Research Database

In this appendix, we describe the numerical methods used to compute an equilibrium in the economy with an inelastic labor supply and in the economy with an elastic labor supply (i.e., our benchmark economy). Although the economy with inelastically supplied labor is a special case of the benchmark economy, the equilibrium in the inelastic labor supply case is much easier to compute and is therefore treated separately. In each case, we start with the consumer's problem, assuming the consumer takes prices as given. We then show how the equilibrium prices are determined. To verify that the methods work well with our problem, we apply them to some related test problems that have known solutions.

A random-matching model (of money) is formulated in which there is complete public knowledge of the trading histories of a subset of the population, called banks, and no public knowledge of the trading histories of the complement of that subset, called nonbanks. Each person, whether a banker or a non banker, is assumed to have the technological capability to create indivisible, distinct and durable objects called notes. If outside money is indivisible and sufficiently scarce, then an optimal mechanism is shown to have note issue and destruction (redemption) by banks.

We study a dynamic version of Meltzer and Richard’s median-voter analysis of the size of government. Taxes are proportional to total income, and they are used for government consumption, which is exogenous, and for lump-sum transfers, whose size is chosen by electoral vote. Votes take place sequentially over time, and each agent votes for the policy that maximizes his equilibrium utility. We calibrate the model and its income and wealth distribution to match postwar U.S. data. This allows a quantitative assessment of the equilibrium costs of redistribution, which involves distortions to the labor-leisure and consumption-savings choices, and of its benefits for the decisive voter. We find that the total size of transfers predicted by our political-economy model is quite close to the size of transfers in the data.

Our thesis is that poor countries are poor because they employ arrangements for which the equilibrium outcomes are characterized by inferior technologies being used, and being used inefficiently. In this paper, we analyze the consequences of one such arrangement. In each industry, the arrangement enables a coalition of factor suppliers to be the monopoly seller of its input services to all firms using a particular production process. We find that the inefficiencies associated with this monopoly arrangement can be large. Whereas other studies have found that inefficiencies induced by monopoly are at most a few percent of output, we find that eliminating this monopoly arrangement could well increase output by roughly a factor of 3 without any increase in inputs.

Between the sixties and the late eighties the percentages of low-saving single-parent households and people living alone have grown dramatically at the expense of high-saving married households, while the household saving rate has declined equally dramatically. A preliminary analysis of population composition and savings by household type seems to indicate that about half of the decline in savings is due to demographic change. We construct a model with agents changing marital status, but where the saving behavior of the households can adjust to the properties of the demographic process. We find that the demographic changes that reduce the number of married households (mainly higher divorce and higher illegitimacy) induce all household types to save more and that the effect on the aggregate saving rate is minuscule. We conclude that the drop in savings since the sixties is not due to changes in household composition.

This paper generalizes the normal probit model of dichotomous choice by introducing mixtures of normals distributions for the disturbance term. By mixing on both the mean and variance parameters and by increasing the number of distributions in the mixture these models effectively remove the normality assumption and are much closer to semiparametric models. When a Bayesian approach is taken, there is an exact finite-sample distribution theory for the choice probability conditional on the covariates. The paper uses artificial data to show how posterior odds ratios can discriminate between normal and nonnormal distributions in probit models. The method is also applied to female labor force participation decisions in a sample with 1,555 observations from the PSID. In this application, Bayes factors strongly favor mixture of normals probit models over the conventional probit model, and the most favored models have mixtures of four normal distributions for the disturbance term.

This paper evaluates the argument that differences in physical and intangible capital can account for the large international income differences that characterize the world economy today. The finding is that they cannot. Savings rate differences are of minor importance. What is all-important is total factor productivity. In addition, the paper presents industry evidence that total factor productivities differ across countries and time for reasons other than differences in the publicly available stock of technical knowledge. These findings lead me to conclude a theory of TFP is needed. This theory must account for differences in TFP that arise for reasons other than growth in the stock of technical knowledge.

