Research Database

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.

Under a narrow set of assumptions, Chamley (1986) established that the optimal tax rate on capital income is eventually zero. This study examines and extends that result by relaxing Chamley’s assumptions, one by one, to see if the result still holds. It does. This study unifies the work of other researchers, who have confirmed the result independently using different types of models and approaches. This study uses just one type of model (discrete time) and just one approach (primal). Chamley’s result holds when agents are heterogeneous rather than identical, the economy’s growth rate is endogenous rather than exogenous, the economy is open rather than closed, and agents live in overlapping generations rather than forever. (With this last assumption, the result holds under stricter conditions than with the others.)

This paper develops a Limited-Dependent Rational Expectations (LD-RE) model where the bounds can be fixed for an extended period, but are subject to occasional jumps. In this case, the behavior of the endogenous variable is affected by the agent's expectations about both the occurrence and the size of the jump. The RE solution for the one-sided and two-sided band are derived and shown to encompass the cases of perfectly predictable and stochastically varying bounds examined by earlier literature. We demonstrate that the solution for the one-sided band exists and is unique when the coefficient of the expectational variable is less than one. In the case of a two-sided band, the RE solution exists for all the parameter values and is unique if the coefficient of the expectational variable is less than or equal to one. These results hold even when the jump probability is stochastically varying and the error terms are conditionally heteroscedastic. As an illustration, we estimate a model of exchange rate determination in a target zone using data for the Franc/Mark exchange rate. Empirical results provide support for the non-linear model with time-varying realignment probability and indicate that the agents correctly anticipated most of the observed changes in the central parity.

This paper develops the Parameterized Expectations Approach (PEA) for solving nonlinear dynamic stochastic models with rational expectations. The method can be applied to a variety of models, including models with strong nonlinearities, sub-optimal equilibria, and many continuous state variables. In this approach, the conditional expectations in the equilibrium conditions are approximated by finite-dimensional classes of functional forms. The approach is highly efficient computationally because it incorporates endogenous oversampling and Monte-Carlo integration, and it does not impost a discrete grid on the state variables or the stochastic shocks. We prove that PEA can approximate the correct solution with arbitrary accuracy on the ergodic set by increasing the size of the Monte-Carlo simulations and the dimensionality of the approximating family of functions.

This essay briefly reviews the professional life and work of economist S. Rao Aiyagari, who died after a heart attack on May 20, 1997, at the age of 45. Aiyagari is described as “one of the ablest economists of his generation.” The essay is accompanied by a complete list of Aiyagari’s published work and reprints of three of his articles in the Federal Reserve Bank of Minneapolis Quarterly Review: “Deflating the Case for Zero Inflation” (Summer 1990), “On the Contribution of Technology Shocks to Business Cycles” (Winter 1994), and “Macroeconomics With Frictions” (Summer 1994).

This paper develops a two-sector neoclassical model of international trade with endogenous capital accumulation and intertemporal optimization. In contrast to the traditional “2x2x2” model, there is a Ricardian implication that countries specialize according to comparative advantage. Consequently, the theory predicts that government expenditure policies are unlikely to affect the established pattern of specialization and trade, but that changes in tax policies can result in a dramatic reorganization of world production. Further, the dynamic “2x2x2” model can explain many of the salient features of international trade that are problematic for the standard Heckscher-Ohlin-Samuelson model.

This paper develops a model of the choice between bank and market finance by entrepreneurial firms that differ in the value of their net worth. The monitoring associated with bank finance ameliorates a moral hazard problem between the entrepreneurs and their lenders. The model is used to analyze the different strands of the credit view of the transmission of monetary policy. In particular, we derive the empirical implications of a broad credit channel, and compare them to those obtained when the model is extended to incorporate some elements of the bank lending channel.

This paper, originally published in the spring 1983 Quarterly Review, explains why flat-rate deposit insurance gives financial intermediaries an incentive to take on too much risk. It also discusses the purposes of deposit insurance and some ways reforms might serve those purposes. Three possible reforms are discussed: abolishing the insurance and requiring depository institutions to either hold safe assets or mark to market, reducing the deposit ceilings for insurance, and risk-adjusting the insurance premia.

In Scott Freeman’s (1996) model, payment system arrangements based on intermediated debt that is settled with money achieve higher welfare than does direct money payment. In a simplified version of Freeman’s model, welfare can be further improved and efficiency achieved by a monetary authority participating in a secondary market for debt or by a private intermediary using a common clearinghouse device. The analysis clarifies that ordinary private agents can assume the role of central bank or clearinghouse; no artificial agent, posited solely to play that role and endowed with special capabilities for it, is necessary. The institutional features required for a central bank or a clearinghouse to achieve efficiency, particularly features related to central bank independence, are discussed informally.

I show that the “indivisible labor” models of Diamond and Mirrlees (1978, 1986), Hansen (1985), Rogerson (1988), Christiano and Eichenbaum (1992) and many others are, when aggregated across persons with the same marginal utility of income, equivalent to the divisible labor model of Lucas and Rapping (1969); any data on aggregate hours and earnings generated by the divisible (indivisible) model can be generated by some parameterization of the indivisible (divisible) model. The same is true when “macro” data are obtained by aggregating over time and across people. This equivalence means that the indivisibility of labor per se does not have implications for macroeconomics. Nor does indivisibility have “aggregate” normative implications.

