Research Database

In this study we contrast fixed and floating exchange rate regimes in a dynamic general equilibrium model. We find that the fundamental difference in the regimes is in the courses they imply for monetary policies. Because of policy coordination requirements, a tighter monetary policy needed to maintain a fixed exchange rate may necessitate a tightening in budget policy as well. We show that under some initial conditions voters or a social planner will favor one regime, but under other conditions they will favor the other. However, the choices of voters and a social planner are almost diametrically opposed.

This paper considers the role of capacity as a strategic entry deterrent for a game in which the incumbent and entrant sequentially precommit to capacity levels before competing in price, possibly using mixed strategies. Depending on the magnitudes of the fixed set-up cost, the cost of capacity, and the relative costs of production, the model produces a wide spectrum of equilibrium behaviors, including some not previously suggested in the literature. Interesting deterrence effects occur because firms need time to build. In contrast to much previous work, the incumbent may hold idle capacity when entry is deterred.

In this paper we present a formal model of vote trading within a legislature. The model captures the conventional wisdom that if projects with concentrated benefits are financed by universal taxation, then majority rule leads to excessive spending. This occurs because the proponent of a particular bill only needs to acquire the votes of half the legislature and hence internalizes the costs to only half the representatives. We show that Pareto superior allocations are difficult to sustain because of a free rider problem among the representatives. We show that alternative voting rules, such as unanimity, eliminate excessive spending on concentrated benefit projects but lead to underfunding of global public goods.

We interpret observed gender differences in education as the equilibrium outcome of a two-sex overlapping generations model where men and women of each generation bargain over consumption, number of children, and investment in education of their children conditional on gender. This model represents a new framework for the analysis of the process of intrahousehold decision making in an intergenerational setting.

We estimate a dynamic general equilibrium model of the U.S. economy that includes an explicit household production sector and stochastic fiscal variables. We use our estimates to investigate two issues. First, we analyze how well the model accounts for aggregate fluctuations. We find that household production has a significant impact and reject a nested specification in which changes in the home production technology do not matter for market variables. Second, we study the effects of some simple fiscal policy experiments and show that the model generates different predictions for the effects of tax changes than similar models without home production.

This is a survey of simulation methods in economics, with a specific focus on integration problems. It describes acceptance methods, importance sampling procedures, and Markov chain Monte Carlo methods for simulation from univariate and multivariate distributions and their application to the approximation of integrals. The exposition gives emphasis to combinations of different approaches and assessment of the accuracy of numerical approximations to integrals and expectations. The survey illustrates these procedures with applications to simulation and integration problems in economics.

This paper provides an exact Bayesian framework for analyzing the arbitrage pricing theory (APT). Based on the Gibbs sampler, we show how to obtain the exact posterior distributions for functions of interest in the factor model. In particular, we propose a measure of the APT pricing deviations and obtain its exact posterior distribution. Using monthly portfolio returns grouped by industry and market capitalization, we find that there is little improvement in reducing the pricing errors by including more factors beyond the first one.

We use a calibrated model of the dynamics of organization capital and industry evolution to measure the size of investment in organization capital in the steady state and the dynamics of organization capital during the transition following a major reform. We find that, in the steady state, aggregate net investment in organization capital is roughly one-fifth of measured output. During the initial phase of transition, the failure rate of plants rises 200-400 percent, measured output and aggregate productivity stagnate, physical investment falls, and net investment in organization capital rises between 300 and 500 percent above its steady-state level.

We study the general equilibrium effects of social insurance on the transition in a model in which the process of moving workers from matches in the state sector to new matches in the private sector takes time and involves uncertainty. As to be expected, adding social insurance to an economy without any improves welfare. Contrary to standard intuition, however, adding social insurance may slow transition. We show that this result depends crucially on general equilibrium interactions of interest rates and savings under alternative market structures.

This paper catalogues formulas that are useful for estimating dynamic linear economic models. We describe algorithms for computing equilibria of an economic model and for recursively computing a Gaussian likelihood function and its gradient with respect to parameters. We apply these methods to several example economies.

