We analyze a Ramsey economy in which gross investment is constrained to be nonnegative. We prove the existence of a competitive equilibrium for the case in which utility need not be bounded from below and the Inada-type conditions need not hold. The analysis is carried out by means of a direct and technically standard approach. This direct approach allows us to obtain detailed results concerning properties of competitive equilibria, and is easily adapted for the analysis of analogous models often found in macroeconomics.

Seasonal fluctuations are as large as cyclical fluctuations. Monetary policy in the United States has dealt with seasonality by smoothing nominal rates of interest. The original motivation for this was that seasonality in nominal interest rates put recurring strain on the banking system. We build a model of monetary policy in the presence of seasonality that puts financial market conditions in the foreground. Our findings are as follows. Insulating nominal rates of interest or rates of inflation from seasonal variation are the basis for a formula for generating indeterminacy of equilibria and excess volatility. Preventing seasonality in the rate of monetary growth does not suffer from this problem. Moreover, under any method for conducting monetary policy, the setting of the target value of the monetary instrument will affect the degree of seasonal variability in most endogenous variables. This is a new channel by which monetary policy can have real effects. The case for eliminating seasonality in nominal rates of interest is strongest when seasonal impulses derive from shifts in money demand. It is weakest when seasonal impulses derive from the real sector.

One usually identifies bubble solutions to linear rational expectations models by extra components (irrelevant lags) arising in addition to market fundamentals. Although there are still many solutions relying on a minimal set of state variables, i.e., relating in equilibrium the current state of the economic system to as many lags as initial conditions, there is a conventional wisdom that the bubble-free (fundamentals) solution should be unique. This paper examines the existence of endogenous stochastic sunspot fluctuations close to solutions relying on a minimal set of state variables, which provides a natural test for identifying bubble and bubble-free solutions. It turns out that only one solution is locally immune to sunspots, independently of the stability properties of the perfect-foresight dynamics. In the standard saddle-point configuration for these dynamics, this solution corresponds to the so-called saddle stable path.

This paper clarifies and extends previous work on the equivalence between monetary regimes and fiscal regimes involving social security systems. We show that monetary regimes of the type we study are equivalent to two alternative types of social security regimes. This result has an important implication. Notably, governments can finance a real expenditure by increasing the inflation rate, or finance the expenditure by increasing the tax rate on social security benefits. Such equivalence should help us better understand the role that monetary policy plays in these economies.This research was begun while Russell was visiting Iowa State University. We gratefully acknowledge helpful conversations with Scott Freeman and Peter Rangazas, and comments from participants at the Midwest Macroeconomics Meetings in Atlanta. The views expressed herein do not necessarily represent the views of the Board of Governors of the Federal Reserve System or the Federal Reserve Bank of Kansas City.

Bruce Smith was a brilliant economist who made important contributions in several fields, most notably monetary and financial economics, monetary history, economic growth, business cycle theory, and development economics. Bruce was a prolific author with nearly 100 published papers and about a dozen unpublished papers. I will try in this short article to describe his way of doing economics and being an economist. Even though Bruce's research agenda was wide, his distinctive style was clear on every page of his writings.

This paper provides an explanation for the supervisory role of the central bank in a monetary general equilibrium model of bank liquidity provision. Under incomplete information on the individual banks' liquidity needs, individual banks find it optimal to invest solely in bank loans holding no cash reserves, and rely on the interbank market for their withdrawal demands. Using the costly state verification approach under uncertainty in aggregate liquidity demands, the supervisory role of the central bank as a large intermediary arises as an incentive-compatible arrangement by which banks hold the correct level of cash reserves. First, it takes up a delegated monitoring role for the banking system. Second, it engages in discount-window lending at a penalty rate, where the discount margin covers exactly the monitoring cost incurred. Finally, under the central banking mechanism, currency premium no longer exists in the sense that currency is worth the same as deposits having an equal face value.

