equilibrium dynamics in an endogenous growth model of money and banking we construct an analytically tractable endogenous growth model of money and banking where money provides liquidity services to facilitate transactions and banks convert non reserve deposits into productive capital we examine both the long and short run effects of changes in the money growth rate or the reserve requirement ratio in response to a change in the required reserve ratio the inflation rate and the growth rates of capital real balances and consumption need not adjust monotonically along the transition path while the balanced growth equilibrium may be either a saddle or a source locally the global dynamical system exhibits flip bifurcation

inflation uncertainty and growth in a cash in advance economy abstract this paper analyzes the effects of inflation variability on economic growth in a model where money is introduced via a cash in advance constraint in this setting we find that inflation adversely affects long run growth even when the cash in advance constraint applies only to consumption at the same time we find that inflation and growth are positively related in the short run furthermore variability increases average growth through a precautionary savings motive since inflation and inflation variability tend to be highly correlated the presence of uncertainty attenuates the negative long run relationship between inflation and real growth it also provides a partial rationale for the apparent lack of robustness in cross country regressions of growth and inflation

impartiality priority and solidarity in the theory of justice the ethic of priority is a compromise between the extremely compensatory ethic of welfare equality and the needs blind ethic of income equality we propose an axiom of priority and characterize resource allocation rules that are impartial prioritarian and solidaristic they comprise a class of rules which equalize across individuals some index of resources and welfare consequently we provide an ethical rationalization for the many applications in which such indices have been used e g the human development index index of primary goods etc

interest on reserves and sunspot equilibria friedman s proposal reconsidered friedman s 1960 proposal to pay interest on required reserves is considered in a setting that eliminates the indeterminacy of steady state equilibrium discussed by sargent and wallace 1985 in an overlapping generations model where the real rate of interest is technologically determined the payment of interest on reserves results in a determinate pareto optimal steady state equilibrium however interest payments on reserves reduce the steady state welfare of all young agents and for many economies result in the existence of stationary sunspot equilibria this is the case even if such equilibria cannot exist when reserves do not earn interest

growth and the effects of inflation abstract in this paper we study the relationship between the rate of increase of the money supply and the rate of growth of output in an economy we show that in some models of endogenous growth inflation has direct effects on the growth rate of the economy despite this the estimated welfare cost of inflation from calibrated examples is similar to that found in exogenous growth models

nonoptimality of the friedman rule with capital income taxation this paper studies the efficient taxation of money and factor income in intertemporal optimizing growth models with infinite horizons transaction costs technologies and flexible prices second best optimality calls for a positive inflation tax and a non zero capital income tax when there are restrictions on taxation of production factors or profits rents our cases of nonoptimality of the friedman rule which differ from those of mulligan and sala i martin 1997 and extend substantially those of schmitt grohe and uribe 2004a follow from the violation of the diamond and mirrlees 1971 principle on production efficiency

a common ground for resource and welfare egalitarianism resource egalitarianism and welfare egalitarianism are two focal conceptions of distributive justice we show in this paper that they share a solid common ground to do so we analyze a simple model of resource allocation in which agents abilities to transform the resource into an interpersonally comparable outcome and starting points may differ both conceptions of egalitarianism are naturally modeled in this context as two allocation rules the two rules are jointly characterized by the combination of three appealing axioms no domination solidarity and composition

priority rules and other asymmetric rationing methods in a rationing problem each agent demands a quantity of a certain commodity and the available resources fall short of total demand a rationing method solves this problem at every level of resources and individual demands we impose three axioms consistency with respect to variations of the set of agents upper composition and lower composition with respect to variations of the available resources in the model where the commodity comes in indivisible units the three axioms characterize the family of priority rules where individual demands are met lexicographically according to an exogeneous ordering of the agents in the more familiar model where the commodity is divisible these three axioms plus scale invariance independence of the measurement unit characterize a rich family of methods it contains exactly three symmetric methods giving equal shares to equal demands these are the familiar proportional uniform gains and uniform losses methods the asymmetric methods in the family partition the agents into priority classes within each class they use either the proportional method or a weighted version of the uniform gains or uniform losses methods

