Tim Kehoe has been an advisor at the Federal Reserve Bank of Minneapolis since 2000. A native of Newport, Rhode Island, he received his B.A. in economics and mathematics from Providence College in 1975, and his Ph.D. in economics from Yale University in 1979.
A professor at the University of Minnesota since 1987, Tim is currently the Distinguished McKnight University Professor in the Department of Economics and a research associate at the National Bureau of Economic Research. His research and teaching center on the theory and application of general equilibrium models. He has advised several foreign governments, including Spain on the impact of joining the European Community in 1986, Mexico on the impact of joining the North America Free Trade Agreement in 1994, and Panama regarding foreign trade and investment reform in 1997–98.
Tim’s distinguished career has included numerous visiting professorships at universities across the globe, authoring more than 100 books and academic articles, and supervising 68 Ph.D. theses in economics. He has received numerous research grants and awards, including nine grants from the National Science Foundation. He has been a Fellow of the Econometric Society since 1991. In 2008 he was made Doctor Honoris Causa by the Universidade de Vigo in Spain.
This paper develops an overlapping generations model to study the macroeconomic effects of an unexpected elimination of Medicare. We ﬁnd that a large share of the elderly respond by substituting Medicaid for Medicare. Consequently, the government saves only 46 cents for every dollar cut in Medicare spending. We argue that a comparison of steady states is insufficient to evaluate the welfare effects of the reform. In particular, we ﬁnd lower ex-ante welfare gains from eliminating Medicare when we account for the costs of transition. Lastly, we ﬁnd that a majority of the current population benefits from the reform but that aggregate welfare, measured as the dollar value of the sum of wealth equivalent variations, is higher with Medicare.
Using data from Chile and Korea, we find that a larger fraction of aggregate productivity growth is due to firm entry and exit during fast-growth episodes compared to slow-growth episodes. Studies of other countries confirm this empirical relationship. We develop a model of endogenous firm entry and exit based on Hopenhayn (1992). Firms enter with efficiencies drawn from a distribution whose mean grows over time. After entering, a firm’s efficiency grows with age. In the calibrated model, reducing entry costs or barriers to technology adoption generates the pattern we document in the data. Firm turnover is crucial for rapid productivity growth.
Applied general equilibrium (AGE) models, which feature multiple countries or regions, multiple sectors, and input-output linkages across sectors in a Walrasian general equilibrium framework, have been the dominant tool for evaluating the impact of trade liberalization since the 1980s. We provide an overview of the historical development of AGE models and a guide as to how they are used to perform policy analysis. We then review and document shortcomings in the performance of AGE models in predicting the sectoral effects of past trade reforms, that is, we show that AGE models often perform poorly. We provide suggestive evidence that incorporating some of the recent advances in quantitative trade theory in AGE models can improve their predictive ability.
We show that a trade model with an exogenous set of heterogeneous firms with fixed operating costs has the same aggregate outcomes as a span-of-control model. Fixed costs in the heterogeneous-firm model are entrepreneurs’ forgone wage in the span-of-control model.
Rostow (1960) hypothesized that taking off into economic growth was a difficult task for countries in the 19th century, requiring major changes in institutions. In the 20th century, however, as the United States and other advanced countries became richer because of improvements in technologies and managerial practices, it became easier for poor countries to take off into rapid growth by adopting some of these improvements.
We hypothesize that, while taking off is now easier, the difficult transition is now from take-off to catch-up, where nations grow closer to the economic leader (now the United States). Doing so often requires major reforms in policies and institutions. Data suggest that when countries reach the limits imposed by their policies and institutions, their growth slows sharply. Even countries like Japan that have joined the United States in economic leadership in defining best practice in some sectors lag behind in other sectors. Our theory suggests that China is currently reaching its limits to rapid growth.
We propose a theory for classifying countries according to their stages of growth and for analyzing the determinants of growth in and between the different stages.