We investigate, by Monte Carlo methods, the finite sample properties of GMM procedures for conducting inference about statistics that are of interest in the business cycle literature. These statistics include the second moments of data filtered using the first difference and Hodrick-Prescott filters, and they include statistics for evaluating model fit. Our results indicate that, for the procedures considered, the existing asymptotic theory is not a good guide in a sample the size of quarterly postwar U.S. data.

It is often argued that with a positively skewed income distribution (median less than mean) majority voting would result in higher tax rates than maximizing average welfare and, hence, lower aggregate savings. We reexamine this view in a capital accumulation model, in which distorting redistributive taxes provide insurance against idiosyncratic shocks and income distributions evolve endogenously. We find small differences of either sign between the tax rates set by a majority voting and a utilitarian government, for reasonable parametric specifications, despite the fact that model simulations produce positively skewed distributions of total income across agents.

The marginal cost of plant capacity, measured by the price of equity, is significantly procyclical. Yet, the price of a major intermediate input into expanding plant capacity, investment goods, is countercyclical. The ratio of these prices is Tobin's q. Following convention, we interpret the fact that Tobin's q differs from unity at all, as reflecting that there are diminishing returns to expanding plant capacity by installing investment goods ("adjustment costs"). However, the phenomenon that interests us is not just that Tobin's q differs from unity, but also that its numerator and denominator have such different cyclical properties. We interpret the sign switch in their covariation with output as reflecting the interaction of our adjustment cost specification with the operation of two shocks: one which affects the demand for equity and another which shifts the technology for producing investment goods. The adjustment costs cause the two prices to respond differently to these two shocks, and this is why it is possible to choose the shock variances to reproduce the sign switch. These model features are incorporated into a modified version of a model analyzed in Boldrin, Christiano and Fisher (1995). That model incorporates assumptions designed to help account for the observed mean return on risk free and risky assets. We find that the various modifications not only account for the sign switch, but they also continue to account for the salient features of mean asset returns. We turn to the business cycle implications of our model. The model does as well as standard models with respect to conventional business cycle measures of volatility and comovement with output, and on one dimension the model significantly dominates standard models. The factors that help it account for prices and rates of return on assets also help it account for the fact that employment across a broad range of sectors moves together over the cycle.

We argue that the rationalization gains often predicted by static applied general equilibrium models with imperfect competition and scale economies are artificially boosted by an unrealistic treatment of fixed costs. We introduce sunk costs into one such model calibrated with real-world data. We show how this changes the oligopoly game in a way significant enough to affect, both qualitatively and quantitatively, the outcome of a trade liberalization exercise.

I argue that Farmer and Guo's one-sector real business cycle model with indeterminacy and sunspots fails empirically and that its failure is inherent in the logic of the model taken together with some simple labor market facts.

This paper considers Marshall's argument that geographic concentration of industry facilitates specialization. I use Census data on manufacturing plants to examine the relationship between localization of industry and vertical disintegration. I find that establishments located near other establishments within the same industry tend to make more intensive use of purchased inputs than establishments without own-industry neighbors. This relationship only holds among industries that are geographically concentrated; having neighbors makes no difference in geographically dispersed industries. I argue that this pattern is consistent with a model in which increased opportunity for specialization is the reason some industries localize.

Our study examines whether there is a systematic relationship between the monetary standard under which a country operates and the rate of inflation it experiences. It also explores whether there are other properties of inflation, money, and output that differ between economies operating under a commodity standard and economies operating under a fiat standard. The basis for our study is price, money, and output data for 15 countries that have operated under both types of monetary standards. For each of these countries the data cover 80 years, and for most the data cover more than 100 years. With these data we are able to establish several facts about the differences in inflation, money growth, and output growth between economies operating under commodity standards and those operating under fiat standards. Specifically, we find that the following facts emerge when comparing commodity standards to fiat standards: inflation, money growth, and output growth are all lower; growth rates of monetary aggregates are less highly correlated with each other; growth rates of monetary aggregates are less highly correlated with inflation; and growth rates of monetary aggregates are more highly correlated with output growth.

