Research Database

This paper describes and evaluates P-Star (P*), a new method to forecast inflation trends which was introduced by the Federal Reserve Board of Governors in the summer of 1989. The paper examines how well P* would have done, compared with eight other forecasting methods, had all of these methods been used to forecast inflation in the 1970s and 1980s. P* turns out to be not an exceptionally good or bad way to forecast inflation.

It is argued that economists ought to recognize that modeling in different styles will be appropriate for different purposes or different stages in the development of an area of economics. As an example, the paper displays simulations of a stochastic general equilibrium model which shed light on the interpretation of widely discussed small macroeconomic vector autoregressive models connecting monetary variables to output and prices.

This model extends one originally constructed by Robert Litterman in 1980 and used continuously since then to prepare quarterly forecasts. The current version is 3 variables larger than Litterman’s original model, and it now allows time variation in coefficients, predictable time variation in forecast error variance, and non-normality in disturbances. Despite this elaboration the model in a sense has just 12 parameters free to fit the behavior of 9 variables in 9 equations. The paper reports the model structure and summarizes some aspects of its recent forecasting performance.

This paper discusses at an undergraduate level how forecast rationality can be tested. It explains that forecasters should correctly use any relevant information they knew in making their predictions. It shows that forecast rationality can be tested by determining whether the forecasters' prediction errors are predictable. After addressing what data and methods can be used for testing rationality, the paper presents tests of the price-forecast rationality of individual professional forecasters. Unlike results of previous studies, the test results show that those forecasters' price predictions appear to be rational.

There are two major differences between Japan and the United States in the way saving is calculated in their national accounts. First, depreciation in Japanese national accounts is based on historical costs, which leads to an understatement of true depreciation and hence an overstatement of net saving. Second, government capital formation is not included in U.S. saving. This article adjusts the official Japanese saving numbers by evaluating depreciation at replacement costs and excluding government capital formation from saving. Doing so significantly reduces the apparent gap between the national saving rates of the two countries. Since 1970 Japan's national saving rate has been declining to the stationary U.S. rate. This trend, however, has been reversed in recent years. In contrast, Japan's wealth-to-income ratio (excluding land), after declining in the late 1950s, has been rising toward the U.S. ratio and has reached the U.S. level in 1987.

Stochastic inflation affects the risk characteristics, measured by the equity premium and the correlation of the equity’s return with consumption, in a fundamental way. The riskiness of a dollar-denominated asset depends on two conditional covariances: the covariance of the marginal rate of substitution (MRS) with the equity price and the covariance of the MRS with the rate of appreciation in the purchasing power of money. The second covariance may take either sign which becomes significant when the risk characteristics of the dollar-denominated asset are compared with the risk characteristics of an indexed asset constructed in a real version of the model.

The effects of stochastic inflation on the assets’ risk characteristics are studied in a parameterized version of a cash-in-advance asset-pricing model. The growth rates of the endowment and monetary transfer evolve according to a VAR. The equity price is a geometric distributed lead of log–normally distributed random variables; an algorithm to express the price as an explicit function of the state variables is described.

This paper evaluates Hayashi's conjecture that Japan's postwar saving experience can be accounted for by the neoclassical model of economic growth as that country's efforts to reconstruct its capital stock that was severely damaged in World War II. I call this the reconstruction hypothesis. I take a simplified version of a standard neoclassical growth model that is in widespread use in macroeconomics and simulate its response to capital destruction. The saving rate path implied by the model differs significantly from the path taken by actual Japanese postwar saving data. I discuss several model modifications which would reconcile the reconstruction hypothesis with Japan's postwar saving experience. For the reconstruction hypothesis to be credible requires independent evidence on the empirical plausibility of the model modifications. It is left to future research to determine whether that evidence exists.

The paper employs three different types of identifying restrictions to calculate the impulse responses for the trivariate series composed of the U.S. unemployment level, real GNP and the money stock. The first two are the zero restrictions, arising from the assumption of the delayed information pattern available in forming a money reaction function. The third assumes a particular simplified structural model. The paper shows that the impulse response patterns are generally insensitive to these alternative specifications. Similar exercises are carried out for the bivariate series composed of the U.S. and the unemployment level.

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.

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.

Previous business cycle models have made the assumption that all the variation in the labor input is either due to changes in hours per worker or changes in number of workers, but not both. In this paper, both vary. We think this a better model for estimating the contribution of Solow technology shocks to aggregate fluctuations. We find that about 70 percent of U.S. postwar cyclical fluctuations are induced by variations in the Solow technology parameter.

This paper estimates the expectations of older male workers in the form of a 130 million element Markov transition probability matrix specifying the joint stochastic process for workers’ income, health, martial and employment status, conditioned on workers’ decisions about labor force participation and collection of Social Security benefits. The estimated transition matrix will be used in subsequent work to estimate the unknown parameters of workers’ utility functions under the assumption that their behavior is governed by the solution to a dynamic programming model. The paper also discusses some of the problems involved in constructing good measures of workers’ states and decisions.

During 1870–1913, Canada had a well-diversified branch banking system while banks in the U.S. unit-banking system were less diversified. Canadian banks could issue large-denomination notes with no restrictions on their backing, while all U.S. currency was essentially an obligation of the U.S. government. Also, experience in the two countries with regard to bank failures and panics was quite different. A general equilibrium business cycle model with endogenous financial intermediation is constructed that captures these historical Canadian and American monetary and banking arrangements as special cases. The model's predictions contradict conventional wisdom about the cyclical effects of banking panics. Support for these predictions is found in aggregate annual time series data for Canada and the United States.