We conclude that, even if they have inefficient institutions and policies, poorer countries can achieve rapid growth by adopting the technologies and managerial practices of countries like the United States. As they become richer, however, their growth rates will decline unless these countries have efficient institutions and policies. For many countries, this requires that they undertake serious institutional and policy reforms.
Our analysis further suggests that world economic leadership is unlikely to be provided by less-developed countries like China.
In what order should a developing country adopt policy reforms? Do some policies complement each other? Do others substitute for each other? To address these questions, we develop a two-country dynamic general equilibrium model with entry and exit of firms that are monopolistic competitors. Distortions in the model include barriers to entry of firms, barriers to international trade, and barriers to contract enforcement. We find that a reform that reduces one of these distortions has different effects depending on the other distortions present. In particular, reforms to trade barriers and barriers to the entry of new firms are substitutable, as are reforms to contract enforcement and trade barriers. In contrast, reforms to contract enforcement and the barriers to entry are complementary. Finally, the optimal sequencing of reforms requires reforming trade barriers before contract enforcement.
We develop a model for analyzing the sovereign debt crises of 2010–2012 in the Eurozone. The government sets its expenditure-debt policy optimally. The need to sell large quantities of bonds every period leaves the government vulnerable to self-fulfilling crises in which investors, anticipating a crisis, are unwilling to buy the bonds, thereby provoking the crisis. In this situation, the optimal policy of the government is to reduce its debt to a level where crises are not possible. If, however, the economy is in a recession where there is a positive probability of recovery in fiscal revenues, the government may optimally choose to “gamble for redemption,” running deficits and increasing its debt, thereby increasing its vulnerability to crises.
We contrast the properties of dynamic Heckscher-Ohlin models with overlapping generations with those of models with infinitely lived consumers under both closed and open international capital markets. In both environments, if capital is mobile, factor price equalization occurs after the initial period. If capital is not mobile, the properties of equilibria differ drastically across environments: With infinitely lived consumers, factor prices equalize in any steady state or cycle and, in general, there is positive trade in any steady state or cycle. With overlapping generations, we construct examples with steady states and cycles in which factor prices are not equalized, and any equilibrium that converges to a steady state or a cycle with factor price equalization has no trade after a finite number of periods.
In January 1995, U.S. President Bill Clinton organized a bailout for Mexico that imposed penalty interest rates and induced the Mexican government to reduce its debt, ending the debt crisis. Can the Troika (European Commission, European Central Bank, and International Monetary Fund) organize similar bailouts for the troubled countries in the Eurozone? Our analysis suggests that debt levels are so high that bailouts with penalty interest rates could induce the Eurozone governments to default rather than reduce their debt. A resumption of economic growth is one of the few ways that the Eurozone crises can end.
This paper develops a methodology for predicting the impact of trade liberalization on exports by industry (3-digit ISIC) based on the pre-liberalization distribution of exports by product (5-digit SITC). Using the results of Kehoe and Ruhl (2013) that much of the growth in trade after trade liberalization is in products that are traded very little or not at all, we predict that industries with a higher share of exports generated by least traded products will experience more growth. Using our methodology, we develop predictions for industry-level changes in trade for the United States and Korea following the U.S.-Korea Free Trade Agreement (KORUS). As a test for our methodology, we show that it performs significantly better than the applied general equilibrium models originally used for the policy evaluation of the North American Free Trade Agreement (NAFTA).
Since the early 1990s, the United States has borrowed heavily from its trading partners. This paper presents an analysis of the impact of an end to this borrowing, an end that could occur suddenly or gradually.
Modeling U.S. borrowing as the result of what Bernanke (2005) calls a global saving glut—where foreigners sell goods and services to the United States but prefer purchasing U.S. assets to purchasing U.S. goods and services—we capture four key features of the United States and its position in the world economy over 1992–2012. In the model, as in the data: (1) the U.S. trade deficit first increases, then decreases; (2) the U.S. real exchange rate first appreciates, then depreciates; (3) the U.S. trade deficit is driven by a deficit in goods trade, with a steady U.S. surplus in service trade; and (4) the fraction of U.S labor dedicated to producing goods—agriculture, mining and manufacturing—falls throughout the period.