One critical aspect of economic development is that productivity growth and a rising standard of living are realized through more roundabout methods of production and increasing specialization of intermediate inputs and producer services. We use an extended version of the Judd-Grossman-Helpman model of dynamic monopolistic competition to show that an economy that inherits a small range of specialized inputs can be trapped into a lower stage of development. The limited availability of specialized inputs forces the final goods producers to use a labor intensive technology, which in turns implies a small inducement to introduce new intermediate products. The start-up costs, which make the intermediate goods producers subject to dynamic increasing returns, and pecuniary externalities that result from the factor substitution in the final goods sector, play essential roles in the model.

This article analyzes some of the potential effects of increased international financial integration within a simple two-country model. In the model, the article considers a switch in the menu of internationally traded financial securities from bonds to complete contingent claims and examines the impact of this switch on the stochastic properties, including the cross-country correlations, of standard macroeconomic aggregates like output, consumption, and labor effort, as well as the trade balance.

This paper analyses how the wage and employment decisions of females are affected by past workforce participation and hours supplied. Our estimation methods exploit the fact that, when markets are complete, the Lagrange multiplier for an agent’s lifetime budget constraint always enters multiplicatively with the prices of (contingent claims to) consumption and leisure. Depending on the properties of the equilibrium price process, it is thus possible to predict the behavior of a wealthy agent by observing that of a poorer person living in a more prosperous world. This provides the key to estimating, nonparametrically, the expectations that enter the calculus of equilibrium decisionmaking, and ultimately the structural parameters which characterize preferences.

We use a regime-switching model of real GNP growth to examine the duration dependence of business cycles. The model extends Hamilton (1989) and Durland and McCurdy (1994) and is estimated using both the postwar NIPA data and the secular data constructed by Balke-Gordon. We find that an expansion is more likely to end at a young age, that a contraction is more likely to end at an old age, that output growth slows over the course of an expansion, that a decline in output is mild at the beginning of a contraction, and that long expansions are followed by long contractions. This evidence taken together provides no support for the clustering of the whole-cycle around seven-to-ten year durations.

Three key features of the employment process in the U.S. economy are that job creation is procyclical, job destruction is countercyclical, and job creation is less volatile than job destruction. These features are also found at the sectoral (goods and services) level. The paper develops, calibrates, and simulates a two sector general equilibrium model including both aggregate and sectoral shocks. The behavior of the model economy mimics the job creation and destruction facts. Sectoral shocks play a significant role in determining the aggregate level of nonemployment.

This essay argues that monetary theories should not contain an undefined object labeled money. Among existing theories that do not satisfy that dictum are models which assume that real balances are arguments of utility or production functions and models which assume cash-in-advance constraints. A main weakness of theories that do not satisfy the dictum is that they cannot address questions about which objects constitute money. Theories that do satisfy the dictum are those which specify assets by their physical properties and which permit the assets’ role in exchange to be endogenous. The essay briefly describes one such theory, a random matching model with assets that differ according to whether they throw off real dividends.

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.

Can neoclassical theory account for the Great Depression in the United States—both the downturn in output between 1929 and 1933 and the recovery between 1934 and 1939? Yes and no. Given the large real and monetary shocks to the U.S. economy during 1929–33, neoclassical theory does predict a long, deep downturn. However, theory predicts a much different recovery from this downturn than actually occurred. Given the period’s sharp increases in total factor productivity and the money supply and the elimination of deflation and bank failures, theory predicts an extremely rapid recovery that returns output to trend around 1936. In sharp contrast, real output remained between 25 and 30 percent below trend through the late 1930s. We conclude that a new shock is needed to account for the Depression’s weak recovery. A likely culprit is New Deal policies toward monopoly and the distribution of income.

There is widespread agreement that a surprise increase in an economy's money supply drives the nominal interest rate down and economic activity up, at least in the short run. This is understood as reflecting the dominance of the liquidity effect of a money shock over an opposing force, the anticipated inflation effect. This paper illustrates why standard general equilibrium models have trouble replicating the dominant liquidity effect. It also studies several factors which have the potential to improve the performance of these models.

Barksy-Miron [1989] find that the postwar U.S. economy exhibits a regular seasonal cycle, as well as the business cycle phenomenon. Are these findings consistent with current equilibrium business cycle theories as surveyed by Prescott [1986]? We consider a dynamic, stochastic equilibrium business cycle model which includes deterministic seasonals and nontime-separable preferences. We show how to compute a perfect foresight seasonal equilibrium path for this economy. An approximation to the stochastic equilibrium is calculated. Using postwar U.S. data, GMM estimates of the structural parameters are employed in the perfect foresight and simulation analyses. As in Constantinides and Ferson [1990], the estimates of consumption preferences exhibit habit-persistence, but a local optimum also exists which exhibits local durability.

The nontime-separable model predicts most of the seasonal patterns found in aggregate quantity time series; notable exceptions are the seasonal patterns in investment and the fourth quarter seasonal in labor hours. An evaluation of the model’s predictions for deseasonalized second moments finds strong support for the parameterization with local durability in consumption. This model broadly displays a seasonal cycle as well as the business cycle phenomenon.

This paper uses micro data to examine differences in the cyclical variability of employment, hours, and wages for skilled and unskilled workers. Contrary to conventional wisdom, we find that, at the aggregate level, skilled and unskilled workers are subject to essentially the same degree of cyclical variation in wages. That is, relative offer wage differentials between skilled and unskilled workers are acyclical. However, we do find important differences in the patterns of employment and hours variation for skilled vs. unskilled workers when a college degree is used as a proxy for skill. Workers with a college degree have little cyclical variation in employment or weekly hours, while uneducated workers have highly procyclical employment and hours. Thus, we find that the quality of labor input per manhour rises in recessions, thereby inducing a countercyclical bias in aggregate wage measures. We find substantial differences across industries in the cyclical variation of employment, hours, and wage differentials. We interpret these results as indicative of important inter-industry differences in labor contracting.