friedman rule in a model with endogenous growth and cash in advance constraint this paper introduces money into an overlapping generations model with endogenous growth the model due to docquier et al 2007 exhibits a positive intergenerational externality which precludes its laissez fair equilibrium to be optimal even if the government can control the level of physical capital and set it to satisfy the modified golden rule the main message of the paper is that as long as the modified golden rule is attained friedman rule is optimal the result holds regardless of the ability of the government to internalize the externality and control the level of human capital other results include i violation of friedman rule for a different second best environment wherein human capital accumulation is controlled but not physical capital accumulation ii existence of a negative relationship between money growth rate and the economy s endogenous growth rate and iii non uniqueness of friedman rule

the friedman rule in an overlapping generations model with nonlinear taxation and income misreporting this paper models a two period overlapping generations economy with money populated with individuals of different skills they face a nonlinear income tax schedule and can engage in tax evasion money serves two purposes the traditional one modeled through a money in the utility function it also facilitates tax evasion the main message of the paper is that income tax evasion in this framework leads to the violation of the friedman rule the paper also shows that even in the absence of tax evasion when optimality requires differential commodity taxation complementarity of real cash balances and labor supply does not guarantee the optimality of the friedman rule as a boundary solution an additional assumption is required

money and endogenous growth the ramsey romer model of endogenous growth is extended to allow for holdings of real money balances and government debt as well as capital and for non interconnected generations of households tax financed increases in government consumption and debt depress growth prospects and boost inflation as long as a positive birth rate ensures that future taxes are shouldered by future yet unborn generations debt financed increases in government consumption depress growth and boost inflation even more money financed increases in government consumption depress growth less but increase inflation by more giving subsidies through an increase in monetary growth is non neutral since this increases real growth and thus inflation increases by a lesser amount than monetary growth bond financed increases in monetary growth lead to a larger increase in real growth and a smaller increase in inflation if there are cost adjustment for investment cuts in monetary growth and increases in government debt and government consumption induce an increase in the real interest rate copyright 1994 by ohio state university press

the friedman rule old and new abstract in overlapping generations models money growth creates intergenerational wealth effects and leads to the breakdown of the friedman rule the rule can be restored via lump sum tax and transfers that neutralize these wealth transfers additionally and in contrast to money in the utility function models the friedman rule is not the unique first best solution in cash in advance constraint models of money a continuum of combinations of money growth rates and consumption taxes implement the first best allocation this paper traces through the intellectual origins of the first old result which was recently restated in bhattacharya et al 2005 monetary policy fiscal policy and the inflation tax equivalence results macroeconomic dynamics 7 647 669 and formally demonstrates the second new result

redistributive taxation in a simple perfect foresight model abstract we investigate the redistributive potential of capital taxation in an intertemporal maximizing model of capital formation first even unanticipated redistributive capital taxation is severely limited in its effectiveness since it depresses wages second under any convergent redistributive tax policy which maximizes a paretian social objective the capital income tax will converge to zero independent of the factor supply elasticities these results are independent of workers holdings of capital

optimal monetary policy and economic growth abstract a question at the center of many analyses of optimal monetary policy is why do central banks never implement the friedman rule to the list of answers to this question we add neoclassical production specifically the tobin effect as one possible explanation to that end we study an overlapping generations economy with capital where limited communication and stochastic relocation create an endogenous transactions role for fiat money we assume a production function with a knowledge externality romer style that nests economies with endogenous growth ak form and those with no long run growth the diamond model the tobin effect is shown to be always operative under crra preferences a mild degree of social increasing returns is sufficient but not necessary for some positive inflation to dominate zero inflation and for the friedman rule to be sub optimal irrespective of the degree of risk aversion