Using this model, we analyze two possible ends to the saving glut: an orderly, gradual rebalancing and a disorderly, sudden stop in foreign lending as occurred in Mexico in 1995–96. We find that a sudden stop would be very disruptive for the U.S. economy in the short term, particularly for the construction industry.
Since the early 1990s, as the United States has borrowed from the rest of the world, employment in U.S. goods-producing sectors has fallen. Using a dynamic general equilibrium model, we find that rapid productivity growth in goods production, not U.S. borrowing, has been the most important driver of the decline in goods-sector employment. As the United States repays its debt, its trade balance will reverse, but goods-sector employment will continue to fall. A sudden stop in foreign lending in 2015–2016 would cause a sharp trade balance reversal and painful reallocation across sectors, but would not affect long-term structural change.
We propose a methodology for studying changes in bilateral commodity trade due to goods not exported previously or exported only in small quantities. Using a panel of 1,900 country pairs, we find that increased trade of these “least-traded goods” is an important factor in trade growth. This extensive margin accounts for 10 percent of the growth in trade for NAFTA country pairs, for example, and 26 percent in trade between the United States and Chile, China, and Korea. Looking at country pairs with no major trade policy change or structural change, however, we find little change in the extensive margin.
In 1950 Mexico entered an economic takeoff and grew rapidly for more than 30 years. Growth stopped during the crises of 1982–1995, despite major reforms, including liberalization of foreign trade and investment. Since then growth has been modest. We analyze the economic history of Mexico 1877–2010. We conclude that the growth 1950–1981 was driven by urbanization, industrialization, and education and that Mexico would have grown even more rapidly if trade and investment had been liberalized sooner. If Mexico is to resume rapid growth — so that it can approach U.S. levels of income — it needs further reforms.
Two years after the rescue package for Greece provided by the European Union and the International Monetary Fund in May 2010, sovereign debt crises continue to threaten a growing number of countries in the eurozone. We develop a theory for analyzing these crises based on the research of Cole and Kehoe (1996, 2000) and Conesa and Kehoe (2012). In this theory, the need to frequently sell large quantities of bonds leaves a country vulnerable to sovereign debt crisis. This vulnerability provides a strong incentive to the country’s government to run surpluses to pay down its debt to a level where a crisis is not possible.
A deep and prolonged recession, like those currently afflicting many eurozone countries, creates a conflicting incentive, however, to “gamble for redemption”—to bet that the recession will soon end, to sell more bonds in order to smooth government spending, and, if indeed the economy recovers, to reduce debt. Under some circumstances, this policy is the best that a government can do for the citizens of its country, but it carries a risk: If the recession continues too long, the government either will have to stop increasing its debt or will have to default on its bonds.
The theory suggests that policies that result in high interest rates on government bonds and high costs of default provide incentives for a government to reduce its debt and avoid sovereign default. On the other hand, policies that result in low interest rates and low costs of default provide incentives for a government to gamble for redemption. We conclude that policy interventions taken to date by the EU and the IMF—by lowering the cost of borrowing and reducing default penalties—have encouraged eurozone governments to gamble for redemption.
Following its opening to trade and foreign investment in the mid-1980s, Mexico’s economic growth has been modest at best, particularly in comparison with that of China. Comparing these countries and reviewing the literature, we conclude that the relation between openness and growth is not a simple one. Using standard trade theory, we find that Mexico has gained from trade, and by some measures, more so than China. We sketch out a theory in which developing countries can grow faster than the United States by reforming. As a country becomes richer, this sort of catch-up becomes more difficult. Absent continuing reforms, Chinese growth is likely to slow down sharply, perhaps leaving China at a level less than Mexico’s real GDP per working-age person.
Studying the experience of countries that have experienced great depressions during the twentieth century teaches us that massive public interventions in the economy to maintain employment and investment during a financial crisis can, if they distort incentives enough, lead to a great depression.
