Research Database

A model is presented in which demand deposits backed by fractional currency reserves and public insurance can be beneficial. The model uses Samuelson's pure consumption-loans model. The case for demand deposits, reserves, and deposit insurance rests on costs of illiquidity and incomplete information. The effect of deposit insurance depends upon how, and at what cost, the government meets its insurer's obligation--something which is not specified in practice. It remains possible that demand deposits and deposit insurance are a distortion, and reserve requirements serve only to limit the size of this distortion.

The fiscal year and the calendar year coincide for a large fraction of firms traded in the New York and American Stock Exchanges. It is therefore possible that part of the large positive abnormal return earned by stocks as a group during the first week of trading in January may be due to temporal resolution of uncertainty accompanying the end of the fiscal year. We study this hypothesis by examining whether stocks of firms with fiscal years ending in months other than December also realize positive abnormal returns, following the end of their fiscal years. We find that there are no excess returns for such firms in the first five trading days following the end of the fiscal year.

These notes are intended as a do-it-yourself course in economic growth along lines suggested by Lucas ("On the Mechanics of Economic Development"). We examine in turn the neoclassical growth model; theories of endogenous growth, including learning-by-doing, increasing returns to scale, and externalities; and dynamic comparative advantage in trade. Salient features of growing economies and microeconomic evidence on production processes are used to evaluate alternatives. Exercises supplement the text.

This paper develops a forecasting procedure based on a Bayesian method for estimating vector autoregressions. The procedure is applied to ten macroeconomic variables and is shown to improve out-of-sample forecasts relative to univariate equations. Although cross-variables responses are damped by the prior, considerable interaction among the variables is shown to be captured by the estimates. We provide unconditional forecasts as of 1982:12 and 1963:3* We also describe how a model such as this can be used to make conditional projections and to analyse policy alternatives. As an example, we analyze a Congressional Budget Office forecast made in 1982:12. While no automatic causal interpretations arise from models like ours, they provide a detailed characterization of the dynamic statistical interdependence of a set of economic variables, which may help in evaluating causal hypotheses, without containing any such hypotheses themselves.

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.

In this paper, we characterize those situations in which after the introduction of futures markets there is either an unambiguous change in the volatility of spot prices or an unambiguous change in welfare. We provide examples of the usefulness of this approach by giving two alternative sets of sufficient conditions for price volatility to decline following the introduction of futures trading. We also provide a set of sufficient conditions for the introduction of futures trading to increase the welfare of all agents.

Current approaches to monetary theory and policy owe much to the "quantity theory of money." However, recent theoretical developments suggest that the manner in which money is introduced is more important, even for price level movements, than the quantity of money. Colonial American experience provides a laboratory for discriminating between these views. It is shown here that the nature of backing, rather than the quantity of money, determined its value. Large secular inflations were ended by changing the nature of backing despite the continuance of large note issues (and despite the absence of a metallic standard). Extremely large note issues and note withdrawals are shown not to have produced inflation (currency depreciation) or deflation (currency appreciation).

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.

Doan, Litterman, and Sims have described a method for estimating Bayesian vector autoregressive (BVAR) forecasting models. The method has been successfully applied to the U.S. macroeconomic dataset, which is relatively long and stable. Despite the brevity and volatility of the post-1976 Chilean macroeconomic dataset, this paper shows that a straightforward application of the DLS method to this dataset, with simple modifications to allow for delays in the release of data, also appears to satisfy at least one criterion of relative forecasting accuracy suggested by Doan, Litterman, and Sims. However, the forecast errors of the Chilean BVARs are still large in absolute terms.Also, the model's coefficients change sharply in periods marked by policy shifts, such as the floating of the peso in 1982.

A model of a labor market is developed in which agents possess private information about their marginal products. As a result, involuntary unemployment may arise as a consequence of attempts by firms to create appropriate self-selection incentives. Moreover, employment lotteries may arise for the same reason despite the fact that, in equilibrium, there is no uncertainty in the model. When employment is random, this is both privately and socially desirable. Finally, it is shown that the unemployment that arises is consistent with (a) pro-cyclical aggregate real wages and productivity, (b) employment that fluctuates (at individual and aggregate levels) much more than real wages.

This paper characterizes the behavior of investment expenditures, optimal capital stocks, and real interest rates in the time-to-build model of investment. These results are used to show that the delivery lag model of investment fails to account for time lags in investment when constructing the cost of capital variable and hence, misspecifies the effects of interest rates on investment expenditures. Second, this paper derives equilibrium pricing relationships involving the prices of existing capital and uses these relationships to obtain simple tests of the underlying investment technology. Despite the widespread use of 'q' in the empirical investment literature, it is shown that the relationship between current investment and an appropriately defined measure of Tobin's 'q' contains no such testable implications. Finally, it is shown that the practice of using stock market data to measure the price of existing capital is invalid when time lags exist in the investment process.

