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CollectionDescription: Working Papers are early drafts of academic research papers written by economists affiliated with the Minneapolis Fed. Working Papers are often preprints of articles that are published in scholarly journals. Many Working Papers later become Staff Reports. The Research Database is the official location for this series, but you can also find them on the Minneapolis Fed website, IDEAS/RePEc, and in EconLit.

Creator: Boyd, John H. and Smith, Bruce D. (Bruce David), 19542002 Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 537 Abstract: We consider an environment in which riskneutral firms must obtain external finance. They have access to two kinds of linear, stochastic investment opportunities. For one, return realizations are costlessly observed by all agents. For the other, return realizations are costlessly observed only by the investing firm; however, they can be (privately) observed by outsiders who bear a fixed verification cost. Thus, the second investment opportunity is subject to a standard costly state verification (CSV) problem of the type considered by Townsend (1979), Gale and Hellwig (1985), or Williamson (1986, 1987).
We examine the optimal allocations of investment between the two kinds of projects, as well as the optimal contract used to finance it. We show that the optimal contractual outcome can be supported by having firms issue appropriate (and determinate) quantities of debt and equity securities to outside investors.
The optimal debtequity ratio necessarily depends (in part) on the firm’s asset structure. Investments in projects subject to CSV problems are associated (in a sense to be made precise) with the use of debt—as might be expected from the existing CSV literature. Investments in projects with publicly observable returns are associated with the use of external equity.
We examine in detail the relationship between the optimal asset and liability structure of the firm. We also describe conditions under which an increase in the cost of state verification shifts the composition of investment towards projects with observable returns, and reduces the optimal debtequity ratio. Interestingly, the optimal debtequity ratio is also shown to depend on factors that are irrelevant to asset allocations.
Finally, a large part of the interest in CSV environments has been due to the fact that they may result in equilibrium credit rationing. Our analysis has strong implications for the possibility of equilibrium credit rationing in more general CSV models.
Subject (JEL): E51  Money Supply; Credit; Money Multipliers and G21  Banks; Depository Institutions; Micro Finance Institutions; Mortgages 
Creator: Chari, V. V., Kehoe, Patrick J., and McGrattan, Ellen R. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 619 
Creator: Chari, V. V. and Jagannathan, Ravi Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 320 Abstract: This paper shows that bank runs can be modeled as an equilibrium phenomenon. We demonstrate that some aspects of the intuitive “story” that bank runs start with fears of insolvency of banks can be rigorously modeled. If individuals observe long “lines” at the bank, they correctly infer that there is a possibility that the bank is about to fail and precipitate a bank run. However, bank runs occur even when no one has any adverse information. Extra market constraints such as suspension of convertibility can prevent bank runs and result in superior allocations.

Creator: Aiyagari, S. Rao Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 312 Abstract: This paper studies the relationship between the existence and optimality of a monetary steadystate and the nonoptimality of nonmonetary steadystates. We construct a sequence of stationary overlapping generations economies with longer and longer lived generations in which all agents maximize a discounted sum of utilities with a common discount rate. Under some assumptions the following result is established: If the discount rate is greater (less) than the population growth rate, then eventually every nonmonetary steadystate is optimal (nonoptimal) and a monetary steadystate does not exist (exists and is optimal).

Creator: Christiano, Lawrence J. and Eichenbaum, Martin S. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 306 Abstract: This paper examines the quantitative importance of temporal aggregation bias in distorting parameter estimates and hypothesis tests. Our strategy is to consider two empirical examples in which temporal aggregation bias has the potential to account for results which are widely viewed as being anomalous from the perspective of particular economic models. Our first example investigates the possibility that temporal aggregation bias can lead to spurious Granger causality relationships. The quantitative importance of this possibility is examined in the context of Granger causal relations between the growth rates of money and various measures of aggregate output. Our second example investigates the possibility that temporal aggregation bias can account for the slow speeds of adjustment typically obtained with stock adjustment models. The quantitative importance of this possibility is examined in the context of a particular class of continuous and discrete time equilibrium models of inventories and sales. The different models are compared on the basis of the behavioral implications of the estimated values of the structural parameters which we obtain and their overall statistical performance. The empirical results from both examples provide support for the view that temporal aggregation bias can be quantitatively important in the sense of significantly distorting inference.

Creator: Christiano, Lawrence J. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 303 Abstract: This paper investigates—in the context of a simple example—the accuracy of an econometric technique recently proposed by Kydland and Prescott. We consider a hypothetical econometrician who has a large sample of data, which is known to be generated as a solution to an infinite horizon, stochastic optimization problem. The form of the optimization problem is known to the econometrician. However, the values of some of the parameters need to be estimated. The optimization problem—presented in a recent paper by Long and Plosser—is not linear quadratic. Nevertheless, its closed form solution is known, although not to the hypothetical econometrician of this paper. The econometrician uses Kydland and Prescott’s method to estimate the unknown structural parameters. Kydland and Prescott’s approach involves replacing the given stochastic optimization problem by another which approximates it. The approximate problem is a element of the class of linear quadratic problems, whose solution is wellknown—even to the hypothetical econometrician of this paper. After examining the probability limits of the econometrician’s estimators under “reasonable” specifications of model parameters, we conclude that the Kydland and Prescott method works well in the example considered. It is left to future research to determine the extent to which the results obtained for the example in this paper applies to a broader class of models.