Three of the arguments made by Temin (2008) in his review of Great Depressions of the Twentieth Century are demonstrably wrong: that the treatment of the data in the volume is cursory; that the definition of great depressions is too general and, in particular, groups slow growth experiences in Latin America in the 1980s with far more severe great depressions in Europe in the 1930s; and that the book is an advertisement for the real business cycle methodology. Without these three arguments — which are the results of obvious conceptual and arithmetical errors, including copying the wrong column of data from a source — his review says little more than that he does not think it appropriate to apply our dynamic general equilibrium methodology to the study of great depressions, and he does not like the conclusion that we draw: that a successful model of a great depression needs to be able to account for the effects of government policy on productivity.
We study the quarterly bilateral real exchange rate and the relative price of non-traded to traded goods for 1225 country pairs over 1980–2005. We show that the two variables are positively correlated, but that movements in the relative price measure are smaller than those in the real exchange rate. The relation between the two variables is stronger when there is an intense trade relationship between two countries and when the variance of the real exchange rate between them is small. The relation does not change for rich/poor country bilateral pairs or for high inflation/low inflation country pairs. We identify an anomaly: The relation between the real exchange rate and relative price of non-traded goods for US/EU bilateral trade partners is unusually weak.
In models in which convergence in income levels across closed countries is driven by faster accumulation of a productive factor in the poorer countries, opening these countries to trade can stop convergence and even cause divergence. We make this point using a dynamic Heckscher-Ohlin model — a combination of a static two-good, two-factor Heckscher-Ohlin trade model and a two-sector growth model — with infinitely lived consumers where international borrowing and lending are not permitted. We obtain two main results: First, countries that differ only in their initial endowments of capital per worker may converge or diverge in income levels over time, depending on the elasticity of substitution between traded goods. Divergence can occur for parameter values that would imply convergence in a world of closed economies and vice versa. Second, factor price equalization in a given period does not imply factor price equalization in future periods.
A sudden stop of capital flows into a developing country tends to be followed by a rapid switch from trade deficits to surpluses, a depreciation of the real exchange rate, and decreases in output and total factor productivity. Substantial reallocation takes place from the nontraded sector to the traded sector. We construct a multisector growth model, calibrate it to the Mexican economy, and use it to analyze Mexico’s 1994–95 crisis. When subjected to a sudden stop, the model accounts for the trade balance reversal and the real exchange rate depreciation, but it cannot account for the decreases in GDP and TFP. Extending the model to include labor frictions and variable capital utilization, we still find that it cannot quantitatively account for the dynamics of output and productivity without losing the ability to account for the movements of other variables.
International trade is frequently thought of as a production technology in which the inputs are exports and the outputs are imports. Exports are transformed into imports at the rate of the price of exports relative to the price of imports: the reciprocal of the terms of trade. Cast this way, a change in the terms of trade acts as a productivity shock. Or does it? In this paper, we show that this line of reasoning cannot work in standard models. Starting with a simple model and then generalizing, we show that changes in the terms of trade have no first-order effect on productivity when output is measured as chain-weighted real GDP. The terms of trade do affect real income and consumption in a country, and we show how measures of real income change with the terms of trade at business cycle frequencies and during financial crises.
This article is a primer on the great depressions methodology developed by Cole and Ohanian (1999, 2007) and Kehoe and Prescott (2002, 2007). We use growth accounting and simple dynamic general equilibrium models to study the depression that occurred in Finland in the early 1990s. We find that the sharp drop in real GDP over the period 1990–93 was driven by a combination of a drop in total factor productivity (TFP) during 1990–92 and of increases in taxes on labor and consumption and increases in government consumption during 1989–94, which drove down hours worked in Finland. We attempt to endogenize the drop in TFP in variants of the model with an investment sector and with terms-of-trade shocks but are unsuccessful.