We develop a model which accounts for the observed equity premium and average risk-free rate, without implying counterfactually high risk aversion. The model also does well in accounting for business-cycle phenomena. With respect to the conventional measures of business-cycle volatility and comovement with output, the model does roughly as well as the standard business-cycle model. On two other dimensions, the model’s business-cycle implications are actually improved. Its enhanced internal propagation allows it to account for the fact that there is positive persistence in output growth, and the model also provides a resolution to the “excess sensitivity puzzle” for consumption and income. Two key features of the model are habit persistence preferences and a multisector technology with limited intersectoral mobility of factors of production.

In this paper we estimate and test a conditional version of the international CAPM. By using a parsimonious parameterization recently proposed by Ding and Engle (1994), we allow risk premia, betas, and correlations to vary through time and test the cross-section restrictions of the model using a relatively large number of assets. One advantage of our test is is that it does not require the market weights to be observed in each period. In support of the international CAPM, we find that world-wide risk is priced whereas country-specific risk is not. Further, we find that the price of world risk is time-varying and has a strong January seasonal. When the price of risk is allowed to vary, a January dummy and the world dividend yield are driven out as independently priced factors. However, contrary to the prediction of the model, differences in risk premia across countries are explained not only by world-wide risk, but also by a constant country-specific factor. The estimated correlations reveal three main facts, cross-country correlations vary through time; they have been affected only to a limited extent by the process of liberalization of the last decade; they tend to increase during severe bear markets in the U.S. However, international correlations are smaller than correlations among U.S. assets. Therefore, investors gain from global diversification, even with contagious bear markets.

Economic development is typically accompanied by a very pronounced migration of labor from rural to urban employment. This migration, in turn, is often associated with large scale urban underemployment. Both factors appear to play a very prominent role in the process of development. We consider a model in which rural-urban migration and urban underemployment are integrated into an otherwise conventional neoclassical growth model. Unemployment arises not from any exogenous rigidities, but from an adverse selection problem in labor markets. We demonstrate that, in the most natural case, rural-urban migration—and its associated underemployment—can be a source of multiple, asymptotically stable steady state equilibria, and hence of development traps. They also easily give rise to an indeterminacy of perfect foresight equilibrium, as well as to the existence of a large set of periodic equilibria displaying undamped oscillation. Many such equilibria display long periods of uninterrupted growth and rural-urban migration, punctuated by brief but severe recessions associated with net migration from urban to rural employment. Such equilibria are argued to be broadly consistent with historical U.S. experience.

We study the general equilibrium effects of social insurance on the transition in a model in which the process of moving workers from matches in the state sector to new matches in the private sector takes time and involves uncertainty. As to be expected, adding social insurance to an economy without any improves welfare. Contrary to standard intuition, however, adding social insurance may slow transition. We show that this result depends crucially on general equilibrium interactions of interest rates and savings under alternative market structures.

I argue that Farmer and Guo's one-sector real business cycle model with indeterminacy and sunspots fails empirically and that its failure is inherent in the logic of the model taken together with some simple labor market facts.

An interpretation of government policy regarding what it accepts in transactions is embedded in a version of the Kiyotaki-Wright model of media of exchange. In an example with two goods and one fiat money, the policies consistent with fiat money being the unique medium of exchange are identified. These uniqueness policies have the government favoring fiat money in its transactions. Benefits and costs accompany any such policy. The benefit is that a worse nonmonetary equilibrium is eliminated; the cost is that a better monetary equilibrium is also eliminated.

We examine deviations from trend of net exports and other components of GNP for the United States and attempt to build models consistent with their behavior. The most striking fact is that net exports have consistently been countercyclical. We show, first, that dynamic pure-exchange models can only produce a negative correlation between net exports and GNP if the variance of consumption exceeds that of output. In the United Slates it does not, so this class of models cannot explain observed comovements between output and trade. We then examine government spending and nontraded goods as potential remedies, but show that their behavior is either inconsistent with the data or can be made consistent with any pattern of comovements. The most promising model introduces production and capital formation. Fluctuations are driven by country-specific productivity shocks, in which high productivity domestically leads to high domestic investment and a deficit in the balance of trade. This theory also receives support from the large negative covariance between net exports and investment in American data.

An intuitively natural consistency condition for contingent plans is necessary and sufficient for a contingent plan to be rationalized by maximization of conditional expected utility. One alternative theory of choice under uncertainty, the weighted-utility theory developed by Chew Soo Hong (1983) does not entail that contingent plans will generally satisfy this condition. Another alternative theory, the minimax theory as formulated by Savage (1972), does entail the consistency condition (at least for singleton-valued plans).