the optimal inflation rate under schumpeterian growth abstract to analyze the relationship between inflation and economic growth we construct an endogenous growth model with creative destruction incorporating sticky prices due to menu costs price changes reduce the reward for innovation and thus lower the frequency of creative destruction central banks can maximize the growth rate by setting their inflation target at the negative of a fundamental growth rate while the optimal inflation rate may be greater than the growth maximizing inflation rate our calibrated model shows that the optimal inflation rate is close to the growth maximizing inflation rate and that a deviation from the optimal level has sizable impacts

optimal fiscal and monetary policy some recent results this paper studies the quantitative properties of fiscal and monetary policy in business cycle models in terms of fiscal policy optimal labor tax rates are virtually constant and optimal capital income tax rates are close to zero on average in terms of monetary policy the friedman rule is optimal nominal interest rates are zero and optimal monetary policy is activist in the sense that it responds to shocks to the economy

resolving differences over the optimal quantity of money optimal steady state monetary policy in models of infinitely lived agents calls for a deflation of the fiat money stock at a rate that equates the rates of return of fiat money and capital this prescription for the optimal quantity of money holds whether the demand for money springs from placing money in the utility function friedman 1969 a cash in advance constraint grandmont and younes 1973 or spatial separation townsend 1980 in contrast monetary models of overlapping generations have counseled the golden rule optimality of a fixed stock of fiat money 1 this model has often been criticized for its lack of a transactions role for money that would distinguish itself from other assets 2 the seeming difference in this model s implications concerning the optimal quantity of money thus raises an obvious question 3 does the overlapping generations model obtain different welfare implications because it assumes a finite lifespan or because it lacks a special transactions role for money recent work has reexamined the optimal quantity of money in overlappinggenerations models featuring transactions roles for money abel 1987 who takes the broadest and clearest look finds that the golden rule optimal monetary policy

distributive justice in taxation abstract a classical criterion for apportioning taxes is that all should sacrifice equally in loss of utility suppose that a method of apportioning taxes is continuous and has the following four properties i the way that taxpayers split a given tax total depends only on their own taxable incomes ii an increase in the tax total implies that everyone pays more iii every incremental increase in tax is apportioned according to taxpayers current after tax incomes iv the ordering of taxpayers by pre tax income and after tax income is the same then there exists a utility function relative to which all sacrifice equally

monetary policy banking crises and the friedman rule banking crises are frequent events gerard caprio and daniela klingebiel 1997 catalog over 80 banking crises during the last 25 years interestingly some banking crises are associated with no output losses whatsoever while others involve massive recessions finally it is known that the probability of a banking crisis rises as the rate of inflation rises see asli demirguc kunt and enrica detragiache 1997 john boyd et al 2001a b while received wisdom exists about the conduct of monetary policy while a crisis is underway there is no formal treatment of how the conduct of monetary policy during normal times affects the potential for banking crises to occur to fill that gap i consider economies where spatial separation and limited communication create a transactions role for money and random shocks to agents liquidity preferences create a role for banks in addition banks confront randomness in withdrawal demand when withdrawal demand is sufficiently high banks exhaust their cash reserves there are good reasons to associate this with a banking panic the output lost during a banking panic depends on how great withdrawal demand is some banking crises generate no output losses while others generate large reductions in resource availability in addition the conduct of monetary policy during normal times affects the probability of a banking crisis the higher the nominal interest rate the inflation rate the higher is the probability of a panic driving the nominal interest rate to zero following the friedman rule eliminates bank panics this constitutes a new rationale for the friedman rule nonetheless conventional methods of implementing the friedman rule never produce an optimal resource allocation in particular low nominal interest rates induce banks to hold large cash reserves thereby forgoing socially more productive investments in effect the friedman rule induces banks to become narrow banks voluntarily the banking system is very safe but it undertakes a suboptimal level of investment less conventional methods for implementing the friedman rule such as allowing unrestricted access to the discount window at a zero nominal interest rate lead either to the nonexistence of equilibrium or to massive indeterminacies none of the equilibria will be consistent with full optimality