We develop a model of commodity money and use it to analyze the following two questions motivated by issues in monetary history: What are the conditions under which Gresham’s Law holds? And, what are the mechanics of a debasement (lowering the metallic content of coins)? The model contains light and heavy coins, imperfect information, and prices determined via bilateral bargaining. There are equilibria with neither, both, or only one type of coin in circulation. When both circulate, coins may trade by weight or by tale. We discuss the extent to which Gresham’s Law holds in the various cases. Following a debasement, the quantity of reminting depends on the incentives offered by the sovereign. Equilibria exist with positive seigniorage and a mixture of old and new coins in circulation.

We find that the welfare gains to being at the optimum quantity of debt rather than the current U.S. level are small, and, therefore, concerns regarding the high level of debt in the U.S. economy may be misplaced. This finding is based on a model of a large number of infinitely-lived households whose saving behavior is influenced by precautionary saving motives and borrowing constraints. This model incorporates a different role for government debt than is found in standard models, and it captures different cost-benefit trade-offs. On the benefit side, government debt enhances the liquidity of households by providing an additional means of smoothing consumption and by effectively loosening borrowing constraints. On the cost side, the implied taxes have adverse wealth distribution and incentive effects. In addition, government debt crowds out capital via higher interest rates and lowers per capita consumption.

In this paper, I estimate the impact on aggregate labor productivity of having government, rather than private industry, produce investment goods. This policy was pursued to varying degrees by Egypt, India, Turkey, among others. The policy has a large impact because there is both a direct effect (on the production function in the investment sector) and a secondary effect (on the economywide capital stock per worker). I estimate that this policy alone accounted for about one-third of Egypt's aggregate labor productivity gap with the United States during the 1960s.

Energy use is inelastic in time-series data, but elastic in international cross-section data. Two models of energy use reproduce these elasticities: a putty-putty model with adjustment costs developed by Pindyck and Rotemberg (1983) and a putty-clay model. In the Pindyck-Rotemberg model, capital and energy are highly complementary in both the short run and the long run. In the putty-clay model, capital and energy are complementary in the short run, but substitutable in the long run. We highlight the differences in the cross-section implications of the models by considering the effect of an energy tax on output in both models. In the putty-putty model, an energy tax that doubles the price of energy leads to a fall in output in the long run of 33%. In contrast, the same tax in the putty-clay model leads to a fall in output of only 5.3%.

The notion of skilled-biased technological change is often held responsible for the recent behavior of the U.S. skill premium, or the ratio between the wages of skilled and unskilled labor. This paper develops a framework for understanding this notion in terms of observable variables and uses the framework to evaluate the fraction of the skill premium's variation that is caused by changes in observables. A version of the neoclassical growth model is used in which the key feature of aggregate technology is capital-skill complementarity: the elasticity of substitution is higher between capital equipment and unskilled labor than between capital equipment and skilled labor. With this feature, changes in observables can account for nearly all the variation in the skill premium over the last 30 years. This finding suggests that increased wage inequality results from economic growth driven by new, efficient technologies embodied in capital equipment.

It is well documented that on average, stock prices drop by less than the value of the dividend on ex-dividend days. This has commonly been attributed to the effect of tax clienteles. We use data from the Hong Kong stock market where neither dividends nor capital gains are taxed. As in the U.S.A. the average stock price drop is less than the value of the dividend; specifically, in Hong Kong the average dividend was HK $0.12 and the average price drop was HK $0.06. We are able to account for this both theoretically and empirically through market microstructure based arguments.

This paper essentially puts together procedures that are used in the computation of equilibria in models with a very large number of heterogeneous agents. It is not a complete description of all procedures used in the literature. It describes procedures that deal with infinitely lived agent versions of the growth model with and without aggregate uncertainty, overlapping generations models, and dynamic political economy models.

We ask what fraction of the variation in incomes across countries can be accounted for by investment distortions. In our neoclassical growth model the relative price of investment to consumption is a good measure of the distortions. Using data on relative prices we estimate a stochastic process for distortions and compare the resulting variance of incomes in the model to that in the data. We find that the variation of incomes in the model is roughly 4/5 of the variability of incomes in the data. Our model does well in accounting for 6 key regularities on income and investment in the data.