This paper documents several advantages associated with using state level consumption data to examine consumption behavior and especially to estimate the Intertemporal Elasticity of Substitution (IES). In contrast to the results of Hall (1988) and Campbell and Mankiw (1989), we provide substantial evidence indicating that the IES is significantly different from zero and probably close to one. Since the overidentifying restrictions of the standard Euler equation are generally rejected, we use these data to explore the nature of these rejections and evaluate an alternative specification of consumer behavior proposed by Campbell and Mankiw (1987, 1989, 1990). We take special care of examining the robustness of our results with respect to problems caused by the mismeasurement of the interest rate. In particular, we identify a common time component in expected consumption growth across states which, under the specifications of the theory, should reflect real interest rate movements. We find that the common time component closely matches the expected real return on Treasury bills as should be expected if the IES is different from zero and if the T-bill rate is an appropriate measure of interest rates.

This article reexamines the conventional wisdom that commercial banking is in severe decline. A careful reading of the evidence does not support it. True, on-balance sheet assets held by commercial banks have declined as a share of total intermediary assets. But this measure ignores the substantial growth in banks' off-balance sheet activities, in off-shore lending by foreign banks, and in the size of the financial intermediation sector. Adjusted for these considerations, the bank-assets measure shows no clear evidence of secular decline. Neither does an alternative measure, constructed using data from the national income accounts. At most, banking may have suffered a slight loss of market share lately. But this loss is a temporary response to a series of adverse shocks rather than the start of a permanent decline.

In this paper we use the common perspective provided by the neoclassical growth model to evaluate the size of the distortions associated with different monetary and fiscal policies designed to finance a given sequence of government expenditures. We construct an artificial monetary economy incorporating the cash-in-advance framework of Lucas and Stokey (1983), calibrate it to match important features of the U.S. economy, and simulate it to provide a quantitative assessment of the welfare costs associated with government policies involving different combinations of taxes on capital and labor income, consumption, and holdings of money. In particular, we evaluate the welfare gains from tax reforms that are designed to replace taxes on capital or labor income with other forms of taxation. Our results suggest that the welfare costs of financing a given sequence of government expenditures are slightly lower in economies that substitute inflation or consumption taxes for the tax on labor income, but dramatically lower for economies that substitute any of these taxes for the tax on capital income. Replacing the capital tax with a consumption tax, for example, eliminates 81 percent of the welfare cost arising from distorting taxation. In addition, we show that these welfare costs can be reduced further by eliminating the capital tax with a nonstationary policy that involves a transition to a temporary policy followed by a new steady state policy rather than an immediate change to a new steady state policy.

This article investigates the business cycle implications of the planning phase of business investment projects. Time to plan is built into a Kydland-Prescott time-to-build model, which assumes that investment projects take four periods to complete. In the Kydland-Prescott time-to-build model, resources for these projects flow uniformly across the four periods; in the time-to-plan model, few resources are used in the first period. The investigation determines that incorporating time to plan in this way improves the model's ability to account for three key features of U.S. business cycles: their persistence, or the fact that when output growth is above (or below) average, it tends to remain high (or low) for a few quarters; the fact that productivity leads hours worked over the business cycle; and the fact that business investment in structures and business investment in equipment lag output over the cycle.

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.

This essay, written around 1779, challenges the simple quantity theory of money. From the perspective of the paper money issued to pay for America’s Revolutionary War—bills of credit, or continentals—the essay rejects the idea that the value of money is determined by the number of pieces of paper issued. That idea ignores the fact that an individual nation is just a small part of the world economy. More relevant than quantity, the essay argues, are two other features: the date the government promises to exchange the pieces of paper for specie and the credibility of that promise.

This paper empirically investigates the restrictions embodied in a popular dynamic monetary model for the cross relations between consumption, money holdings, inflation and assets’ returns using quarterly data for the high-inflation economy in Israel, 1970–1988. The model considered includes money in agents’ utility function. A set of the estimated parameters is used in the analysis to assess the model’s quantitative implications for seigniorage and for the welfare costs of inflation. The estimates are found to account well for the observed stability over time of seigniorage in Israel and imply sizeable welfare costs of inflation.

We provide a new interpretation of the statistical relation between the trade balance and the terms of trade. This relation includes the J-curve, the tendency for trade balances to be negatively correlated with contemporaneous movements in the terms of trade, positively correlated with lagged movements. We document this property in international data and show that it arises, as well, in a two-country stochastic growth model. In the model trade dynamics result, in large part, from fluctuations in investment. A favorable productivity shock in the domestic economy leads to an increase in domestic output, a decrease in its relative price, and a rise in the terms of trade. The increase in domestic productivity also leads to a temporary investment boom. This boom results in an initial trade deficit, followed by future surpluses, and thus a J-curve. We also use the model to provide a new perspective on earlier theories of trade and price dynamics.

This article describes changes in the number of average weekly hours of market work per person in the United States since World War II. Overall, this number has been roughly constant; for various groups, however, it has shifted dramatically—from males to females, from older people to younger people, and from single- to married-person households. The article provides a unique look at how the lifetime pattern of work hours has changed since 1950 for different demographic groups. The article also documents several factors that may be related to the changes in hours worked: simultaneous changes in Social Security benefits, fertility rates, and family structure. The data presented are based on those collected by the U.S. Bureau of the Census during the 1950–90 decennial censuses.

