Friedman Rule Research Articles

MONETARY POLICY AND ENDOGENOUS MARKET STRUCTURE IN A SCHUMPETERIAN ECONOMY

This study develops a monetary Schumpeterian model with endogenous market structure (EMS) to explore the effects of monetary policy on the number of firms, firm size, economic growth, and social welfare. EMS leads to different results from previous studies in which market structure is exogenous. In the short run, a higher nominal interest rate reduces the growth rates of innovation, output, and consumption and decreases firm size through reduction in labor supply. In the long run, a higher nominal interest rate reduces the equilibrium number of firms but has no steady-state effect on economic growth and firm size because of EMS. Although monetary policy has no long-run growth effect, increasing the nominal interest rate permanently reduces the levels of output, consumption, and employment. Taking transition dynamics into account, we find that welfare is decreasing in the nominal interest rate and the Friedman rule is optimal in this economy.

The Friedman rule and inflation targeting

We use concepts from the financial economics discipline – and in particular the methods of continuous time finance – to develop a monetarist model under which the rate of inflation evolves in terms of a first-order mean reversion process based on a ‘white noise’ error structure. The Fokker–Planck (i.e. the Chapman–Kolmogorov) equation is then invoked to retrieve the steady-state (i.e. unconditional) probability distribution for the rate of inflation. Monthly data for the UK Consumer Price Index (CPI) covering the period from 1988 until 2012 are then used to estimate the parameters of the probability distribution for the UK inflation rate. The parameter estimates are compatible with the hypothesis that the UK inflation rate evolves in terms of a slightly skewed and highly leptokurtic probability distribution that encompasses non-convergent higher moments. We then determine the Hamilton–Jacobi–Bellman fundamental equation of optimality corresponding to a monetary policy loss function defined in terms of the squared difference between the targeted rate of inflation and the actual inflation rate. Optimising and then solving the Hamilton–Jacobi–Bellman equation shows that the optimal control for the rate of increase in the money supply will be a linear function of the difference between the current rate of inflation and the targeted inflation rate. The conditions under which the optimal control will lead to the Friedman rule are then determined. These conditions are used in conjunction with the Fokker–Planck equation and the mean reversion process describing the evolution of the inflation rate to determine the probability distribution for the inflation rate under the Friedman rule. This shows that whilst the empirically determined probability distribution for the UK inflation rate meets some of the conditions required for the application of the Friedman rule, it does not meet them all.

On the optimality of the Friedman rule in a New Monetarist model

We study a monetary model in which buyers choose search intensity and prices are considered as given in a decentralized market. We indicate that the Friedman rule may not be optimal.

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.

An information-based theory of international currency

This paper develops an information-based theory of international currency based on search frictions, private trading histories, and imperfect recognizability of assets. Using an open-economy search model with multiple competing currencies, the value of each currency is determined without requiring agents to use a particular currency to purchase a country's goods. Strategic complementarities in portfolio choices and information acquisition decisions generate multiple equilibria with different types of payment arrangements. While some inflation can benefit the country issuing an international currency, the threat of losing international status puts an inflation discipline on the issuing country. When monetary authorities interact in a simple policy game, the temptation to inflate can lead optimal policy to deviate from the Friedman rule. The calibrated model can produce a welfare cost of losing international status for the issuing country larger than previous findings, though estimates depend critically on inflation rates and information costs.

R&D AND ECONOMIC GROWTH IN A CASH‐IN‐ADVANCE ECONOMY

R&D investment has well‐known liquidity problems, with potentially important consequences. In this study, we analyze the effects of monetary policy on economic growth and social welfare in a Schumpeterian growth model with cash‐in‐advance (CIA) constraints on R&D investment, consumption, and manufacturing. Our main results can be summarized as follows. Under the CIA constraints on R&D and consumption (the CIA constraint on manufacturing), an increase in the nominal interest rate decreases (increases) R&D and economic growth. We also analyze the optimality of Friedman rule and find that Friedman rule can be suboptimal due to a unique feature of the Schumpeterian model.