optimal accumulation in an endogenous growth setting with human capital this paper considers a three overlapping generations model of endogenous growth wherein human capital is the engine of growth it first contrasts the laissez faire and the optimal solutions three possible accumulation regimes are distinguished then it discusses a standard set of tax transfer instruments that allow for decentralization of the social optimum within the limits of our model the rationale for the standard pattern of intergenerational transfers the working aged financing the education of the young and the pension of the old is seriously questioned on pure efficiency grounds the case for generous public pensions is rather weak

anticipated inflation in a monetary economy with endogenous growth this paper makes a new attempt to investigate the role of anticipatedmonetary growth in economic growth combining the barro 1990 rebelo 1991 type endogenous growth model with sidrauski s 1967 framework we show that the pre announcement of money supply behaviour may have significant effects on the rate of growth during the transition process the key factor indetermining adjustment patterns of the economy to anticipated monetary changes is the degree of relative risk aversion however changes in the rate of monetary growth do not affect the rate of long run growth regardless of the degree of relative risk aversion

the role of money in two alternative models when is the friedman rule optimal and why abstract in models of money with an infinitely lived representative agent ilra models the optimal monetary policy is almost always the friedman rule in overlapping generations og models by contrast the friedman rule may not be optimal in this paper we use this difference in monetary policy prescriptions to help us identify and study the key difference between these two models as models of money we study the welfare properties of monetary policy in a simple og model under two very different money demand specifications and two alternative assumptions about the generational timing of taxes for money retirement we conclude that the key difference between ilra and og monetary models is that in the latter the standard method for constructing a monetary regime causes transactions involving money to become intergenerational transfers under alternative government fiscal monetary regimes that offset these intergenerational transfers the friedman rule is always optimal

monetary policy overlapping generations and patterns of growth this paper investigates the role of monetary policy in economic growth using an infinitely lived overlapping generations model with a simple convex technology that can yield endo genous growth we show that money supply behaviour of the government may have significant effects on the long run economic growth in addition to the effect on the long term growth rate of the economy the policy may determine whether the economy stays in the exogenous growth process restricted by the growth rate of labour supply or realizes the endogenous growth that sustains continuous growth of pep capita income and consumption effect of inflation on capital accumulation has been one of the central topics in macroeconomics using an ad hoc model tobin shows that a rise in the rate of inflation deepens capital formation whereas sidrauski presents an opti mizing model in which money is superneutral that is inflation has no effect on capital formation in the long run these studies have been extended by a number of studies such as dornbusch and frenkel 1973 and wang and yip 1992 however the concern of these studies is restricted to the analysis of the level effect of inflation on capital accumulation recent developments in endogenous growth theory present a useful analytical framework for re examin ing the effect of inflation on capital accumulation and economic growth in contrast to the strong emphasis on the importance of fiscal policy for long run economic growth seen in mino 1989 barro 1990 and king and rebelo 1990 the role of monetary policy has been mostly ignored in the endogenous growth literature recalling that the effect of money growth on capital formation has been the central issue in money and growth literature it is rather curious that recent studies on endogenous economic growth focus exclusively on the real side of the economy there is however a small number of authors investigating the role of money in endogenously growing economies marquis and reffet 1991 and mino 1991 introduce money into two sector models involving human capital accumulation via a cash in advance constraint they conclude that an increase in the rate of nominal money supply generally depresses the long term economic growth as long as the cash in advance con straint applies to investment demand for either physical or human capital wang and yip 1991 extend the uzawa lucas model of endogenous growth by assuming that households allocate their available time between production transaction and human capital formation the transaction time is assumed to be a decreasing function of real money balances and therefore a reduction in real balances arising from an increase in the monetary expansion rate increases c the london school of economics and political science 1995

sharing the cost of a public good an incentive constrained axiomatic approach we study the problem of provision and cost sharing of a public good in large economies where exclusion complete or partial is possible we search for incentive constrained efficient allocation rules that display fairness properties population monotonicity says that an increase in population should not be detrimental to anyone demand monotonicity states that an increase in the demand for the public good in the sense of a first order stochastic dominance shift in the distribution of preferences should not be detrimental to any agent whose preferences remain unchanged under suitable domain restrictions we give an explicit characterization of all incentive constrained efficient allocation rules we then show that there exists a unique incentive constrained efficient and demand monotonic allocation rule the so called serial rule in the binary public good case the serial rule is also the only incentive constrained efficient and population monotonic rule