We consider a Diamond-type model of endogenous growth in which there are three assets: fiat money, government bonds, and equity. Because of productivity shocks, the equity return is uncertain, and risk-averse investors require a positive equity premium. Typically, there exist two steady states, but only one of them turns out to be stable. Tight monetary policy is harmful for growth in the stable steady state. These results hold under four different monetary policy strategies applied by the monetary authority. A monetary contraction increases the bond return and reduces the equity premium and thereby capital investment and growth.The research on this paper originated while Gerd Weinrich was visiting the Institute of Advanced Studies, Vienna. The authors thank an anonymous associate editor, Klaus Ritzberger, participants at the EEA2000 Congress, and seminar participants at the Catholic University of Milan for helpful comments. All remaining errors and shortcomings are our own responsibility.

The title speaks for itself: This special issue focuses attention on dynamical models in which expectations matter and in which expectational coordination is not taken for granted. This is a subject that has generated a lot of research in the past 20 years; the sample of papers presented here is witness to the present activity and the ongoing progress of our understanding. Here, as in previous research, the rational expectations construct remains the anchor of the analysis of expectational coordination, but it is subject to the additional critical scrutiny for which the present state of our knowledge calls more and more.

This paper analyzes the optimal inflation tax in economies with structural imperfections in labor, commodity, and currency markets. The Friedman rule is a classic result in economics that claims that the optimal monetary policy is to set a zero nominal interest rate. This Ramsey equilibrium is robust in a wide range of environments without imperfections in input, output, or financial markets. In many developing countries, however, a large fraction of activity takes place in the “informal” sector. Roughly speaking, the informal sector is the untaxed and unregulated market sometimes referred to as the underground economy. We obtain three results. First, we show that when structural imperfections such as an informal sector exist, the optimal inflation tax is positive. Second, we show that structural imperfections introduce an important asymmetry in the welfare cost function. Third, we provide quantitative results.

The authors are indebted to the anonymous referee for a very detailed and insightful report on an earlier version of this paper that has led to many improvements in the current version. Address correspondence to: Tony He, School of Finance and Economics, University of Technology, Sydney, P.O. Box 123 Broadway, NSW 2007, Australia; e-mail: [email protected]. This paper studies the dynamics of a simple discounted present-value asset-pricing model where agents have different risk attitudes and follow different expectation formation schemes for the price distribution. A market-maker scenario is used as the market-clearing mechanism, in contrast to the more usual Walrasian scenario. In particular, the paper concentrates on models of fundamentalists and trend followers who follow recursive geometric-decay (learning) processes (GDP) with both finite and infinite memory. The analysis depicts how the dynamics are affected by various key elements (or parameters) of the model, such as the adjustment speed of the market maker, the extrapolation rate of the trend followers, the decay rate of the GDP, the lag length used in the learning GDP, and external random factors.

We analyze expectations coordination on a stationary sunspot equilibrium (SSE) using an eductive approach in which agents forecast the forecasts of others. This approach is grounded in some common-knowledge assumptions. We show that two institutional contexts may be envisaged; we also distinguish between stationary and nonstationary beliefs. We show that the conditions for eductive stability depend mainly on whether stationarity of beliefs is imposed. We also prove the existence of eductively stable SSEs by means of the Poincaré–Hopf theorem and show that eductively stable SSEs exist in a neighborhood of some indeterminate steady states.

Several papers show that a privatization of the social security system will not be politically supported by the current generations. The asymmetry in the timing of welfare gains and losses is what generates a status quo bias in favor of the unfunded system. We explore a simple mechanism to offset the status quo problem using a general-equilibrium overlapping generations model with endogenous labor supply calibrated to the Spanish economy. The mechanism implies a privatization of the social security system together with the elimination of compulsory retirement rules. Along the transition path, this mechanism drastically shortens (from three decades to only one decade) the convergence to the new steady state, diminishing the asymmetry in the timing of welfare gains and losses. As a result, there is an increase beyond 50% in the fraction of individuals that are better off with the implementation of such a reform.This work has benefited from useful comments by Jonathan Heathcote, Antonio Manresa, and seminar participants at CREB, Carlos III de Madrid, ESF Network in Social Insurance, and Stockholm School of Economics. We acknowledge financial support from Ministerio de Ciencia y Tecnología (SEC2000-0796) and Generalitat de Catalunya (SGR00-016).

For a sample of U.S. industries, nominal wage and price inflation follow aggregate price inflation closely during economic expansions. Hence, fluctuations in profit markup and real output are moderate in the face of expansionary demand shocks. In contrast, workers' real standard of living decreases during recessions, while producers attempt to maintain, or even increase, industrial real-price inflation. The increase in profit markup correlates with larger output contraction during recessions.