Floor systems for implementing monetary policy: Some unpleasant fiscal arithmetic

An increasing number of central banks implement monetary policy via a channel system or a floor system. We construct a general equilibrium model to study the properties of these systems. We find that a floor system is weakly optimal if and only if the target rate satisfies the Friedman rule. Unfortunately, the optimal floor system requires either transfers from the fiscal authority to the central bank or a reduction in seigniorage payments from the central bank to the government. This is the unpleasant fiscal arithmetic of a floor system. When the central bank faces financing constraints on its interest expense, we show that it is strictly optimal to operate a channel system.

The Effects of Interest Rate on the Optimal Consumption Path in a Bewley Model with the Co-existence of Currency and Credit

The Effects of Interest Rate on the Optimal Consumption Path in a Bewley Model with the Co-existence of Currency and Credit

Optimal Monetary Policy in OLG Models with Long‐Lived Agents: A Note

AbstractThis note reexamines Crettez, Michel, and Wigniolle (), who studied a two‐period overlapping generations model with cash‐in‐advance constraints and showed that a combination of saving tax and monetary policy involving positive nominal interest rates could achieve the first‐best allocation. The note shows that their result does not hold if agents live for three periods. The implementation of the first best requires the Friedman rule. If agents are long‐lived, saving tax cannot offset a distortion caused by the positive nominal interest rate.

Inflation and Welfare in Retail Markets: Prior Production and Imperfectly Directed Search

This paper considers the effect of monetary policy and inflation on retail markets: goods are dated and produced prior to being retailed; buyers direct their search on price and general quality; buyers’ match‐specific tastes are private information. Sellers set the same price for all buyers, some of whom do not value the good highly enough to buy it. The market economy is typically inefficient as a social planner would have the good consumed. Under free entry of sellers, the Friedman rule is optimal policy. When the upper bound on the number of participating sellers binds, moderate levels of inflation can be welfare improving.

Can growth-enhanced monetary policy improve welfare when people seek social status?

This paper examines the growth and welfare effects from an increase in the rate of money supply in an Ak type growth model with a relative wealth-enhanced social status motive, production externalities, and liquidity constraints. When only consumption is constrained by liquidity, fast money supply can hasten output growth unless seigniorage revenue is wasted and production externalities do not exist. We find that even though money growth normally promotes economic growth, it does not improve welfare when capital stock is over-accumulated. In general, an optimal monetary policy minimizes seigniorage. Our results also conclude that the optimal monetary policy rarely follows the Friedman rule.

Incentive-feasible deflation

For competitive economies in which the real rate of return on money is too low, the standard prescription is to engineer a deflation—that is, to operate monetary policy according to the Friedman rule. Implicit in this recommendation is the availability of a lump-sum tax instrument. In this paper, I view lump-sum tax obligations as a form of debt subject to default. While individuals may want to honor such obligations ex ante, a lack of commitment (the sine qua non of modern monetary theory) may prevent them from the following through on their promises ex post. When this is the case, there may exist an incentive-induced limit to deflationary policy.

Optimal Monetary Policy with the Cost Channel and Monopolistically-Competitive Commercial Banks

This paper studies the optimal nominal policy interest rate in a model with the cost channel and imperfect competition in the banking sector. Due to this market power, the interest rate on deposits is relatively low; in particular it is lower than the policy interest rate. This, in turn, leads to a suboptimal level of deposits and, as a result, to a low level of intermediation. Deviations from the Friedman Rule are optimal in this setup regardless of the assumption about price rigidity; since households can hold their assets in the form of cash or deposits, taxing money, which is an imperfect substitute for deposits, is optimal in order to increase the level of deposits and encourage intermediation. They main results of the paper are robust to the introduction of market power in the loan market as well as stickiness in both the deposit and the loan markets.