Typical models of bankruptcy and collateral rely on incomplete asset markets. In fact, bankruptcy and collateral add contingencies to asset markets. In some models, these contingencies can be used by consumers to achieve the same equilibrium allocations as in models with complete markets. In particular, the equilibrium allocation in the debt constrained model of Kehoe and Levine (2001) can be implemented in a model with bankruptcy and collateral. The equilibrium allocation is constrained efficient. Bankruptcy occurs when consumers receive low income shocks. The implementation of the debt constrained allocation in a model with bankruptcy and collateral is fragile in the sense of Leijonhufvud’s “corridor of stability,” however: If the environment changes, the equilibrium allocation is no longer constrained efficient.
This paper studies the relation between the United States’ bilateral real exchange rate and the associated bilateral relative price of nontraded goods for five of its most important trade relationships. Traditional theory attributes fluctuations in real exchange rates to changes in the relative price of nontraded goods. We find that this relation depends crucially on the choice of price series used to measure relative prices and on the choice of trade partner. The relation is stronger when we measure relative prices using producer prices rather than consumer prices. The relation is stronger the more important is the trade relationship between the United States and a trade partner. Even in cases where there is a strong relation between the real exchange rate and the relative price of nontraded goods, however, a large fraction of real exchange rate fluctuations is due to deviations from the law of one price for traded goods.
This paper evaluates the performances of three of the most prominent multisectoral static applied general equilibrium models used to predict the impact of the North American Free Trade Agreement. These models drastically underestimated the impact of NAFTA on North American trade. Furthermore, the models failed to capture much of the relative impacts on different sectors. Ex-post performance evaluations of applied GE models are essential if policymakers are to have confidence in the results produced by these models. Such valuations also help make applied GE analysis a scientific discipline in which there are well-defined puzzles with clear successes and failures for competing theories. Analyzing sectoral trade data indicates the need for a new theoretical mechanism that generates large increases in trade in product categories with little or no previous trade. To capture changes in macroeconomic aggregates, the models need to be able to capture changes in productivity.
Currently, Argentina is experiencing what the government describes as a “great depression.” Using the “Great Depressions” methodology developed by Cole and Ohanian (1999) and Kehoe and Prescott (2002), we find that the primary determinants of both the boom in Argentina in the 1990s and the subsequent depression were changes in productivity, rather than changes in factor inputs. The timing of events links the boom to the currency-board-like Convertibility Plan and the crisis to its collapse. To gain credibility, the Argentine government took measures to make abandoning the plan more costly. Because the government was unable to enforce fiscal discipline, however, these increased costs failed to make the plan more credible and instead made the crisis far worse when it failed.
Both Chile and Mexico experienced severe economic crises in the early 1980s, yet Chile recovered much faster than Mexico. This study analyzes four possible explanations for this difference and rules out three, explanations based on money supply expansion, real wage and real exchange rate declines, and foreign debt overhangs. The fourth explanation is based on government policy reforms in the two countries. Using growth accounting and a calibrated growth model, the study determines that the only policy reforms promising as explanations are those that primarily affect total factor productivity, or how inputs are used, not the inputs themselves. Interpreting historical evidence with economic theory, the study concludes that the crucial difference between Chile and Mexico in the 1980s and 1990s is earlier government policy reforms in Chile, particularly reforms in policies affecting the banking system and bankruptcy procedures.
Chile and Mexico experienced severe economic crises in the early 1980s. This paper analyzes four possible explanations for why Chile recovered much faster than did Mexico. Comparing data from the two countries allows us to rule out a monetarist explanation, an explanation based on falls in real wages and real exchange rates, and a debt overhang explanation. Using growth accounting, a calibrated growth model, and economic theory, we conclude that the crucial difference between the two countries was the earlier policy reforms in Chile that generated faster productivity growth. The most crucial of these reforms were in banking and bankruptcy procedures.