Creator: Christiano, Lawrence J. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 338 Abstract: This paper investigates two methods of approximating the optimal decision rules of a stochastic, representative agent model which exhibits growth in steady state and cannot be expressed in linear–quadratic form. Both methods are modifications on the linear quadratic approximation technique proposed by Kydland and Prescott. It is shown that one of the solution methods leads to bizarre dynamic behavior, even with shocks of empirically reasonable magnitude. The other solution technique does not exhibit such bizarre behavior.

Creator: Altug, Sumru and Miller, Robert A. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 341 Abstract: This paper investigates the role of aggregate shocks on household consumption and labor supply. It posits, estimates and tests a model where the equilibrium behavior of agents sometimes leads them to locate on the boundary of their respective choices sets. The framework is rich enough to nest much previous empirical work on life cycle labor supply and consumption based asset pricing. It also yields a structural interpretation of wage regressions on unemployment. An important feature of our model is that markets are complete. Consequently, aggregate shocks only enter through two price sequences, namely real wages, and a sequence comprising weighted prices for future contingent consumption claims which are ultimately realized. We examine the properties of this latter sequence, whose elements may be represented as mappings from real wages and aggregate dividends.
Our empirical findings may be grouped into three. First, aggregate shocks play a significant role in determining the choices people make. Second, we reject for males some of the restrictions implicit in structural interpretations of wage unemployment regressions. Moreover when these restrictions are imposed, we find wages are countercyclical, but cannot reject the null hypothesis of no effect. Third, the null hypothesis that markets are complete is not invariably rejected. However, the orthogonality conditions associated with the asset pricing equation are rejected, even though our specification of preferences incorporates types of heterogeneity which violate the necessary conditions for aggregating to a representative agent formulation. Finally, we reject the crossequation restrictions between the labor supply of spouses implied by equilibrium behavior.
Keyword: Complete markets, Tests of orthogonality conditions, Labor supply and consumption, Asset returns data, Nonseparability, Simple factor structure, and Panel data 
Creator: Aiyagari, S. Rao Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 356 Abstract: We prove the existence of a competitive equilibrium in an overlapping generations model in which each generation has a preference ordering over its own and its descendents’ consumptions. The model is one of pure exchange with many goods in each period and two period lived generations. The bequest from one generation to the next is required to be nonnegative and is endogenous. In equilibrium, some sequences of agents of successive generations may be continually “linked” by positive bequests and act as infinitely lived agents. Other sequences of agents may not be so linked and therefore behave as sequences of finite lived agents. We give three examples which illustrate the following points: (i) multiple equilibria may exist some of which resemble those of standard overlapping generations models, whereas in others some sequences of agents behave as if infinitely lived, (ii) multiple steady states of the above two types may exist in which the latter are unstable and the former are stable, and (iii) if agents have preferences given by discounted sums of utilities with different discount rates, then not all sequences of generations can be continually linked and hence behave as infinitely lived agents.

Creator: Boyd, John H., Prescott, Edward C., and Smith, Bruce D. (Bruce David), 19542002 Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 385 Abstract: Three economic environments are reviewed, and in each organizations play an essential role. For an adverse selection insurance economy, we find that when mutual insurance arrangements are permitted an equilibrium necessarily exists and is optimal. This example, and the two others, illustrate the problems that may result from imposing organizational structure on an environment rather than permitting the structure to be determined endogenously.

Creator: Aiyagari, S. Rao Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 393 Abstract: This paper demonstrates a connection between failure of Walras’ Law and nonoptimal equilibria in a quite general overlapping generations model. Consider the following implication of Walras’ Law in finite economies. Suppose that all prices are positive and that all agents are on their budget lines. Then, no matter how the set of goods is partitioned, there cannot be an excess supply (in value terms) for some other set in the partition with excess demand (in value terms) for some other set in the partition. We use the Cass (1972), Benveniste (1976, 1986), Balasko and Shell (1980), and Okuno and Zilcha (1980) price characterization of optimality of equilibria in pure exchange overlapping generations models to show the following link between the above implication of Walras’ Law and optimality of a competitive equilibrium. A competitive equilibrium is nonoptimal if and only if the above implication of Walras’ Law fails in its neighborhood.

Creator: Kehoe, Timothy Jerome, 1953, Levine, David K., and Woodford, Michael, 1955 Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 404 Abstract: 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 seigniorage in our model are redistributed in lumpsum 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.