Much economic activity takes place within the home. Unfortunately, it is difficult to assess the cyclical properties of home production because the available data are too sporadic. Under the assumption that each observation of historical U.S. data on consumption, investment, and hours worked is consistent with optimal behavior on the part of a representative agent, we construct quarterly data on three variables that would otherwise be unobservable at a quarterly frequency: hours worked in the home sector, hours spent in leisure, and the consumption of goods produced in the home sector. Three results emerge: leisure is highly countercyclical while nonmarket hours are acyclical; there has been a large decrease in hours spent in home production since the 1970s; fluctuations in market output are a good measure of fluctuations in individual utility as long as home consumption and market consumption are either extreme complements or extreme substitutes in the production of utility. The sensitivity of results to the parametric assumptions is examined.

We examine an otherwise standard model of capital accumulation to which spatial separation and limited communication create a role for money and shocks to portfolio needs create a role for banks. In this context we examine the existence, multiplicity, and dynamical properties of monetary equilibria with positive nominal interest rates. Moderate levels of risk aversion can lead to the existence of multiple monetary steady states, all of which can be approached from a given set of initial conditions. In addition, even if there is a unique monetary steady state, monetary equilibria can be indeterminate, and oscillatory equilibrium paths can be observed. Thus financial market frictions are a potential source of both indeterminacies and endogenously arising economic volatility.

We also consider the consequences of monetary policy actions that rearrange the composition of government liabilities. Contractionary monetary policy activities can have complicated consequences, depending especially on the nature of the steady state equilibrium that obtains when there are multiple steady states. Under plausible conditions, however, a permanent contractionary change in monetary policy raises both the nominal rate of interest and the rate of inflation, and reduces long-run output levels. Thus liquidity provision by a central bank—just as by the banking system as a whole—can be growth promoting. Loose monetary policy also is conducive to avoiding development trap phenomena.

This article asks whether or not the overall welfare of U.S. residents would be greater if U.S. federal law prohibited state governments from offering tax breaks to particular businesses. The answer of a formal model is yes, making such tax breaks illegal could increase a summary measure of total welfare in the economy. According to the model, the policy could increase welfare because it would increase the tax revenue collected from capital agents, and that revenue could finance an increase in spending on public goods. The policy would also spread the tax burden more evenly in the economy and so reduce the deadweight loss of taxation per dollar collected. In addition, the policy would lead to a more efficient pattern of industry locations in the economy.

We study transition in a model in which the process of moving workers from matches in the state sector to new matches in the private sector takes time and involves uncertainty. When there are incentive problems in this rematching process, the optimal scheme may involve forced layoffs, involuntary unemployment, and a recession.

The reduced rank regression model arises repeatedly in theoretical and applied econometrics. To date the only general treatment of this model have been frequentist. This paper develops general methods for Bayesian inference with noninformative reference priors in this model, based on a Markov chain sampling algorithm, and procedures for obtaining predictive odds ratios for regression models with different ranks. These methods are used to obtain evidence on the number of factors in a capital asset pricing model.

This paper provides a general and efficient method for computing density ratio class bounds on posterior moments, given the output of a posterior simulator. It shows how density ratio class bounds for posterior odds ratios may be formed in many situations, also on the basis of posterior simulator output. The computational method is used to provide density ratio class bounds in two econometric models. It is found that the exact bounds are approximated poorly by their asymptotic approximation, when the posterior distribution of the function of interest is skewed. It is also found that posterior odds ratios display substantial variation within the density ratio class, in ways that cannot be anticipated by the asymptotic approximation.

We consider a two country growth model with international capital markets. These markets fund capital investment in both countries, and operate subject to a costly state verification (CSV) problem. Investors in each country require some external finance, but also provide internal finance, which mitigates the CSV problem. When two identical (except for their initial capital stocks) economies are closed, they necessarily converge monotonically to the same steady state output level. Unrestricted international financial trade precludes otherwise identical economies from converging, and poor countries are necessarily net lenders to rich countries. Oscillation in real activity and international capital flows can occur.

