carry out Bayesian inference when discrete weight is given to the unit root null hypothesis in a univariate model.

In this paper, we develop a model of money and reserve-holding banks. We allow for private liabilities to circulate as media of exchange in a random-matching framework. Some individuals, which we identify as banks, are endowed with a technology to issue private notes and to keep reserves with a clearinghouse. Bank liabilities are redeemed according to a stochastic process that depends on the endogenous trades. We find conditions under which note redemptions act as a force that is sufficient to stabilize note issue by the banking sector.

The state vector in the innovation representation is asymptotically the most efficient instrumental variable estimator for the observation matrix C. The paper compares small sample properties of IV estimators for C, the dynamic matrix A and other matrices with the system theoretic estimators described in Aoki (1987) by a small scale Monte Carlo simulations. The IV estimators appear to be about the same as the system theoretic ones as far as their small sample properties are concerned. The covariance matrix of the state vector calculated from the IV point of view are also compared with the solutions of the Riccati equations. The simulation results show that they have quite similar sample means and standard deviations. This method of calculating the state vector covariance matrices may be computationally faster than solving the Riccati equation by the Schur decomposition algorithm.

This paper takes up Bayesian inference in a general trend stationary model for macroeconomic time series with independent Student-t disturbances. The model is linear in the data, but nonlinear in parameters. An informative but nonconjugate family of prior distributions for the parameters is introduced, indexed by a single parameter which can be readily elicited. The main technical contribution is the construction of posterior moments, densities, and odds ratios using a six-step Gibbs sampler. Mappings from the index parameter of the family of prior distribution to posterior moments, densities, and odds ratios are developed for several of the Nelson-Plosser time series. These mappings show that the posterior distribution is not even approximately Gaussian, and indicate the sensitivity of the posterior odds ratio in favor of difference stationarity to the choice of the prior distribution.

For at least the next two years, the U.S. economy will grow more slowly than it has on average since World War II. This is the forecast of a Bayesian vector autoregression model developed and used by researchers at the Minneapolis Federal Reserve Bank. The model's previous forecast—of a very weak start to the 1991–92 recovery—was remarkably accurate. Both forecasts are supported by evidence on long-term problems among consumers, in the commercial real estate industry, and at all levels of government. These problems will most likely constrain economic growth for years, although short spurts of strength could appear anytime, due to unpredictable special factors.

Often, researchers wish to analyze nonlinear dynamic discrete-time stochastic models. This paper provides a toolkit for solving such models easily, building on log-linearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the method of undetermined coefficients. The innovation here is to demonstrate that log-linearizing the nonlinear equations can usually be done without the need for explicit differentiation, to extend the method of undetermined coefficients to models with more endogenous state variables than expectational equations, to provide a general solution and to provide frequency-domain techniques to calculate the second order properties of the model in its HP-filtered version without resorting to simulations. Since the method is an Euler-equation based approach rather than an approach based on solving a social planners problem, models with externalities or distortionary taxation do not pose additional problems. MATLAB programs to carry out the calculations in this paper are made available. This paper should be useful for researchers and Ph.D. students alike.