Research Database

We propose a definition of time consistent policy for infinite horizon economies with competitive private agents. Allocations and policies are defined as functions of the history of past policies. A sustainable equilibrium is a sequence of history-contingent policies and allocations that satisfy certain sequential rationality conditions for the government and for private agents. We provide a complete characterization of the sustainable equilibrium outcomes for a variant of Fischer’s (1980) model of capital taxation. We also relate our work to recent developments in the theory of repeated games.

We analyze a general equilibrium model with search frictions and differentiated commodities. Because of the many differentiated commodities, barter is difficult because it requires a double coincidence of wants, and this provides a medium of exchange role for fiat money. We prove the existence of equilibrium with valued fiat money and show it is robust to certain changes in the environment, including imposing transactions costs, storage costs, and taxes on the use of money. Rate of return dominance, liquidity, and the potential welfare improving role of fiat money are discussed.

During the period 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 banking 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 predictions of the model contradict conventional wisdom with regard to the cyclical effects of banking panics. Support for these predictions is found in aggregate annual time series data for Canada and the United States.

We examine the limiting behavior of cooperative and noncooperative fiscal policies as countries’ market power goes to zero. We show that these policies converge if countries raise revenues through lump-sum taxation. However, if there are unremovable domestic distortions, such as distorting taxes, there can be gains to coordination even when a single country’s policy cannot affect world prices. These results differ from the received wisdom in the optimal tariff literature. The key distinction is that, unlike in the tariff literature, the spending decisions of governments are explicitly modeled.

Using a simple model, we show why previous empirical studies of budget policy effects are flawed. Due to an identification problem, those studies’ findings can be shown to be consistent with either policies mattering or not.

This paper presents a simple general equilibrium model of optimal taxation similar to that of Lucas and Stokey (1983), except that we let the government default on its debt. As a benchmark, we consider Ramsey equilibria in which the government can precommit its policies at the beginning of time. We then consider sustainable equilibria in which both government and private agent decision rules are required to be sequentially rational. We concentrate on trigger mechanisms which specify reversion to the finite horizon equilibrium after deviations by the government. The main result is that no Ramsey equilibrium with positive debt can be supported by such trigger mechanisms.

We propose a definition of involuntary unemployment which differs from that traditionally used in implicit labor contract theory. We say that a worker is involuntarily unemployed if the marginal wage implied by the optimal contract exceeds the marginal rate of substitution between leisure and consumption. We construct a model where risk-neutral firms have monopoly power and show that such monopoly power is necessary for involuntary unemployment to arise in the optimal contract. We numerically compute examples and show that such unemployment occurs for a wide range of parameter values.

This paper presents a simple general equilibrium model of optimal taxation in which both private agents and the government can default on their debt. As a benchmark we consider Ramsey equilibria in which the government can precommit to its policies at the beginning of time, but in which private agents can default. We then consider sustainable equilibria in which both government and private agent decision rules are required to be sequentially rational. We completely characterize the set of sustainable equilibria. In particular, we show that when there is sufficiently little discounting and government consumption fluctuates enough, the Ramsey allocations and policies (in which the government never defaults) can be supported by a sustainable equilibrium.

Recent advances in duality theory have made it easier to discover relationships between asset prices and the portfolio choices based on them. But this approach to arbitrage-free securities markets has yet to be extended and applied to economies with transactions costs. This paper does so, within the context of a general state-preference model of securities markets. Several applications are developed to illustrate the nature of the theory and its potential to resolve a host of issues surrounding the effects of transactions costs on securities markets.

Optimal linear regulator methods are used to represent a class of models of endogenous equilibrium seasonality that has so far received little attention. Seasonal structure is built into these models in either of two equivalent ways: periodically varying the coefficient matrices of a formerly nonseasonal problem or embedding this periodic-coefficient problem in a higher-dimensional sparse system whose time-invariant matrices have a special pattern of zero blocks. The former structure is compact and convenient computationally; the latter can be used to apply familiar convergence results from the theory of time-invariant optimal regulator problems. The new class of seasonality models provides an equilibrium interpretation for empirical work involving periodically stationary time series.

We consider a production economy with a finite number of heterogeneous, infinitely lived consumers. We show that, if the economy is smooth enough, equilibria are locally unique for almost all endowments. We do so by converting the infinite-dimensional fixed point problem stated in terms of prices and commodities into a finite-dimensional Negishi problem involving individual weights in a social value function. By adding artificial fixed factors to utility and production functions, we can write the equilibrium conditions equating spending and income for each consumer entirely in terms of time-zero factor endowments and derivatives of the social value function.

Arrow-Debreu competitive equilibrium analysis is extended to environments with information sets differing in space as well as in time and with people moving between locations. Equilibrium is shown to exist and to be optimal and the equilibrium price system is characterized. Such environments include many of those studied in the equilibrium search literature.

This article studies the accuracy of two versions of Kydland and Prescott's (1980, 1982) procedure for approximating optimal decision rules in problems in which the objective fails to be quadratic and the constraints fail to be linear. The analysis is carried out using 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 existing value-function iteration procedures. I find the Kydland-Prescott approximate decision rules are very similar to those implied by value-function iteration.