This paper establishes the stylized fact that medieval debasements were accompanied by unusually large minting volumes and revenues. This fact is a puzzle under the commonly held view that metallic coins are commodity money and exchange by weight. An existing explanation is that debased coins were used to reduce the real burden of nominally denominated debts. This explanation is logically flawed: nothing prevents agents from renegotiating contracts and avoid incurring minting costs. The paper also establishes other facts about monetary mutations, which altogether pose a challenge to monetary economics.

This paper provides structural estimates of a dynamic model of schooling, work, and occupational choice decisions based on 11 years of observations on a sample of young men from the 1979 youth cohort of the National Longitudinal Surveys of Labor Market Experience (NLSY). The structural estimation framework that we adopt fully imposes the restrictions of the theory and permits an investigation of whether such a theoretically restricted model can succeed in quantitatively fitting the observed data patterns. We find that a suitably extended human capital investment model can in fact do an excellent job of fitting observed data on school attendance, work, occupational choices, and wages in the NLSY data on young men and also produces reasonable forecasts of future work decisions and wage patterns.

This paper is motivated by observations concerning the size of the banking sector and the growth rate of the economy before and after successful stabilizations of high inflations. The facts suggest that the relative size of the banking sector increases during a period of accelerating inflation and decreases immediately following a successful monetary stabilization. Furthermore, the GDP growth rate is lower during the high inflation period than after stabilization. The goal of this paper is to develop a monetary growth model which is qualitatively consistent with these observations. The model we use is a variant of the Lucas and Stokey (1987) model of cash and credit goods. The main innovation in our model is that while cash goods and credit goods are perfect substitutes in consumption we posit different technologies for their production. We show that the model’s predictions on the impact of a permanent stabilization are consistent with the main real and monetary observations on high inflation countries.

The normal linear model, with sign or other linear inequality constraints on its coefficients, arises very commonly in many scientific applications. Given inequality constraints Bayesian inference is much simpler than classical inference, but standard Bayesian computational methods become impractical when the posterior probability of the inequality constraints (under a diffuse prior) is small. This paper shows how the Gibbs sampling algorithm can provide an alternative, attractive approach to inference subject to linear inequality constraints in this situation, and how the GHK probability simulator may be used to assess the posterior probability of the constraints.

One of the long-standing issues in the literature on transfer programs for the U.S. low-income population concerns the high cumulative marginal tax rate on earnings induced by participation in the multiplicity of programs offered by the government. Empirical work on the issue has reached an impasse partly because the analytic solution to the choice problem is intractable and partly because the model requires the estimation of multiple sets of equations with limited dependent variables, an estimation problem which until recently has been computationally infeasible. In this paper we estimate a model of labor supply and multiple program participation using methods of simulation estimation that enable us to solve both problems. The results show asymmetric wage and tax rate effects, with fairly large wage elasticities of labor supply but very inelastic responses to moderate changes in cumulative marginal tax rates, implying that high welfare tax rates do not necessarily induce major reductions in work effort.

We evaluate the ability of models with putty-clay capital and stochastic energy prices to account for the dynamics of energy use and output. Economists have noted a close relationship between changes in the price of energy and changes in output. Moreover, they have documents that this relationship is asymmetric: energy price increases are associated with large output charges while energy prices decreases are associated with small output changes. Finally, following energy price changes, energy use adjusts slowly over time. Standard models with putty-putty capital fail to reproduce the features of the data. In our study of putty-clay models, we first develop a simple characterization of equilibrium. We apply these results to solve a prototype model. Preliminary results suggest that models with putty-clay capital improve on putty-putty models in accounting for the data.

This paper develops a model of small business failure and sale that is motivated by recent evidence concerning how the failure and sale of small businesses vary with the age of the business and the tenure of the manager. This evidence motivates two key features of the model: A match between the manager and the business, and characteristics of businesses that survive beyond the current match. The parameters of the model are estimated, and the properties of this parametric model are studied. This analysis results in a simple characterization of the workings of the small business sector.

We provide a theoretical treatment of temporal aggregation in models that exhibit long-term endogenously-generated steady growth; hence generalizing our previous analysis (Econometrica 62, 1994, pp. 635–56). We introduce the property of steady-growth invariance—that the long-term growth of the continuous-time economy not be affected by the discretization—which imposes consistency restrictions on the joint formulation of preferences and stock accumulation of the discrete-time approximation. We establish, under mild conditions, these restrictions in the form of necessary and sufficient conditions on the discretization.