The paper itself is followed by three appendices: Appendix 1 describing the log-likelihood function, Appendix 2 describing the construction of labor share of income associated with the production of consumption and investment goods, and the Data Appendix.

This study uses data from the Panel Survey of Income Dynamics (PSID) to address a number of questions about life cycle earnings mobility. It develops a dynamic reduced form model of earnings and marital status that is nonstationary over the life cycle. The study reaches several firm conclusions about life cycle earnings mobility. Incorporating non-Gaussian shocks makes it possible to account for transitions between low and higher earnings states, a heretofore unresolved problem. The non-Gaussian distribution substantially increases the lifetime return to post-secondary education, and substantially reduces differences in lifetime wages attributable to race. In a given year, the majority of variance in earnings not accounted for by race, education and age is due to transitory shocks, but over a lifetime the majority is due to unobserved individual heterogeneity. Consequently, low earnings at early ages are strong predictors of low earnings later in life, even conditioning on observed individual characteristics.

This paper analyzes the U.S. congressional proposal to instruct the Federal Reserve to, in the next five years, lower inflation to zero from its current rate of around 5 percent. The paper concludes that, when other policy options are considered, the zero inflation policy is not advisable. Its benefits would be very small—possibly negative—while its costs would probably be significant. Other, more direct policy options could produce most of the same benefits with fewer costs. Among these alternative policies are deregulating interest rates on demand deposits, paying interest on financial institution reserves, lowering the federal tax rate on capital income, and indexing the federal tax code to inflation.

We study a random-matching, absence-of-double-coincidence environment in which people cannot precommit and in which there are two imperfect ways of keeping track of what other people have done in the past: money and a public record of all past actions that is updated with an average lag. We study how the magnitude of that lag affects the allocations that are optimal from among allocations that are stationary and feasible and that satisfy incentive constraints which arise from the absence of commitment and the imperfect ways of keeping track of what others have done in the past.

We consider a simple environment in which individuals receive income shocks that are unobservable to others and can privately store resources. We show that this ability to privately store can undercut the ability to shift resources across individuals to the extent that the efficient allocation only involves consumption smoothing over time, as opposed to insurance (consumption smoothing over states) if the rate of return on savings is not too far below the rate of time preference, or, alternatively, if the worst possible outcome is sufficiently dire. We also show that unlike environments without unobservable storage, the symmetric efficient allocation is decentralizable through a competitive asset market in which individuals trade risk-free bonds among themselves.

This study establishes several facts about medieval monetary debasements: they were followed by unusually large minting volumes and by increased seigniorage; old and new coins circulated concurrently; and, at least some of the time, coins were valued by weight. These facts constitute a puzzle because debasements provide no additional inducements to bring coins to the mint. On theoretical and empirical grounds, the authors reject explanations based on by-tale circulation, nominal contracts, and sluggish price adjustment. They conclude that debasements pose a challenge to monetary economics.

In the postwar period velocity has risen so sharply in the U.S. that the ratio of money to nominal output has fallen by a factor of three. We analyze the implications of shrinking money for the real effects of a monetary shock in two classes of equilibrium monetary business cycle models: limited participation (liquidity) models and predetermined (sticky) price models. We show that the liquidity model predicts that a rise in velocity leads to a substantial reduction in the real effects of a monetary shock. In sharp contrast, we show that the real effects of a monetary shock in the sticky price model are largely invariant to changes in velocity. We provide evidence that suggests that the real effects of monetary shocks have fallen over the postwar period.

We consider the problem of an insurer who enters into a repeated relationship with a set of risk averse agents in the presence of ex post verification costs. The insurer wishes to minimize the expected cost of providing these agents a certain expected utility level. We characterize the optimal contract between the insurer and the insured agents. We then apply the analysis to the provision of deposit insurance. Our results suggest—in a deposit insurance context—that it may be optimal to utilize the discount window early on, and to make deposit insurance payments only later, or not at all.