This paper is a study of bank panics under the U.S. National Banking System in 1864–1913. During this period, bank deposits in the United States, like those in Great Britain and Canada, were not insured by the government. Unlike the United States, however, neither of those countries had any bank panics. The U.S. panics were caused essentially by two unique features of the U.S. banking system: prohibitions on bank branching and pyramiding of bank reserves. In the paper, a model which includes these features is constructed, and it is shown that bank panics can occur even though all agents are rational. In this model, bank panics can be eliminated by a combination of reserve requirements, central bank loans, and occasional restrictions on cash payments by banks. The conclusion is that to eliminate bank panics, deposit insurance is not necessary.

The effects of stochastic inflation on equity prices and the equity premium are studied in a pure-endowment asset-pricing model with a cash-in-advance constraint. Stochastic inflation affects the equity premium through two channels: the assessment of an inflation tax and the presence of an inflation premium. Real and monetary versions of the model are simulated and the comparative dynamic results corroborate the conclusion that inflation has quantitatively important effects.

The other important result is that the equity premium in the real version of a model—a continuous state-space generalization of Mehra and Prescott (1985)—and the monetary model is very sensitive to the conditional variance of endowment growth. When the standard deviation of endowment growth is increased from 3.49 percent (the estimated value) to 5.59 percent, the real model can generate an equity premium of 2.8 percent in the range of the risk aversion parameters considered by Mehra and Prescott. The monetary model displays similar sensitivity and can generate an equity premium of 5.81 percent.

For the first-order univariate autoregression without constant term, the joint p.d.f (corresponding to a flat prior) for the true coeffecient p and the least squares estimate p-hat is estimated by Monte Carlo and graphically displayed. The graphs show how the symmetric distribution of p|p-hat coexists with the assymetric distribution of p-hat|p. Treating tail areas of the p-hat|p distribution as if they summarized evidence in the data about the location of p amounts to ignoring the shrinkage in the variance of p-hat|p as p approaches one. Prior p.d.f.'s implicit in treating classical significance levels as if they were Bayesian conditional probabilities are calculated. They are shown to depend sensitively on p-hat and to put substantial probability on p's above one.

This paper reports an optimistic forecast of U.S. output and inflation trends in 1990–91. Generated by a Bayesian vector autoregression (BVAR) model of the U.S. economy using data available on November 30, 1989, the forecast is more optimistic than a consensus forecast. The key to the model's greater optimism for real growth is its outlook for strong consumer spending. The model's optimism is defended by examining historical precedents as well as comparing the track records of the model and consensus forecasts. The model's measures of forecast uncertainty, however, suggest that its predictions should be taken cautiously. An appendix explains how the model can be used to generate conditional forecasts.

This paper describes a method developed to predict the advance (first) estimate of inflation-adjusted gross national product (real GNP) using hours-worked data. Besides generating fairly accurate forecasts of advance GNP, the method has two implications. First, the Commerce Department seems to weigh the hours-worked data most heavily in its early estimates of real GNP but less and less so in its revised estimates. Second, analysts attempting to predict current-quarter outcomes in real time need to consider the availability and reliability of data at the time the forecasts are made.

In this paper I develop a practical extension of the Method of Simulated Moments (MSM) estimator for limited dependent variable models to the panel data case. The method is based on a factorization of the MSM first order condition into transition probabilities, along with the development of a new highly accurate method for simulating these transition probabilities. A series of Monte-Carlo tests show that this MSM estimator performs quite well relative to quadrature-based ML estimators, even when large numbers of quadrature points are employed. The estimator also performs well relative to simulated ML, even when a highly accurate method is used to simulate the choice probabilities. In terms of computational speed, complex panel data models involving random effects and ARMA errors may be estimated via MSM in times similar to those necessary for estimation of simple random effects models via ML-quadrature.

This paper studies the accuracy of two versions of the procedure proposed by Kydland and Prescott (1980, 1982) for approximating the optional decision rules in problems in which the objective fails to be quadratic and the constraints linear. The analysis is carried out in the context of a particular example: a version of the Brock-Mirman (1972) model of optimal economic growth. Although the model is not linear quadratic, its solution can nevertheless be computed with arbitrary accuracy using a variant of the value function iteration procedures described in Bertsekas (1976). I find that the Kydland-Prescott approximate decision rules are very similar to those implied by value function iteration.

The paper discusses a new, fully recursive approach to the adaptive modeling, forecasting and seasonal adjustment of nonstationary economic time-series. The procedure is based around a time variable parameter (TVP) version of the well known “component” or “structural” model. It employs a novel method of sequential spectral decomposition (SSD), based on recursive state-space smoothing, to decompose the series into a number of quasi-orthogonal components. This SSD procedure can be considered as a complete approach to the problem of model identification and estimation, or it can be used as a first step in maximum likelihood estimation. Finally, the paper illustrates the overall adaptive approach by considering a practical example of a UK unemployment series which exhibits marked nonstationarity caused by various economic factors.

Leamer (1983) suggested to study the range of estimators β˅0 in the model y=Xβ + δ when imposing linear constraints of the form M (Cβ - c) = 0 where only C and c are fixed. However the extremes may come from models with a bad R^2, say. In this paper we give the exact bounds when only considering models with R^2 ≥ (1 - δ) R^2 max + δR^2 min. These exact bounds can be found from calculating only two regressions. We apply our techniques to study the velocity of money.