This article investigates the relationship between inflation and output, in the data and in standard models. The article reports that empirical cross-country studies generally find a nonlinear, negative relationship between inflation and output, a relationship that standard models cannot come close to reproducing. The article demonstrates that the models' problem may be due to their standard narrow assumption that all money is held by the public for making transactions. When the models are adjusted to also assume that banks are required to hold money, the models do a much better job. The article concludes that researchers interested in studying the effects of monetary policy on growth should shift their attention away from printing money and toward the study of banking and financial regulations.

This paper investigates the one-sector growth model where agents experience idiosyncratic endowment shocks and face a borrowing constraint. It is shown that a steady-state capital level lies strictly above the steady state in the model without shocks. In addition, the capital stock increases monotonically when it is sufficiently far below a steady state. However, near a steady state there can be interesting (nonmonotonic) economic dynamics.

Recent research in evaluating the effects of monetary policy is potentially tainted by the problem of time aggregation: that is, effects may be incorrectly estimated using quarterly data if the effects of policy occur rapidly. This study evaluates whether time aggregation is a serious problem in a simple vector autoregression. It shows time aggregation has little impact on evaluating the effect of monetary policy in a simple vector autoregression including total reserves, nonborrowed reserves, and the federal funds rate. This finding suggests that time aggregation is unlikely to be important in evaluating the effects of monetary policy in models including a goal variable, such as GDP growth.

This article analyzes several proposals to build work incentives into the U.S. welfare system. It concludes that the most cost effective way to do that is to offer a work subsidy to all low-income single parents—in other words, to simply pay them for working in the labor market. This conclusion is based on a model of the labor force participation behavior of low-income single mothers that the author developed with Robert Moffitt. Among the proposals evaluated in the article, besides the work subsidy, are proposals to reduce the rate that welfare benefits are reduced when welfare recipients work, to provide wage subsidies to low-wage workers, to expand the earned income tax credit, and to subsidize the fixed costs of working.

A two-country Real Business Cycle (RBC) model is used to study the behavior of the United States trade balance. In this model, economic fluctuations are driven by productivity shocks and by variations in government purchases and in distorting taxes. The model is simulated using quarterly data on total factor productivity, government purchases, and the average tax rate in the seven major industrial countries during the period 1975–91. A version of the model that postulates complete international asset markets—as frequently assumed in the International RBC literature (see, e.g., Backus, Kehoe, and Kydland 1992)—fails to explain the observed behavior of the U.S. trade balance. In contrast, a version with incomplete asset markets, in which only debt contracts can be used for international capital flows, tracks the behavior of the U.S. trade balance fairly closely.

We study a representative agent, open economy in which government-provided services that enter the domestic production function must be financed with distortionary taxes, and focus on the optimal size of government and the associated optimal tax rate. If the government can precommit its actions, it maximizes individual welfare by announcing and implementing a constant tax rate, which we label the “orthodox” tax rate. This tax rate is time inconsistent, and under discretion the government implements a tax that maximizes each period’s output. We label this the “populist” tax rate. It may be higher or lower than the “orthodox” rate, depending on whether the elasticity of substitution in production between private and public inputs is below or above one. We also characterize the second-best tax rate that can be sustained through trigger strategies. This best sustainable tax rate is constant and lies between the “orthodox” and “populist” extremes.

This paper describes a dynamic model in which the provision mechanism for a public project is itself the object of locational choice of individuals. Individuals in an ongoing society must choose between a Majority Rule mechanism and a Voluntary Contribution mechanism. Each mechanism determines a funding decision for a local public project which is repeated over time. Generations of individuals asynchronously supercede their “parents,” creating an entry/exit process that allows individuals with possibly different beliefs to enter society. A self confirming equilibrium (SCE) belief process describes an evolution of beliefs in this society consistent with a self confirming equilibrium of the repeated location/provision game. Due to Fudenberg and Levine (1993), SCE is weaker than Nash as it requires correct forecasts of an individual only along the realized path during the individual's lifetime. Since individuals' beliefs on out-of-equilibrium behavior may vary, an SCE belief process may admit random and heterogenous forecasts in the form of mutations of beliefs across generations as newborn individuals enter the system. It is shown that the process with belief mutation results in a globally absorbing state in which the Majority Rule mechanism is the unique survivor of the two.