This article argues that the poor performance of the U.S. banking industry in the 1980s was due mainly to the risk-taking of the largest banks, which was encouraged by the U.S. government's too-big-to-fail policy. The article documents the recent trend toward riskier bank portfolios and the corresponding decline in bank profitability. A breakdown of the data by location and by asset size reveals that bank problems were concentrated in areas with troubled industries (oil, real estate, and agriculture) and among banks with the largest assets. In a statistical study controlling for location, asset size remains a significant factor in bank performance. The article concludes with a rough quantitative estimate of the cost to the industry of the poor performance of large banks.

This article describes the current state of economic theory intended to explain the unequal distribution of wealth among U.S. households. The models reviewed are heterogeneous agent versions of standard neoclassical growth models with uninsurable idiosyncratic shocks to earnings. The models endogenously generate differences in asset holdings as a result of the household's desire to smooth consumption while earnings fluctuate. Both of the dominant types of models—dynastic and life cycle models—reproduce the U.S. wealth distribution poorly. The article describes several features recently proposed as additions to the theory based on changes in earnings, including business ownership, higher rates of return on high asset levels, random capital gains, government programs to guarantee a minimum level of consumption, and changes in health and marital status. None of these features has been fully analyzed yet, but they all seem to have potential to move the models in the right direction.

Most models of aggregate economic activity, like the standard neoclassical growth model, ignore the fact that equipment and structures are maintained and repaired. Once physical capital is purchased in these models, there are typically no more decisions made regarding its use. The theme of this article is that there is evidence to suggest that incorporating expenditures on the maintenance and repair of physical capital into models of aggregate economic activity will change the quantitative answers to some key questions that have been addressed with these models. This evidence is primarily from a little-used economywide survey in Canada. The survey shows that the activity of maintaining and repairing equipment and structures is an activity that is generally both large relative to investment and a substitute for investment to some extent—and to a large extent during some episodes.

This study examines the behavior of money, inflation, and output under fiat and commodity standards to better understand how changes in monetary policy affect economic activity. Using long-term historical data for 15 countries, the study finds that the growth rates of various monetary aggregates are more highly correlated with inflation and with each other under fiat standards than under commodity standards. Money growth, inflation, and output growth are also higher under fiat standards. In contrast, the study does not find that money growth is more highly correlated with output growth under one type of standard than under the other.

Recent monetary history has been characterized by monetary authorities that appear to shift periodically between distinct policy regimes associated with higher or lower average rates of money creation. As policy regimes are not directly observable and as the rate of monetary expansion varies for reasons other than regime changes, the general public must form beliefs over current monetary policy based on historical realizations of money growth rates. Depending on the parameters governing the behaviour of monetary policy, beliefs (and therefore inflation forecasts) may evolve very slowly in the wake of actual regime changes, thereby exacerbating the costs of a disinflation policy. The quantitative importance of slowly adjusting beliefs is evaluated in the context of a computable general equilibrium model.

We provide a simple explanation for the observation that the variance of job destruction is greater than the variance of job creation: job creation is costlier at the margin than job destruction. As Caballero [2] has argued, asymmetric employment adjustment costs at the establishment level need not imply asymmetric volatility of aggregate job flows. We construct an equilibrium model in which (S,s)-type employment policies respond endogenously to aggregate shocks. The microeconomic asymmetries in the model can dampen the response of total job creation to an aggregate shock and cause it to be less volatile than total job destruction. This is so even though aggregate shocks are symmetrically distributed.

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

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

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

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

We analyze a real business cycle model in which the government optimally chooses public investment and nonmilitary current expenditures, to maximize the welfare of the representative private agent. We characterize the optimal response of endogenous spending to shocks to technology and to military expenditures. Comovements between the components of government spending and other macroeconomic aggregates predicted by the model are compared with the corresponding comovements in the U.S. data. The model captures the qualitative features of the relative volatilities of the components of government spending quite well, but predicts too high correlations between the components of government spending and output.

This paper describes and analyzes the 1990–92 economic forecasts of a Bayesian vector autoregression model developed by researchers at the Minneapolis Fed. The model's 1990 forecast was pretty bad—too optimistic about both inflation and economic growth, especially growth in consumption and housing. An analysis of the model's errors, however, turns up no reason to think the model is unsound. Based on data available on November 30, 1990, the model predicts weak economic conditions for the next two years: a likely recession in 1991 and moderate inflation and weak overall growth in 1991–92. The paper includes a technical appendix that describes how to statistically compare the accuracy of two sets of forecasts.

Previous investigations of whether the volatility of the U.S. economy diminished after World War II have been inconclusive because of questionable prewar macroeconomic aggregates. We examine, more broadly, the hypothesis of the stabilization of the postwar economy by focusing on the duration of business cycles, rather than their amplitude; in the process, we avoid the debate about the quality of prewar aggregates. Using distribution-free statistics, we find clear evidence of postwar duration stabilization in terms of a shift toward longer expansions and shorter contractions. Moreover, we find no shift in whole-cycle durations, which suggests a reallocation of the business cycle away from contraction and toward expansion.

Many traditional macroeconomic models do not have determinate predictions for the path of inflation: even for a given specification of money supplies, many paths of inflation are consistent with equilibrium. According to the fiscal theory of the price level, fiscal policy can be used to select which of these many paths actually occur. This article explains the fiscal theory of the price level and discusses its empirical and policy implications. The article argues that the theory is equivalent to giving the government an ability to choose among equilibria.