Creator: Backus, David, Kehoe, Patrick J., and Kydland, Finn E. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 426 Abstract: We ask whether a twocountry real business cycle model can account simultaneously for domestic and international aspects of business cycles. With this question in mind, we document a number of discrepancies between theory and data. The most striking discrepancy concerns the correlations of consumption and output across countries. In the data, outputs are generally more highly correlated across countries than consumptions. In the model we see the opposite.

Creator: Aiyagari, S. Rao and Wallace, Neil Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 428 Abstract: We prove the general existence of steady states with positive consumption in an N goods and fiat money version of the KiyotakiWright (“On money as a median of exchange,” Journal of Political Economy 1989, 97 (4), 927–54) model by admitting mixed strategies. We also show that there always exists a steady state in which everyone accepts a least costlytostore object. In particular, if fiat money is one such object, then there always exists a monetary steady state. We also establish some other properties of steady states and comment on the relationship between steady states and (incentive) feasible allocations.

Creator: Kehoe, Timothy Jerome, 1953, Levine, David K., and Romer, Paul Michael, 1955 Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 436 Abstract: 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.

Creator: Kehoe, Timothy Jerome, 1953 and Levine, David K. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 445 Abstract: 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.

Creator: Aiyagari, S. Rao, Christiano, Lawrence J., and Eichenbaum, Martin S. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 456 Abstract: This paper investigates the impact on aggregate variables of changes in government consumption in the context of a stochastic, neoclassical growth model. We show, theoretically, that the impact on output and employment of a persistent change in government consumption exceeds that of temporary change. We also show that, in principle, there can be an analog to the Keynesian multiplier in the neoclassical growth model. Finally, in an empirically plausible version of the model, we show that the interest rate impact of a persistent government consumption shock exceeds that of a temporary one. Our results provide counterexamples to existing claims in the literature.

Creator: Todd, Richard M. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 459 Abstract: Forecasts are routinely revised, and these revisions are often the subject of informal analysis and discussion. This paper argues (1) that forecast revisions are analyzed because they help forecasters and forecast users to evaluate forecasts and forecasting procedures, and (2) that these analyses can be sharpened by using the forecasting model to systematically express its forecast revision as the sum of components identified with specific subsets of new information, such as data revisions and forecast errors. An algorithm for this purpose is explained and illustrated.

Creator: Kehoe, Timothy Jerome, 1953 Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 460 Abstract: 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.

Creator: Kehoe, Timothy Jerome, 1953, Polo, Clemente, and Sancho, Ferran Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 480 Abstract: 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.

Creator: Kehoe, Timothy Jerome, 1953 Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 491 Abstract: 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.

Creator: Christiano, Lawrence J. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 301 Abstract: This paper presents a completely worked example applying the frequency domain estimation strategy proposed by Hansen and Sargent [1980, 1981a]. A bivariate, high order continuous time autoregressive moving average model is estimated subject to the restrictions implied by the rational expectations model of the term structure of interest rates. The estimation strategy takes into account the fact that one of the data series are pointintime observations, while the other are time averaged. Alternative strategies are considered for taking into account nonstationarity in the data. Computing times reported in the paper demonstrate that estimation using the techniques of Hansen and Sargent is inexpensive.

Creator: Litterman, Robert B. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 297 Abstract: Optimal control theory can be combined with the probability structure of a vector autoregression to investigate the tradeoffs available to policymakers. Such an approach obtains results based on a minimal set of assumptions about the economy and the structure of policy actions. This paper takes this approach to analyze the potential effectiveness of countercyclical monetary policy.

Creator: Sargent, Thomas J. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 293 
Identification and Estimation of a Model of Hyperinflation With a Continuum of "Sunspot" Equilibrium
Creator: Sargent, Thomas J. and Wallace, Neil Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 280 Abstract: This paper constructs a model with two structural equations: the Government budget constraint and a linear version of Cagan’s portfolio balance equation. The model contains a continuum of equilibria with “sunspot equilibria.” Closed forms for the solutions are found. Even though there is a continuum of equilibria, the model is overidentified econometrically, so that the model restricts time series data on price levels and currency stocks. We describe how the free parameters of the model can be estimated, including some parameters that serve to index particular members of the continuum of equilibria. The sunspot equilibria hold out some promise of explaining anomalies in the observed behavior of inflation and real balances during hyperinflations.

Creator: Miller, Preston J. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 244 Abstract: This study examines the shape of an optimal income tax schedule in a monetary economy. In equilibrium, money’s role is to allocate resources across generations, while a taxtransfer scheme serves as a form of social insurance. It is found that the optimal real income tax with money can be progressive.

Creator: Smith, Bruce D. (Bruce David), 19542002 Series: Working paper (Federal Reserve Bank of Minneapolis. Research Department) Number: 216 Abstract: A definition of a transactions medium is proposed. This is that a transactions medium permits the attainment of otherwise unattainable resource allocations. It is shown that by this definition money can be a transactions medium in a pure exchange, overlapping generations economy. It is also shown that money is a transaction medium only if there are informational asymmetries of a particular type. Finally, it is shown that the set of economies for which money is a transactions medium is not isolated, in a welldefined sense.