This paper provides estimates of the welfare cost of volatility attributable to monetary and fiscal policy shocks. It uses a continuous-time stochastic dynamic general equilibrium model based on a recursive utility function that disentangles risk aversion from intertemporal substitution. We find that monetary and fiscal policy shocks may lead to opposite welfare effects: negative for monetary growth shocks, but positive for government expenditure shocks. Furthermore, we find that welfare costs are sensitive to the parameter values chosen for risk aversion and intertemporal substitution, and we conclude that welfare costs are potentially much larger than that found by Lucas, forcing some modification of the policy conclusions associated with Lucas's pioneering work.

This paper presents an endogenous growth model in which the research activity is financed by intermediaries that are able to reduce the incidence of researcher's moral hazard. It is shown that financial activity is growth promoting because it increases research productivity. It is also found that a subsidy to the financial sector may have larger growth effects than a direct subsidy to research. Moreover, because of the presence of moral hazard, increasing the subsidy rate to R&D may reduce the growth rate. I show that there exists a negative relation between the financing of innovation and the process of capital accumulation. Concerning welfare, the presence of two externalities of opposite sign stemming from financial activity may cause the no-tax equilibrium to provide an inefficient level of financial services. Thus, policies oriented to balance the effects of the two externalities will be welfare improving.

We test the expectations theory of the term structure of U.S. interest rates in nonlinear systems. These models allow the response of the change in short rates to past values of the spread to depend upon the level of the spread. The nonlinear system is tested against a linear system, and the results of testing the expectations theory in both models are contrasted. We find that the results of tests of the implications of the expectations theory depend on the size and sign of the spread. The long maturity spread predicts future changes of the short rate only when it is high.

A long-standing area of research and policy interest is the construction of a measure of monetary policy stance. One measure that has been proposed, as an alternative to indices that employ monetary aggregates or exchange rates, is the spread between the actual real interest rate and its flexible-price, or natural-rate, counterpart. We examine the properties of the natural real interest rate and real-interest-rate gap using a dynamic stochastic general equilibrium model. Issues we investigate include the response of the gap and its components to fundamental economic shocks and the indicator and forecasting properties of the real-interest-rate gap for inflation, both in the model and in the data. Our results suggest that the real-interest-rate gap has value as an inflation indicator, supporting a neo-Wicksellian framework.

We investigate local strong rationality (LSR) in a one-step-forward-looking univariate model with memory one. Eductive arguments are used to determine when common knowledge (CK) that the solution is near some perfect-foresight path is sufficient to trigger complete coordination on that path (i.e., the path is LSR). Coordination of expectations is shown to depend on three factors: the nature of the CK initial beliefs, the degree of structural heterogeneity, and the information structure. Our sufficient conditions for LSR precisely reflect these features and provide basic consistent justifications for the choice of the saddle-path solution.

Several papers show that a privatization of the social security system will not be politically supported by the current generations. The asymmetry in the timing of welfare gains and losses is what generates a status quo bias in favor of the unfunded system. We explore a simple mechanism to offset the status quo problem using a general-equilibrium overlapping generations model with endogenous labor supply calibrated to the Spanish economy. The mechanism implies a privatization of the social security system together with the elimination of compulsory retirement rules. Along the transition path, this mechanism drastically shortens (from three decades to only one decade) the convergence to the new steady state, diminishing the asymmetry in the timing of welfare gains and losses. As a result, there is an increase beyond 50% in the fraction of individuals that are better off with the implementation of such a reform.This work has benefited from useful comments by Jonathan Heathcote, Antonio Manresa, and seminar participants at CREB, Carlos III de Madrid, ESF Network in Social Insurance, and Stockholm School of Economics. We acknowledge financial support from Ministerio de Ciencia y Tecnología (SEC2000-0796) and Generalitat de Catalunya (SGR00-016).

It has been widely known that neoclassical growth models with sufficient increasing returns in production may feature indeterminacy. This note analytically shows that investment adjustment costs increase the required degree of increasing returns for indeterminacy to arise. Under empirically plausible levels of investment adjustment costs, we need an implausibly large degree of increasing returns to generate indeterminacy.