This paper studies a general equilibrium model with multiple stages of production and asynchronized price setting that provides a new explanation for the observed persistent real effects of monetary shocks. The key feature of the model is a vertical chain-of-production structure. In this model, the effects of monetary shocks on price adjustment are gradually dampened via the interactions of firms through their input-output relations and the timing of their price decisions. The model predicts that prices adjust by a smaller amount and less rapidly at later stages than at earlier stages, which is supported by empirical evidence. More importantly, an increase in the total number of stages in the model leads to not only uniformly larger and longer-lasting real effects but also flatter paths of aggregate output response. With sufficiently many stages, the price level adjustment becomes arbitrarily close to zero and the aggregate output tends to carry the full burden of adjustment. Thus, the chain-of-production mechanism goes a long way in propagating the shocks.

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.

Using a calibrated growth model, the dynamic effects of NAFTA on Mexican development are studied. Two scenarios are analyzed. In the first, NAFTA is assumed to stimulate inflows of physical capital into Mexico. These inflows reduce the interest rate and raise the wage rates for both skilled and unskilled labor. The skilled wage rises more sharply, however, increasing the skill premium and rapidly accelerating the accumulation of human capital. In the second scenario, NAFTA is assumed to have the effect of fully integrating Mexico with the U.S. and Canada. Integration also reduces the interest rate and raises both wage rates in Mexico, but in this case the skill premium falls and human capital accumulation speeds up only a little. The welfare gains are large in both cases.

A traditional explanation for why sovereign countries repay debt is that they want to keep a good reputation so they can easily borrow more. This explanation does not hold if a country has access to an adequate means of savings regardless of the country's past actions. With such access, a country gets only transient benefits from maintaining a good relationship with bankers, and such benefits cannot support borrowing. However, if a country is involved in a myriad of trust relationships, the country's reputation can spill over to a nondebt relationship which has enduring benefits. Such a spillover can allow a country's reputation to support a large amount of borrowing.

In this paper, we describe and analyze the basic structure of the applied general equilibrium (AGE) models used to assess the effects of government trade policies. Once we have constructed the basic model, we extend it to cover features such as increasing returns to scale, imperfect competition, and differentiated products, following the AGE modeling trend of the past 10 years. We then compare a static AGE model's predictions with the actual data on how Spain was affected by entering the European Community and find that, when exogenous effects are included, a static AGE model's predictions are fairly accurate.

We argue that changes in the life insurance industry have created a nontrivial moral hazard. We document the industry's shift from sales of life insurance to sales of mainly rate-of-return oriented investments like single premium deferred annuities (SPDAs) and guaranteed investment contracts (GICs). We describe the system of explicit and implicit guarantees that state governments and the industry provide to SPDA and GIC investors. We argue that these guarantees create moral hazards that have contributed to insurance company failures and misallocation of resources. We summarize reformers' proposals to enhance both the explicit guarantees and the regulation of insurance companies and argue that maintaining the degree of regulatory tightness required for such proposals to succeed will be difficult. We suggest an alternative: eliminate guarantees of SPDAs, GICs, and similar products (and possibly promote full disclosure practices and earmarked investments like variable annuities).

This paper describes an algorithm that takes advantage of parallel computing to solve discrete-time recursive systems that have an endogenous state variable.

During the 1882–1914 period, U.S. national banks could issue circulating notes backed by specified government securities. Earlier attempts to explain yields on those securities by costs of note issue discovered a paradox: yields were too high. We point out two previously ignored sources of costs: idle notes and note redemptions that were highly variable, thereby exacerbating the problem of managing reserves. We present data on idle notes and estimate, from partial data on redemptions, the uncertainty due to redemptions. We also present a semiannual time series of an upper bound on the average additional return on equity a national bank would earn by fully using its note issue privilege. Since the median of this series is 0.5 percent and since this upper bound does not include the average costs stemming from the exacerbated reserve management problem, we conclude that the specified government securities did not have paradoxically high yields.

This paper argues that the reporting of facts in light of theory fosters the development of theory. Dynamic neoclassical macro theory guided the selection of facts to report. The hope is that these facts will foster the further development of this theory. A finding is that the price level is countercyclical in the post-Korean War period. This finding debunks the myths that the price level is procyclical, with the postwar period being no exception.

A version of the permanent income model is developed in which the bliss point of the agent is stochastic. The bliss point depends on realizations of the stochastic process generating labor income and a random shock. The model predicts consumption and labor income share a common trend and that a linear combination of current consumption, current labor income, and once lagged consumption is stationary. Empirically, consumption appears more serially correlated than the model is capable of supporting. Further, the volatility of consumption appears sensitive to time variation in real interest rates.

Financial planners typically advise people to shift investments away from stocks and toward bonds as they age. The planners commonly justify this advice in three ways. They argue that stocks are less risky over a young person’s long investment horizon, that stocks are often necessary for young people to meet large financial obligations (like college tuition for their children), and that younger people have more years of labor income ahead with which to recover from the potential losses associated with stock ownership. This article uses economic reasoning to evaluate these three different justifications. It finds that the first two arguments do not make economic sense. The last argument is valid—but only for people with labor income that is relatively uncorrelated with stock returns. If a person’s labor income is highly correlated with stock returns, then that investor is better off shifting investments toward stocks over time.

Does the magnitude of a trough in employment differ from the magnitude of a peak in employment, and is the time employment spends in rising from a trough to a peak longer than the time spends in falling from a peak to a trough? In this paper we measure the “asymmetry of magnitudes” and the “asymmetry of durations” of seven US postwar employment series. The series are detrended using the Hodrick-Prescott filter prior to the analysis. Appropriate measurements of the two types of asymmetry are the skewness of the detrended series and the skewness of the first differenced detrended series, respectively. Monte Carlo and bootstrapping procedures are used to evaluate the significance levels. Five out of seven series show negative skewnesses in levels as well as in first differences. The skewnesses of “magnitudes” and “durations” of US aggregate employment are significant, and yield –0.50 and –0.60 respectively.