This paper quantitatively tests the “new trade theory” based on product differentiation, increasing returns, and imperfect competition. We employ a standard model, which allows both changes in the distribution of income among industrialized countries, emphasized by Helpman and Krugman (1985), and nonhomothetic preferences, emphasized by Markusen (1986), to effect trade directions and volumes. In addition, we generalize the model to allow changes in relative prices to have large effects. We test the model by calibrating it to 1990 data and then “backcasting” to 1961 to see what changes in crucial variables between 1961 and 1990 are predicted by the theory. The results show that, although the model is capable of explaining much of the increased concentration of trade among industrialized countries, it is not capable of explaining the enormous increase in the ratio of trade to income. Our analysis suggests that it is policy changes, rather than the elements emphasized in the new trade theory, that have been the most significant determinants of the increase in trade volume.
We characterize the values of government debt and the debt’s maturity structure under which financial crises brought on by a loss of confidence in the government can arise within a dynamic, stochastic general equilibrium model. We also characterize the optimal policy response of the government to the threat of such a crisis. We show that when the country’s fundamentals place it inside the crisis zone, the government is motivated to reduce its debt and exit the crisis zone because this leads to an economic boom and a reduction in the interest rate on the government’s debt. We show that this reduction may be quite gradual if debt is high or the probability of a crisis is low. We also show that, while lengthening the maturity of the debt can shrink the crisis zone, credibility-inducing policies can have perverse effects.
This paper explores the extent to which the Mexican government’s inability to roll over its debt during December 1994 and January 1995 can be modeled as a self-fulfilling debt crisis. In the model there is a crucial interval of debt for which the government, although it finds it optimal to repay old debt if it can sell new debt, finds it optimal to default if it cannot sell new debt. If government debt is in this interval, which we call the crisis zone, then we can construct equilibria in which a crisis can occur stochastically, depending on the realization of a sunspot variable. The size of this zone depends on the average length of maturity of government debt. Our analysis suggests that for a country, like Mexico, with a very short maturity structure of debt, the crisis zone is large and includes levels of debt as low as that in Mexico before the crisis.
To illustrate the use of social accounting matrices (SAMs) in applied general equilibrium (GE) modeling, we use an aggregated SAM for the Spanish economy to calibrate a simple applied GE model. The idea is to construct artificial people—households, government, and a foreign sector—who make the same transactions in the equilibrium of the model economy as do their counterparts in the data. This calibration procedure can be augmented, or partially substituted for, by statistical estimation of key parameters. We show the usefulness of such a model by presenting the results of a comparative exercise that mimics the policy changes that took place in Spain during its 1986 integration into the European Community. Sub-sequent data shows the model results to be remarkably accurate, especially if we account for other major shocks affected the Spanish economy in 1986.
In 1985–86 the authors were members of a team that constructed a static applied general equilibrium model that was used to analyze the impact on the Spanish economy of the 1986 fiscal reform, which accompanied Spain’s entry into the European Community. This paper compares the results obtained to recently published data for 1985–87; we find that the model performed well in predicting the changes in relative prices and resource allocation that actually occurred, particularly if we incorporate exogenous shocks that affected the Spanish economy in 1986. We also analyze the sensitivity of the results to alternative specifications of the labor market and macroeconomic closure rules; we find that the central results are robust.
We examine the results of four static applied general equilibrium (AGE) modeling teams’ analyses of the effects of NAFTA. What they show is that Mexico’s economy, because it’s the smallest, will see the biggest NAFTA-produced increase in economic welfare: from 2 to 5 percent of GDP. The U.S. welfare increase will be small, around 0.1 percent of GDP; Canada will notice no welfare increase due to NAFTA. We then discuss two examples of dynamic phenomena—labor force adjustment and capital flows—which are likely to influence NAFTA’s welfare impact, but that aren’t easy to incorporate into static AGE models. Early results indicate that this is an important direction for future study.
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 look for the scale effects predicted by some theories of trade and growth based on the dynamic returns to scale that arise from learning by doing, investment in human capital, or development of new products. We find little empirical evidence of a relation between the growth rate of GDP per capita and the measures of scale implied by the theory. Restricting attention to the manufacturing sector, however, we find a significant relation between the growth rate of output per worker and the relevant scale variables. We also find that growth rates are significantly related to measures of intra-industry trade.