We derive the empirical implications of a popular class of international macroeconomic models. The real economy is a stochastic exchange model with complete markets. A standard result is that cross-country risk sharing implies perfect correlation between consumption paths across countries. With mild restrictions on the endowment process ii also implies a positive correlation between net exports and output in every country. We introduce money using cash-in-advance constraints and show that the implications for real variables carry over into the monetary economy. These dichotomy and neutrality propositions generalize those in the literature to stochastic environments with heterogeneous agents, and do not require the cash-in-advance constraint to bind in every state. They imply that any correlation between the nominal exchange rate and the balance of trade can be made consistent with the theory.

We propose a definition of time consistent policy for infinite horizon economies with competitive private agents. Allocations and policies are defined as functions of the history of past policies. A sustainable equilibrium is a sequence of history-contingent policies and allocations that satisfy certain sequential rationality conditions for the government and for private agents. We provide a complete characterization of the sustainable equilibrium outcomes for a variant of Fischer's (1980) model of capital taxation. We also relate our work to recent developments in the theory of repeated games.

Models of low-frequency behavior of time series may have strongly conflicting substantive implications while fitting the data nearly equally well. We should develop methods which display the resulting uncertainty rather than adopt modeling conventions which hide it. One step toward this goal may be to consider “overparameterized” stationary ARMA models.

We compare the statistical properties of prices of U.S. treasury bills to those generated by a theoretical dynamic exchange economy with complete markets. We show that the model can account for neither the sign nor the magnitude of average risk premiums in forward prices and holding-period returns. The economy is also incapable of generating enough variation in risk premiums to account for rejections of the expectations hypothesis with treasury bill data. These conclusions add to the growing list of empirical deficiencies of the representative agent model of asset pricing.

No, and maybe not.

We develop a Q model of investment with multiple capital goods that delivers a one-to-one relation between the growth rate of the capital aggregate and the stock market-based Q. We estimate the growth-Q relation using a panel of over six hundred Japanese manufacturing firms taking into account the endogeneity of Q. Identification is achieved by combining the theoretical structure of the Q model and an assumed serial correlation structure of the technology shock that comprises the error term in the growth-Q relation. The Q variable is significantly related to firm growth. Much, but not all, of the apparent explanatory power of cash flow disappears if its endogeneity is corrected for. The estimated Q coefficient is not implausibly small if the growth rate of the capital aggregate contains measurement error.

The paper first locates quarters in the early 1970s at which the covariance matrices of the innovation vectors have shifted for the real GNPs of the USA, West Germany and Japan treated as univariate series. The paper then exhibits differences in the impulse response time profiles of the two models estimated from the data primarily before and after the break as a concise summary of the changes in dynamic interactions of the three real GNPs.

The motive to hold inventories purely in the hope of profiting from a price increase is called the speculative motive. This motive has received considerable attention in the literature. However, existing studies do not have a clear implication for how large it is quantitatively. This paper incorporates the speculative motive for holding inventories into an otherwise standard real business cycle model and finds that empirically plausible parameterizations of the model result in an average inventory stock to output ratio that is virtually zero. For this reason, we conclude that the quantitative magnitude of the speculative role for holding inventories in this model is quite small. This suggests the possibility that the study of aggregate economic phenomena can safely abstract from inventory speculation.

This paper presents a unified approach to nonlinear and nonstationary time-series analysis for a fairly wide class of linear time variable parameter (TVP) or nonlinear systems. The method theory exploits recursive filtering and fixed interval smoothing algorithms to derive TVP linear model approximations to the nonlinear or nonstationary stochastic system, on the basis of data obtained from the system during planned experiments or passive monitoring exercises. This TVP model includes the State Dependent type of Model (SDM) as a special case, and two particular SDM forms, due to Priestly and Young, are discussed in detail. The paper concludes with three practical examples: the first based on the modelling of data from a simulated nonlinear growth equation; the second concerned with the adaptive forecasting and smoothing of the Box-Jenkins Airline Passenger data; and the third providing a critical appraisal of state dependent modelling applied to the famous Sunspot time-series.

Two mechanisms are considered through which money can play a role in a real business cycle model. One is in the form of aggregate price surprises when there is heterogeneity across individuals or groups of individuals (“islands”). These shocks affect the accuracy of information about real compensation that can be extracted from observed wage rates. Another, perhaps complementary, mechanism is that the amount of desired liquidity services varies over the cycle due to a trade-off between real money and leisure. This mechanism leads to price fluctuations even when the nominal money stock does not fluctuate. As is the case for the U.S. economy over the postwar period, the price level is then countercyclical. A key finding is that with neither mechanism do nominal shocks account for more than a small amount of variability in real output and in hours worked. Indeed, output variability may very well be lower the larger the variance of price surprises is.

In a stochastic equilibrium model some stochastic processes are usually exogenously given, while others are either chosen optimally by agents or emerge from market equilibrium conditions. When we simulate such a model, often we aim at studying the relations among variables in the model as we vary parameters of policy and of behavior of economic agents. We are no more certain (indeed often less certain) of what is reasonable or interesting behavior for the exogenous variables (some of which may be unobservable) than of the variables chosen by agents or fixed in markets. It turns out that if we are flexible about which variables’ behavior we take as given in the model solution computation, freeing ourselves from the convention that the variables exogenous to the model economy must be taken as given in the simulation computations, great computational savings may result.

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.

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.

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.