In the second part of the paper a nonlinear AR model is derived from the theory of Hermitian type polynomials that have the potential to realize stochastic asymmetric self-sustained oscillations. In contrast with the standard linear AR model, the nonlinear AR model, fitted to the employment series, accurately generates the two types of asymmetry.

In this paper we use micro panel data to examine the effects of oil price shocks on employment and real wages, at the aggregate and industry levels. We also measure differences in the employment and wage responses for workers differentiated on the basis of skill level. We find that oil price increases result in a substantial decline in real wages for all workers, but raise the relative wage of skilled workers. The use of panel data econometric techniques to control for unobserved heterogeneity is essential to uncover this result, which is completely hidden in OLS estimates. While the short-run effect of oil price increases on aggregate employment is negative, the long-run effect is negligible. We find that oil price shocks induce substantial changes in employment shares and relative wages across industries. However, we find little evidence that oil price shocks cause labor to flow into those sectors with relative wage increases.

Purchasing power parity is one of the most important equilibrium conditions in international macroeconomics. Empirically, it is also one of the most hotly contested. Numerous recent studies, for example, have sought to determine the validity of purchasing power parity using data from the post-Bretton-Woods float and have reached different conclusions. We assert that most such studies are flawed for two reasons. First, the post-1973 data contain, by definition, only a very limited amount of the low-frequency information relevant for examination of long-run parity. Second, the dynamic econometric techniques used to model deviations from parity are typically quite crude with respect to the modeling of low-frequency dynamics. Both deficiencies are rectified in the present paper, with dramatic results. We construct a new dataset of sixteen real exchange rates covering more than a century of the classic gold standard period, and we study deviations from parity using long-memory models that allow for subtle forms of mean reversion. For each real exchange rate, we find that parity holds in the long run.

This paper presents new empirical evidence to support the hypothesis that positive money supply shocks drive short-term interest rates down. We then present a quantitative, general equilibrium model which is consistent with this hypothesis. The two key features of our model are that (i) money shocks have a heterogeneous impact on agents and (ii) ex post inflexibilities in production give rise to a very low short-run interest elasticity of money demand. Together, these imply that, in our model, a positive money supply shock generates a large drop in the interest rate comparable in magnitude to what we find in the data. In sharp contrast to sticky nominal wage models, our model implies that positive money supply shocks lead to increases in the real wage. We report evidence that this is consistent with the U.S. data. Finally, we show that our model can rationalize a version of the Real Bills Doctrine in which the monetary authority accommodates technology shocks, thereby smoothing interest rates.

We describe the postwar U.S. business cycle for the durable and nondurable goods producing sector. The business cycle is characterized by positive comovement of output, employment, and investment across the two sectors. We develop a two sector growth model to explain the observed pattern of comovements, and suggest that intermediate inputs produced by the nondurable goods sector for the durable goods sector play a crucial role.

Two observations have sometimes been viewed as evidence that the equilibrium allocations of intermediated credit markets are inefficient. First, low-income households' marginal propensity to consume is close to unity. Second, even high-income households seem to face nonprice constraints during recessions. This paper presents a model that possesses both of these features. (A recession is modeled as an economy in which the equilibrium level of investment is at its lowest possible level.) However, contrary to the conventional view, the equilibrium of this model is ex ante efficient. The model also sheds light on some historical episodes of credit restraint.

This note shows that basic theorems of dynamic programming hold when the return function is homogeneous of degree theta <= 1.

This paper develops a model of competitive economy which is used to study the effect that distortionary taxes have on the business cycle and on agents’ welfare. In the presence of distortions, the equilibria are not Pareto optimal and standard computational techniques cannot be used. Instead, methods that take into account the presence of distorting taxes are applied. Maximum likelihood estimates of taste, technology and policy parameters from U.S. post-war time series are used to obtain several results. I find that a significant portion of the variance of the aggregate consumption, output, hours worked, capital stock, and investment can be attributed to the factor tax and government spending processes. Also, I compute the deadweight loss due to alternative tax changes and compare these estimates to others in the literature. Specification of taxes as constant versus state-contingent can have a significant effect on the results.

COMPUSTAT data on 12,000 firms for the years 1956–1992 indicate that large firms hold less cash as a percentage of sales than do small ones. Whether comparisons are made within or across industries, the elasticity of cash balances with respect to sales is about 0.75. Firms headquartered in counties with high wages hold more money for a given level of sales, a finding consistent with the idea that time can substitute for money in the provision of transactions services. The estimates are consistent with both scale economies in the holding of money and secular declines in velocity.

The extent to which there are aggregate returns to scale at the level of aggregate production has important implications both for the types of shocks generating business cycles and for optimal policy. However, prior attempts to measure the extent of these returns using instrumental variable techniques have yielded quite imprecise estimates. In this article, we show that the production shocks implied by a range of returns to scale that encompasses both large increasing returns and large decreasing returns are almost identical. This makes clear that there is a fundamental reason for the imprecision of prior estimates and casts doubt on our ability to generate more precise estimates.

We examine nominal and real exchange rates, interest rates, prices, and evolutions of real variables in a two-country, monetary general-equilibrium model that includes a financial sector and shocks to technologies and money growth rates. Qualitative properties of the model are provided and moment predictions from a calibrated version of the model are compared to moments of time series drawn from actual economies. We focus on international monetary shock transmissions, and effects of monetary innovations on nominal and real exchange rates and nominal interest rates.