money and growth revisited abstract conventional wisdom is that if public policy can affect the growth rate of the economy the welfare implications of alternative policies will be large in this paper a stochastic dynamic general equilibrium model with endogenous growth and money is examined in this setting inflation lowers growth through its effect on the return to work however the welfare costs of higher inflation are modest the endogenous labor supply is important in producing this result

equality of resources implies equality of welfare if one is an egalitarian should one try to equalize resources available to agents or to equalize their welfares with a suitably general conception of what resources are these two conceptions cannot be distinguished an allocation mechanism is defined on a space of economies and is required to satisfy various axioms that are necessary conditions for equalizing resources among a population the unique mechanism satisfying these axioms on a large domain of economies is the one that allocates commodities so as to equalize utilities of the agents methodologically the theorem is a generalization of bargaining theory because the mechanisms are defined on commodity space

axiomatic bargaining theory on economic environments abstract axiomatic bargaining theory is reexamined by focusing upon the economic exhange environment instead of the traditional utility possibility set it is argued that the axioms of the traditional theory impose stronger restrictions than can be supported by their motivating economic intuitions weaker alternative axioms making explicit use of economic information are used to characterize the standard bargaining solutions a key idea is to impose consistency of the solution with respect to changes in the dimension of the commodity space even these weaker economic axioms however may be unrealistic restrictions to impose on the bargaining solution in the context of many economic bargaining problems

optimality of the friedman rule in economies with distorting taxes abstract we find conditions for the friedman rule to be optimal in three standard monetary models our main contribution is to shed light on two issues in the literature first the conventional view maintains that when money is a final good its services should be taxed moreover if money demand is interest inelastic its services should be taxed heavily we show that this view is incorrect second there is an ongoing controversy about whether the optimality of the friedman rule is connected to the intermediate goods result from public finance we resolve this controversy by showing a deep connection between these results

optimal taxation of capital income in general equilibrium with infinite lives this paper analyzes the optimal tax on capital income in general equilibrium models of the second best agents have infinite lives and utility functions which are extensions from the koopmans form the population is heterogeneous the important property of the models is the equality between the social and the private discount rates in the long run i find that the optimal tax rate is zero in the long run for a special case of additively separable utility functions i then determine the tax rates along the dynamic path and conditions that are sufficient for the local stability of the steady state

the liquidity trap the real balance effect and the friedman rule this paper studies the behavior of the economy and the efficacy of monetary policy under zero nominal interest rates using a model with population growth that nests as a special case a more conventional specification in which there is a single infinitely lived representative agent the paper shows that with a growing population monetary policy has distributional effects that give rise to a real balance effect thereby eliminating the liquidity trap these same distributional effects however can also work to make many agents much worse off under zero nominal interest rates than they are when the nominal interest rate is positive

equity in exchange economies abstract let be a fair choice correspondence i e associates to every economy in some initial position a set of final allocations at which the gains from trade have been fairly distributed we propose to declare equitable any final allocation which is invariant under arbitrary permutations among the agents of the components of the initial allocation followed by the operation of we also formulate a series of other criteria patterned on this model and we investigate the existence of allocations satisfying these criteria for several natural choices of

lump sum taxation and the superneutrality and optimum quantity of money in life cycle growth models abstract the question of superneutrality and the optimum quantity of money is addressed in a model where money services enter the utility function and where individuals have finite lives it is demonstrated that the existing result in the literature regarding a positive relationship between money creation and the steady state capital intensity and welfare is not due to monetary policy per se on the contrary this is shown to arise because of the intergenerational wealth effects embedded in the manner in which money is created assuming that preferences are separable between consumption goods and real balances and that the consumption goods are normal it is proved that i money is superneutral and ii any other money supply rule is pareto inferior to the chicago rule provided that the government also embarks on a policy of wealth redistribution across generations through the imposition of appropriate lump sum taxes and transfers