The Diamond-Dybvig model of banking (Journal of Political Economy, 1983) is amended by introducing communication barriers - these being implicit in their model and in most explanations of why people hold so-called liquid assets. These barriers imply the sequential-service constraint that Diamond and Dybvig imposed on private intermediation and have other implications: infeasibility of the policy that Diamond and Dybvig identify with deposit insurance and desirability of dependence of the realized return on deposits on the random order of withdrawals.

The consequences of costly divisibility of assets are studied using a model with the following features. The demand for assets is generated from an overlapping generations model with a continuum of agents in each generation and with intra-generation trade (intermediation) ruled out. There is a once-for-all supply of a stock of nonnegative-dividend assets in a large size, and there is a costly technology for dividing them into smaller sizes. Stationary equilibria are shown to exist. In contrast with similar models with costless divisibility of assets, competitive equilibria are not necessarily desirable; there can be Pareto-ordered equilibria.

A popular method of investigating the market effects of multibank holding company (MBHC) affiliation involves regression of banks' local market share on a dummy variable for MBHC affiliation. The usefulness of this procedure is called into question by means of a theoretical counterexample.

In this paper we analyze the constraints imposed by dynamic consistency in a model of optimal taxation. We assume that only distorting taxes are available to finance government consumption. Optimal fiscal policy requires the use of debt to smooth distortions over time. Dynamic consistency requires that governments at each point in time not have an incentive to default on the inherited debt. We consider policy functions which map the history of the economy including the actions of past governments into current decisions. A sustainable plan is a sequence of history-contingent policies which are optimal at each date given that future policies will be selected according to the plan. We show that if agents discount the future sufficiently little and if government consumption fluctuates then optimal sustainable plans yield policies and allocations which are identical to those under full commitment. We contrast our notion of dynamic consistency with other definitions.

The existence of fixed points for monotone maps on spaces of measures is established. The case of monotone Markov processes is analyzed and a uniqueness and global stability condition is developed. A comparative statics result is presented and the problem of approximation to the invariant distribution is discussed. The conditions of the theorems are verified for the cases of Optimal Stochastic Growth and Industry Equilibrium.

This note presents a model whose competitive equilibrium can be consistent with the observation that current labor market conditions affect the well-being of new entrants more than they do that of senior workers. The model uses the notion that new entrants are not around soon enough to participate in risk-sharing contingent on the shocks that determine the equilibrium marginal products of first-period employment. This timing notion is formalized using a stochastic overlapping generations model.

This article studies the accuracy of two versions of Kydland and Prescott's (1980, 1982) procedure for approximating optimal decision rules in problems in which the objective fails to be quadratic and the constraints fail to be linear. The analysis is carried out using a version of the Brock-Mirman (1972) model of optimal economic growth. Although the model is not linear quadratic, its solution can nevertheless be computed with arbitrary accuracy using a variant of existing value-function iteration procedures. I find the Kydland-Prescott approximate decision rules are very similar to those implied by value-function iteration.

We derive the empirical implications of a popular class of international macroeconomic models. The real economy is a stochastic exchange model with complete markets. A standard result is that cross-country risk sharing implies perfect correlation between consumption paths across countries. With mild restrictions on the endowment process ii also implies a positive correlation between net exports and output in every country. We introduce money using cash-in-advance constraints and show that the implications for real variables carry over into the monetary economy. These dichotomy and neutrality propositions generalize those in the literature to stochastic environments with heterogeneous agents, and do not require the cash-in-advance constraint to bind in every state. They imply that any correlation between the nominal exchange rate and the balance of trade can be made consistent with the theory.

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 well-known—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.

An overlapping generations model is developed that contains labor markets in which adverse selection problems arise. As a response to these problems, quantity rationing of labor occurs. In addition, the model is capable of generating (a) random employment and prices despite the absence of underlying uncertainty in equilibrium; (b) a statistical (nondegenerate) Phillips curve; (c) procyclical movements in productivity; (d) correlations between aggregate demand and unemployment (and output); (e) an absence of correlation between unemployment (employment) and real wages. In addition, the Phillips curve obtained typically has the "correct" slope. Finally, the model reconciles the theoretical importance and observed unimportance of intertemporal substitution effects, and explains why price level stability may be a poor policy objective.