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 effect on the growth of an economy of alternative financing opportunities in a stochastic growth model with incentive constraints. Efficient accumulation mechanisms are designed and computed for economies that differ in their incentive structure. We show that when borrowing is subject to information constraints, there is a computable efficient transfer mechanism that does not affect capital accumulation and investment patterns, even though consumption patterns and the distribution of wealth are affected. In contrast, enforcement constraints can severely reduce the outside financing opportunities and affect investment patterns and economic growth. We adapt numerical algorithms for obtaining numerical solutions of these models.

In Japan, as in the United States, stocks that are more sensitive to changes in the monthly growth rate of labor income earn a higher return on average. Whereas the stock-index beta can only explain 2 percent of the cross-sectional variation in the average return on stock portfolios, the stock-index beta and the labor-beta together explain 75 percent of the variation. We find that the labor-beta drives out the size effect but not the book-to-market-price effect that is documented in the literature. We explore the extent to which these results are an artifact of seasonal patterns in labor-income growth rates as well as asset returns. In Japan, the book-to-market-price characteristic can be adequately captured by a particular factor-beta, as suggested by Fama and French (1993). This is in contrast to the findings reported by Daniel and Titman (1997) for the United States.

This paper is a case study of the use of vector autoregression (VAR) models to test economic theories. It focuses on the work of Christopher A. Sims, who in 1980 found that relationships in economic data generated by a small VAR model were inconsistent with those implied by a simple form of monetarist theory. The paper describes the work of researchers who criticized Sims' results as not robust and Sims' response to these critics. The paper reexamines all of this work by estimating hundreds of variations of Sims' model. The paper concludes that both Sims and his critics are right: Sims' conclusion about monetarism is robust, but some of his other statistical results are not. In general, the paper concludes that VAR models can be used to test theories, but that any relationships they uncover in the data must be carefully checked for robustness.

We propose and evaluate an explicit test of the null hypothesis of no difference in the accuracy of two competing forecasts. In contrast to previously developed tests, a wide variety of accuracy measures can be used (in particular, the loss function need not be quadratic, and need not even be symmetric), and forecast errors can be non-Gaussian, nonzero mean, serially correlated and contemporaneously correlated.

A real business cycle model with heterogeneous agents is parameterized, calibrated, and simulated to see if it can account for some stylized facts characterizing postwar U.S. business cycle fluctuations, such as the countercyclical movement of labor’s share of income, and the acyclical behavior of real wages. There are two types of agents in the model, workers and entrepreneurs, who participate on an economy-wide market for contingent claims. On this market workers purchase insurance from entrepreneurs, through optimal labor contracts, against losses in income due to business cycle fluctuations. The model is used to study the allocation of risk and the distribution of income over the business cycle.

Why did states agree to a U.S. Constitution that prohibits them from issuing their own money? This article argues that two common answers to this question—a fear of inflation and a desire to control what money qualifies as legal tender—do not fit the facts. The article proposes a better answer: a desire to form a viable monetary union that both eliminates the variability of exchange rates between various forms of money and avoids the seigniorage problem that otherwise occurs in a fixed exchange rate system. Supporting evidence is offered from three periods of U.S. history: the colonial period (1690–1776), the Revolutionary War (1776–83), and the Confederation period (1783–89).

Estimates of interindustry wage differentials are obtained using a fixed-effects estimator on a long panel, the National Longitudinal Survey of Young Men (NLS). After controlling for observable worker characteristics, 84 percent of the residual variance of log wages across industries is explained by individual fixed-effects. Only 16 percent of the residual variance is “explained” by industry dummies. Since no controls for specific job characteristics are used, job characteristics that vary across industries could potentially explain this rather small residual across-industry log wage variance that is not attributable to individual effects. Clearly then, these data do not force us to resort to noncompetitive explanations of interindustry wage differentials, such as efficiency wage theory. Furthermore, efficiency wage theories predict that wages in efficiency wage paying (or primary) industries should be relatively rigid. Therefore, industry wage differentials should widen in recessions. However, no such tendency is found in the data.

This study overturns the conclusion of a 1990 study by David Humphrey and Allen Berger, which found that check float is responsible for the popularity of checks despite their high resource cost compared to electronic payment instruments. The new study examines recent data on the costs of checks and automated clearinghouse (ACH) payments. It finds that the value of check float has decreased significantly since the 1990 study and is no longer large enough to make checks more attractive than ACH payments. The study also questions whether the idea that float could be responsible for the persistent use of checks is reasonable given standard assumptions about the behavior of economic agents. The study ends by speculating on why checks are used more than less-costly alternatives and by encouraging policymakers to wait for researchers to adequately answer that question before intervening in the market for payment instruments.

This paper provides an algorithm for computing Markov Perfect Nash Equilibria (Maskin and Tirole, 1988a and b) for dynamic models that allow for heterogeneity among firms and idiosyncratic (or firm specific) sources of uncertainty. It has two purposes. To illustrate the ability of such models to reproduce important aspects of reality, and to provide a tool which, given appropriate parameter estimates, can be used for both descriptive and policy analysis in a setting which allows firms to differ from one another in ways that are consistent with the information in firm level data sets.

We illustrate by computing the policy functions, and simulating the industry structures, generated by a class of dynamic differentiated product models in which the idiosyncratic uncertainty is due to both the random outcomes of each firm's research process, and to an autonomous aggregate demand process. The illustration focuses on comparing the effect of different regulatory and behavioral assumptions on market structure and on welfare for one particular set of parameter values. The results here are of some independent interest and can be read without delving into the technical detail of the computational algorithm.