This paper investigates why high income households in the United States save on average more than low income households in cross-section data. The three explanations considered are (1) age differences across households, (2) temporary earnings shocks, and (3) the structure of transfer payments. We use a calibrated life-cycle model to evaluate the quantitative importance of these explanations and find that age and the structure of transfers are quantitatively important in producing the cross-section pattern of United States savings rates. Temporary shocks are of secondary importance.

This article develops a simple model that captures a concern for relative standing, or status. This concern is instrumental, in the sense that individuals do not get utility directly from their relative standing, but, rather, the concern is induced because their relative standing affects their consumption of standard commodities. The article investigates the consequences of a concern for relative wealth in models in which individuals are making labor/leisure decisions. The analysis shows how individuals' decisions are affected by the aggregate income distribution and how the concern for relative wealth can generate behavior that can be interpreted as conspicuous consumption when wealth is not directly observable.

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.

This article describes three long-run monetary facts derived by examining data for 110 countries over a 30-year period, using three definitions of a country's money supply and two subsamples of countries: (1) Growth rates of the money supply and the general price level are highly correlated for all three money definitions, for the full sample of countries, and for both subsamples. (2) The growth rates of money and real output are not correlated, except for a subsample of countries in the Organisation for Economic Co-operation and Development, where these growth rates are positively correlated. (3) The rate of inflation and the growth rate of real output are essentially uncorrelated.

This article describes the academic debate about the usefulness of the capital asset pricing model (the CAPM) developed by Sharpe and Lintner. First the article describes the data the model is meant to explain—the historical average returns for various types of assets over long time periods. Then the article develops a version of the CAPM and describes how it measures the risk of investing in particular assets. Finally the article describes the results of competing studies of the model's validity. Included are studies that support the CAPM (Black; Black, Jensen, and Scholes; Fama and MacBeth), studies that challenge it (Banz; Fama and French), and studies that challenge those challenges (Amihud, Christensen, and Mendelson; Black; Breen and Korajczyk; Jagannathan and Wang; Kothari, Shanken, and Sloan). The article concludes by suggesting that, while academic debate continues, the CAPM may still be useful for those interested in the long run.

Historically, competition, or the extension of markets, has repeatedly brought tremendous increases in wealth. However, there is still plenty of uncertainty among economists as to why that is so. This article develops a model in which competition, modeled as the movement of goods between two areas, reduces resistance to new technology and, hence, leads to increased technology adoption and wealth. Here, the extension of markets leads to wealth increases because it reduces activities that block the use of new, more productive technology.

We study the aggregate implications of (S,s) inventory policies in a dynamic general equilibrium model. Firms in the model's retail sector face idiosyncratic demand risk, and (S,s) inventory policies are optimal because of fixed order costs. The model economy replicates salient features of the business cycle and reconciles evidence that orders are more volatile than sales, and that inventory investment is positively correlated with sales. There are two main results. First, we find that general equilibrium effects and the optimal order size are important for the economy's response to exogenous shocks. Second, we find that key features of our results are independent of the presence of idiosyncratic risk.

The paper examines the literature that attempts to resolve the equity premium and riskfree rate puzzles. It demonstrates that the puzzles will confront any model of asset prices that relies on three crucial assumptions: preferences have a particular parametric form, asset markets are complete, and asset trade is frictionless. A survey of the literature that relaxes these assumptions reveals that there are now several plausible explanations of the seemingly low riskfree rate, but the large size of the equity premium remains a puzzle.

In this paper we develop a discretized version of the dynamic programming algorithm and derive error bounds for the approximate value and policy functions. We show that under the proposed scheme the computed value function converges quadratically to the true value function and the computed policy function converges linearly, as the mesh size of the discretization converges to zero. Moreover, the constants involved in these orders of convergence can be computed in terms of primitive data of the model. We also discuss several aspects of the implementation of our methods, and present numerical results for some commonly studied macroeconomic models.