We study an overlapping generations model which contains a capital good that resembles actual gold. This capital good can he stored without physically depreciating and can, by using other resources, be converted back and forth between gold jewelry which yields utility directly and raw gold which does not.Under the assumption that the three utility-yielding objects - first and second period consumption and jewelry - are gross substitutes, stationary equilibria are shown to exist and are characterized; for some parameter values, there are inefficient equilibria, while for others there are efficient equilibria. Both types can be interpreted as commodity money equilibria.

This paper comments on "The Real Bills Doctrine vs. the Quantity-Theory: a Reconsideration" by T. Sargent and N. Wallace. It argues that there exists a class of models similar to theirs that is (a) favorable to the quantity theory view of price stability, (b) supports the imposition of 100 percent reserve requirements, and (c) explains a long history of legal credit restrictions. In particular, lending restrictions stabilize price levels and result in Pareto improvements.

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.

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 a set of 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.

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.

In this paper we consider a particular international economic policy regime: the laissez-faire regime, the distinguishing features of which are unrestricted portfolio choice and floating exchange rates. And as we show, that regime, although favored by many economists, is not economically feasible. It does not have a determinate equilibrium. That is an implication of an over-lapping-generations model. But as we argue in the paper, that is no reason for doubting the indeterminacy of the laissez-faire regime equilibrium.

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 non-negative 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.

This paper considers a view commonly associated with the "quantity theory of money": that banks should face 100 percent reserve requirements. It argues first that the objectives of the quantity theorists' proposals were more than merely price level stability, and that in fact, price level stability was at most a secondary objective of their proposals. Second, it argues that these theorists had a world with distortions in mind with respect to their proposals. These are present in a special setting examined that (a) supports the imposition of 100 percent reserve requirements (on the basis of an unconstrained Pareto criterion), and (b) supports the view that these restrictions stabilize the price level and make its movements more "predictable."

A model of a labor market is developed in which agents possess private information about their own productivities. This has the property that firms may use unemployment to create appropriate self-selection incentives. When this is the case, existence of an equilibrium may require that employment be stochastic. This is true even though all uncertainty is necessarily resolved prior to hiring. Even when existence is not at issue, it may be privately as well as socially desirable to randomize employment prospects. Finally, it is argued that this "adverse selection" approach is consistent with traditional "Keynesian" approaches to macroeconomics, but avoids some of the arbitrary features of several "Keynesian models."

A simple model of backed money without a store of value function is presented, discussed, and defended. The function of money in the model is to replace complex contingent contracts traded on a centralized exchange with simple trades in decentralized markets.

We present a model of vintage human capital. The economy exhibits exogenous deterministic technological change. Technology requires skills that are specific to the vintage. A stationary competitive equilibrium is defined and shown to exist and be unique, as well as Pareto optimal. The stationary equilibrium is characterized by an endogenous distribution of skilled workers across vintages. The distribution is shown to be single peaked and there is diffusion of technology in the sense that there is a lag between the time when a technology appears and the peak of its usage. An increase in the rate of exogenous technological change shifts the distribution of human capital to more recent vintages and increases the relative wage of the unskilled workers in each vintage.

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 tax-transfer scheme serves as a form of social insurance. It is found that the optimal real income tax with money can be progressive.

A critical roadblock to modelling inventories of finished goods has been the claim that production and inventory decisions of a perfectly competitive firm are determined independently of each other. A basic goal of this study is to specify fundamental preferences of economic agents, technologies, constraints and market structures that are, in a rough way, capable of generating patterns of serial correlation and cross correlation between inventories and employment of factors of production that are consistent with those observed in the data. The claim is made that the time series for inventories, output and employment can be interpreted as emerging from a well specified dynamic, stochastic competitive equilibrium in which economic agents are assumed to form rational expectations about variables not included in their information sets. Inventories and employment will not be related in a direct way if and only if the price elasticity of demand for output is equal to infinity.

General competitive analysis is extended to cover a dynamic, pure-exchange economy with privately observed shocks to preferences. In the linear, infinite-dimensional space containing lotteries we establish the existence of optima, the existence of competitive equilibria, and that every competitive equilibrium is an optimum. An example illustrates that rationing and securities with contrived risk have an equilibrium interpretation.

In a monetary model, it is shown that if there is a unique Pareto inefficient barter equilibrium, then a monetary equilibrium exists when traders are sufficiently patient.

The existence of fixed points for monotone maps on spaces of measures is established. The case of monotone Markov processes is analyzed and a uniqueness and global stability condition is developed. A comparative statics result is presented and the problem of approximation to the invariant distribution is discussed. The conditions of the theorems are verified for the cases of Optimal Stochastic Growth and Industry Equilibrium.