The last part of the paper begins with an explicit consideration of the computational burden of the algorithm, and then introduces approximation techniques designed to make computation easier. The purpose of this section is to enable us to compute equilibria for industries in which a large number of firms are typically active. Its major result is analytic. We show that if the value function of a given firm is exchangeable in the state vectors of its competitors, then the number of polynomial coefficients one needs for a given order of a polynomial approximation to that function is both independent of the number of firms active in the market, and a relatively small number. This enables us to use the approximation technique to reduce the computational burden of the algorithm dramatically.

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 recent years, monopolistic competition models have frequently been applied in macroeconomics, international and interregional economics, and economic growth and development. In this paper, I present a highly selective review in this area, with special emphasis on the complementarity and its role of generating multiplier processes, agglomeration, underdevelopment traps, regional disparities, and sustainable growth, or more generally, what Myrdal (1957) called the “principle of circular and cumulative causation.”

Since the primary role of international financial linkages is to facilitate consumption smoothing in the face of country-specific shocks, the degree of international financial integration should play an important role in the international transmission of business cycles. This paper therefore studies the business cycle implications of restricting international trade in financial assets. The key restriction is that domestic residents must hold all risky claims to domestic output, trading only noncontingent bonds on the international asset markets. We find that restricting asset trade may or may not change the business cycle implications of the model relative to complete markets, depending on the parameterization of the stochastic process for productivity. When there are important differences, these stem largely from differential wealth effects. We also find that restricting asset trade can resolve the chief problem inherent in complete markets models, which is their predictions of too-high consumption correlations and too-low output correlations. When technology follows a random walk process, the restricted asset markets model predicts that cross-country output correlations are positive, and cross-country consumption correlations are smaller than the output correlations, as is typically observed in the data.

This article reports the recent progress made by researchers trying to build business cycle models that can reliably reproduce aggregate U.S. time series. The article first describes some features of the U.S. data that the models are meant to reproduce. Then it describes a version of the standard business cycle model, along with the indivisible labor extension of that model, both of which assume that fluctuations in economic activity are caused only by shocks to technology. Finally, it describes a version of recent other extensions which assume that shocks to fiscal variables also contribute to the fluctuations. Adding fiscal shocks to standard business cycle models is shown to significantly improve their ability to mimic some of the data.

This article reviews recent work comparing properties of international business cycles with those of dynamic general equilibrium models. Two discrepancies between theory and data are described. One concerns the correlation across countries of fluctuations in consumption, output, and productivity: in the data, the output correlation is generally the largest; in theoretical economies, however, for a wide range of parameter values, the consumption correlation is the largest. The other discrepancy concerns relative price movements: the standard deviation of the terms of trade is considerably larger in the data than in theoretical economies. Also described here are several changes in theoretical structure that researchers have attempted, without success, to bring the theory and the data closer together.

In a world where time series show clear seasonal fluctuations, rational agents will take account of those fluctuations in planning their own behavior. Using seasonally adjusted data to model behavior of such agents throws away information and introduces possibly severe bias. Nonetheless it may be true fairly often that rational expectations modeling with seasonally adjusted data, treating the adjusted data as if it were actual data, gives approximately correct results; and naive extensions of standard modeling techniques to seasonally unadjusted data may give worse results than naive use of adjusted data. This paper justifies these claims with examples and detailed arguments.

This paper identifies a novel form of dynamic inconsistency of stabilization policy in increasing returns models that generate multiple equilibria. We present a two-period version of the Benhabib-Farmer (1994) externalities model and derive closed-form solutions for all endogenous variables in every perfect foresight equilibrium. We provide conditions under which the stabilization policy that maximizes time zero consumer welfare is not time consistent. Furthermore, we characterize the time consistent stabilization policy. Our results cast doubts on the usefulness of government coordination of economic activity when the government lacks a commitment mechanism. Without commitment, a benevolent government can rule out multiplicity only by ensuring that a pareto dominated equilibrium obtains.

Using U.S. data it is shown that as the stock market goes into a period of high volatility, nondurables consumption is unaffected but durables consumption falls substantially. It is argued that a plausible explanation for this is that consumers face irreversibilities when adjusting their durables stock. They will thus apply Ss-type rules with bandwidths with widths that vary over time as in Hassler (1996). To quantify the aggregate implications of such behavior an aggregated irreversible investment model for consumer durables is estimated on U.S. It is found that a shift to higher risk leads to a simultaneous widening of individual Ss-bands which causes demand to fall substantially. This effect diminishes over time but is substantial also after a year.

We study the existence and robustness of expectationally-driven price volatility in experimental overlapping generation economies. Iin the theoretical model under study there exist “pure sunspot” equilibria which can be “learned” if agents use some adaptive learning rules. Our data show the existence of expectationally-driven cycles, but only after subjects have been exposed to a sequence of real shocks and “learned” a real cycle. In this sense, we show evidence of path-dependent price volatility.

A current U.S. policy is to introduce a new style of currency that is harder to counterfeit, but not immediately to withdraw from circulation all of the old-style currency. This policy is analyzed in a random matching model of money, and its potential to decrease counterfeiting in the long run is shown. For various parameters of the model, three types of equilibria are found to occur. In only one does counterfeiting continue at its initial high level. In the other two, both genuine and counterfeit old-style money go out of circulation—immediately in one and gradually in the other. There are objectives and expectations that can reasonably be imputed to policymakers, under which the policy that they have chosen can make sense.