In U.S. elections, voters often vote for candidates from different parties for president and Congress. Voters also express dissatisfaction with the performance of Congress as a whole and satisfaction with their own representative. We develop a model of split-ticket voting in which government spending is financed by uniform taxes but the benefits from this spending are concentrated. While the model generates split-ticket voting, overall spending is too high only if the president’s powers are limited. Overall spending is too high in a parliamentary system, and our model can be used as the basis of an argument for term limits.

The classic example of a privately created and well-functioning interbank payments system is the Suffolk Banking System that existed in New England between 1825 and 1858. This System, operated by the Suffolk Bank, was the first regionwide net-clearing system for bank notes in the United States. While it operated, notes of all New England banks circulated at par throughout the region. The achievements of the System have led some to conclude that unfettered competition in the provision of payments services can produce an efficient payments system. In this paper, we reexamine the history of the Suffolk Banking System and present some facts that call this conclusion into question. We find that the Suffolk Bank earned extraordinary profits and that note clearing may have been a natural monopoly. There is no consensus in the literature about whether unfettered operation of markets in the presence of natural monopolies produces an efficient allocation.

Some economists argue that as long as governments can earn the market rate of return by saving abroad, standard reputation models cannot support debt. We argue that these standard reputation models are partial in the sense that actions of agents in one arena affect reputation in that arena only. We develop a general model of reputation in which if a government is viewed as untrustworthy in one relationship, this government will be viewed as untrustworthy in other relationships. We show that our general model of reputation can support large amounts of debt.

We consider the large class of dynamic games in which each player's actions are unobservable to the other players, and each player's actions can influence a state variable that is unobservable to the other players. We develop an algorithm that solves for the subset of sequential equilibria in which equilibrium strategies are Markov in the privately observed state.

This paper shows that some key stylized facts of exchange-rate-based stabilization plans can be explained by the uncertain duration of the plans themselves. Uncertain duration is modeled to reflect evidence showing that devaluation probabilities are higher when the plans are introduced and abandoned than in the period in between. If contingent-claims markets are incomplete, this uncertain duration distortion introduces temporary fiscal cuts with large wealth effects. Investment and employment are also distorted, and the resulting supply-side effects play a critical role. Stabilizations of uncertain duration entail large welfare costs, but they are preferred to persistent high inflation. México’s experience is examined in the light of these predictions.

We determine the second best rule for the inflation tax in monetary general equilibrium models where money is dominated in rate of return. The results in the literature are ambiguous and inconsistent across different monetary environments. We compare the derived optimal inflation tax solutions across the different environments and find that Friedman’s policy recommendation of a zero nominal interest rate is the right one.

This study describes a model built on the long-held view that the use of money as a medium of exchange is the result of an absence of double coincidence of wants. The model can account for two of the most challenging observations facing monetary theory: The disparate short-run and long-run effects of changes in the quantity of money and the coexistence of money and assets with higher rates of return. For both observations, the model's ability to provide a rich analysis depends on little more than the ingredients implicit in the absence-of-double-coincidence view.

This article is a progress report on research that attempts to include one type of market incompleteness and frictions in macroeconomic models. The focus of the research is the absence of insurance markets in which individual-specific risks may be insured against. The article describes some areas where this type of research has been and promises to be particularly useful, including consumption and saving, wealth distribution, asset markets, business cycles, and fiscal policies. The article also describes work in each of these areas that was presented at a conference sponsored by the Federal Reserve Bank of Minneapolis in the fall of 1993.

This paper examines entrepreneurship in order to analyze, first, the degree to which the opportunity to start or own a business affects the household's saving behavior and the implication of this behavior for the distribution of wealth and, second, the relationship between the extent of entrepreneurship in the economy and socioeconomic mobility, that is, the movement of families across wealth classes over time. First, a number of stylized facts based on data from the Panel Study of Income Dynamics (PSID) and the Survey of Consumer Finances (SCF) are outlined. They show relevant differences in asset holdings and wealth mobility between entrepreneurs—economic agents that own a business—and workers. Second, a dynamic general equilibrium model of income and wealth distribution with an explicit entrepreneurial choice is developed. The model is calibrated to match the key features of the data, and it is then used to obtain an estimate of the quantitative importance for capital accumulation and wealth concentration of households that undertake entrepreneurial activities, via their different microeconomic behavior. Through the modeling of the entrepreneurial activities, the model economy developed in this study generates a stationary distribution of wealth with a degree of concentration that accounts for the inequality observed in the U.S. economy. The model also successfully replicates the main patterns of socioeconomic mobility in which entrepreneurs experience higher upward mobility than workers.