The current tool of choice for analyzing the impact of a potential North American Free Trade Agreement on the economies of Canada, Mexico, and the United States is the static applied general equilibrium model. Although this type of model can do a good job in analyzing, and even in predicting, the impact of trade liberalization or tax reform on relative prices and resource allocation over a short time horizon, it does not attempt to capture the impact of government policy on growth rates. For this we need a dynamic model. This paper outlines some of the issues that confront a researcher interested in building a dynamic general equilibrium model to assess the potential economic impact of a NAFTA, including the impact on growth rates. Simple calculations based on preliminary empirical work indicate that the dynamic benefits of increased openness could dwarf the static benefits found by more conventional applied general equilibrium models.
We develop a theory of general equilibrium with endogenous debt limits in the form of individual rationality constraints similar to those in the dynamic consistency literature. If an agent defaults on a contract, he can be excluded from future contingent claims markets trading and can have his assets seized. He cannot be excluded from spot markets trading, however, and he has some private endowments that cannot be seized. All information is publicly held and common knowledge, and there is a complete set of contingent claims markets. Since there is complete information, an agent cannot enter into a contract in which he would have an incentive to default in some state. In general there is only partial insurance: variations in consumption may be imperfectly correlated across agents; interest rates may be lower than they would be without constraints; and equilibria may be Pareto ranked.
Economic equilibria are usually solutions to fixed point problems rather than solutions to convex optimization problems. This leads to two difficulties that are closely related: First, equilibria may be difficult to compute. Second, a model economy may have more than one equilibrium. This paper explores these issues for a number of stylized economies, including static economies that involve both pure exchange and production, economies that have infinite numbers of goods because of time and uncertainty, and economies with distortionary taxes and externalities. There are numerous numerical examples that illustrate the theory and could serve as test problems for algorithms.
We extend the analysis of Kiyotaki and Wright, who study an economy in which the different commodities that serve as media of exchange are determined endogenously. Kiyotaki and Wright consider only symmetric, steady-state, pure-strategy equilibria, and find that for some parameter values no such equilibria exist. We consider mixed-strategy equilibria and dynamic equilibria. We prove that a steady-state equilibrium exists for all parameter values and that the number of steady-state equilibria is generically finite. We also show, however, that there may be a continuum of dynamic equilibria. Further, some dynamic equilibria display cycles.
We characterize equilibria of general equilibrium models with externalities and taxes as solutions to optimization problems. This characterization is similar to Negishi’s characterization of equilibria of economies without externalities or taxes as solutions to social planning problems. It is often useful for computing equilibria or deriving their properties. Frequently, however, finding the optimization problem that a particular equilibrium solves is difficult. This is especially true in economies with multiple equilibria. In a dynamic economy with externalities or taxes there may be a robust continuum of equilibria even if there is a representative consumer. This indeterminacy of equilibria is closely related to that in overlapping generations economies.
This paper uses a simple general equilibrium model in which agents use money holdings to self insure to address the classic question: What is the optimal rate of change of the money supply? The standard answer to this question, provided by Friedman, Bewley, Townsend, and others, is that this rate is negative. Because any revenues from seinorage in our model are redistributed in lump-sum form to agents and this redistribution improves insurance possibilities, we find that the optimal rate is sometimes positive. We also discuss the measurement of welfare gains or losses from inflation and their quantitative significance.
We consider a production economy with a finite number of heterogeneous, infinitely lived consumers. We show that, if the economy is smooth enough, equilibria are locally unique for almost all endowments. We do so by converting the infinite-dimensional fixed point problem stated in terms of prices and commodities into a finite-dimensional Negishi problem involving individual weights in a social value function. By adding artificial fixed factors to utility and production functions, we can write the equilibrium conditions equating spending and income for each consumer entirely in terms of time-zero factor endowments and derivatives of the social value function.