This article contends that the various measures of the contribution of technology shocks to business cycles calculated using the real business cycle modeling method are not corroborated. The article focuses on a different and much simpler method for calculating the contribution of technology shocks, which takes account of facts concerning the productivity/labor input correlation and the variability of labor input relative to output. Under several standard assumptions, the method predicts that the contribution of technology shocks must be large (at least 78 percent), that the labor supply elasticity need not be large to explain the observed fluctuation in labor input, and that the contribution of technology shocks can be estimated fairly precisely. The method also estimates that the contribution of technology shocks could be lower than 78 percent under alternative assumptions.

This paper shows that globalization of securities markets exacerbates the volatility of capital flows by strengthening incentives for herding behavior. This is a prediction of a mean-variance portfolio optimization model with imperfect information, in which investors acquire country-specific expertise at a fixed cost and incur variable reputational costs. The model produces equilibria in which incentives to confirm rumors decrease with globalization. Simulations based on equity markets data and country credit ratings suggest that herd behavior can induce large capital outflows from emerging markets.

This article describes some facts about financial inequality in the United States that a good theory of inequality must be able to explain. These include the facts that labor earnings, income, and wealth are all unequally distributed among U.S. households, but the distributions are significantly different. Wealth is much more concentrated than the other two. Wealth is positively correlated with earnings and income, but not strongly. The movement of households up and down the economic scale is greater when measured by income than by earnings or wealth. Differences across the three variables remain when the data are disaggregated by age, employment status, educational level, and marital status of the heads of U.S. households. Each of these classifications also has significant differences across households. All the facts are based on data taken from the 1992 Survey of Consumer Finances and the 1984–85 and 1989–90 Panel Study of Income Dynamics.

This paper studies a version of the neoclassical growth model where heterogenous establishments are subject to partial irreversibilities in investment. Under such investment technology, the optimal decision rules of establishments are of the (S,s) variety. A novel contribution of the paper is the analysis of the general equilibrium dynamics arising from aggregate productivity shocks. This is a difficult task given the high dimensionality of the state vector, which includes the distribution of establishments across capital levels and idiosyncratic shocks. The paper overcomes this difficulty by developing a suitable computational approach. The model is used to study the importance of investment irreversibilities for macroeconomic dynamics. It is found that investment irreversibilities have no major implications for aggregate fluctuations, even though they are crucial for establishment level dynamics. This result contradicts previous conclusions in the literature which rely on partial equilibrium analysis.

We study economies where government currency and electronic money, drawn from interest bearing deposits in private financial intermediary institutions, are full substitutes. We analyze the impact of competition on policy outcomes under different assumptions regarding: the objectives of the central bank, the ability of the monetary authorities to commit to future policies, and the legal restrictions—in the form of reserve requirements—on financial intermediaries. Electronic money competition can discipline a revenue maximizing government and result in lower equilibrium inflation rates, even when there is imperfect commitment. The efficient Friedman rule policy, of zero nominal interest rates, is only implemented if the government maximizes households preferences, in which case, electronic money competition may either have no role, or weaken the incentive effects of the “reputational mechanism.” We also show how an independent choice of the reserve requirements can be an effective policy rule to enhance the disciplinary role of electronic money competition.

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).

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.

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 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.

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.

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.

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.

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.

When marginal utility of consumption depends on leisure, investors will take this into account when allocating their wealth among different assets. This paper presents a multi-country general equilibrium model driven by productivity shocks, where labor-leisure and consumption are chosen endogenously. We use this framework to study the effect of leisure for optimal international diversification. We find that in the symmetric case the model’s ability to help explain home-bias depends crucially on the level of substitutability between consumption and leisure.