Anticipation of Future Consumption: A Monetary Perspective

We adapt the monetary model (Sidrauski 1967) to study the hypothesis of anticipation of future consumption. We assume that anticipation of future consumption affects an agent’s instantaneous utility and that all effects of future consumption on current well‐being are captured by the stock of future consumption. Monetary policy effectiveness is thereby reduced and a zero nominal lower interest rate (and thus the Friedman rule) is destabilizing. Given this, we can derive a “just stable” equilibrium nominal interest rate with matching definitions for inflation and monetary growth. We demonstrate that these implied lower bounds match their historical analogues well.

Monetary Policy with Asset-Backed Money

We study the use of asset-backed money in a neoclassical growth model with illiquid capital. A mechanism is delegated control of productive capi- tal and issues claims against the revenue it earns. These claims constitute a form of asset-backed money. The mechanism determines (i) the number of claims outstanding, (ii) the dividends paid to claim holders, and (iii) the structure of redemption fees. We find that for capital-rich economies, the first-best allocation can be implemented and price stability is optimal. However, for sufficiently capital-poor economies, achieving the first-best allocation requires a strictly positive rate of inflation. In general, the minimum infiation necessary to implement the first-best allocation is above the Friedman rule and varies with capital wealth.

Floor Systems for Implementing Monetary Policy: Some Unpleasant Fiscal Arithmetic

An increasing number of central banks implement monetary policy via a channel system or a floor system. We construct a general equilibrium model to study the properties of these systems. We find that a floor system is weakly optimal if and only if the target rate satisfies the Friedman rule. Unfortunately, the optimal floor system requires either transfers from the fiscal authority to the central bank or a reduction in seigniorage payments from the central bank to the government. This is the unpleasant fiscal arithmetic of a floor system. When the central bank faces financing constraints on its interest expense, we show that it is strictly optimal to operate a channel system.

Growth and welfare effects of monetary policy with endogenous fertility

This paper investigates the economic growth and social welfare implications of monetary policy in an endogenous growth model with endogenous fertility. We show that, in the money-in-the-utility-function framework, endogenous fertility governs the validity of money superneutrality, the transitional dynamics of an anticipated monetary policy, and the optimal monetary policy. Along a balanced growth path, monetary growth increases fertility and reduces the economic growth rate if consumption and real balances are complements or are independent. However, monetary expansion may decrease fertility and increase economic growth if consumption and real balances are substitutes. Generally speaking, the superneutrality of money does not hold in the presence of endogenous fertility. More importantly, with endogenous fertility, the Friedman (1969) rule is no longer a welfare-maximizing monetary policy. We also show that an anticipated inflation induces the transitional dynamics of fertility and the economic growth rate even though the intertemporal elasticity of substitution equals unity. This differs from the conventional notion in the existing literature.

Money is an experience good: Competition and trust in the private provision of money

The interplay between competition and trust as efficiency-enhancing mechanisms in the private provision of money is studied. With commitment, trust is automatically achieved and competition ensures efficiency. Without commitment, competition plays no role. Trust does play a role but requires a bound on efficiency. Stationary inflation must be non-negative and, therefore, the Friedman rule cannot be achieved. The quality of money can be observed only after its purchasing capacity is realized. In this sense, money is an experience good.

Liquidity, Monetary Policy, and the Financial Crisis: A New Monetarist Approach

A model of public and private liquidity integrates financial intermediation theory with a New Monetarist monetary framework. Non-passive fiscal policy and costs of operating a currency system imply that an optimal policy deviates from the Friedman rule. A liquidity trap can exist in equilibrium away from the Friedman rule, and there exists a permanent nonneutrality of money, driven by an illiquidity effect. Financial frictions can produce a financial-crisis phenomenon that can be mitigated by conventional open market operations working in an unconventional manner. Private asset purchases by the central bank are either irrelevant or they reallocate credit and redistribute income. (JEL E13, E44, E52, E62, G01)

A QUANTITATIVE ANALYSIS OF TAX ENFORCEMENT AND OPTIMAL MONETARY POLICY

This paper explores the consequences of tax enforcement policies for monetary policy. Agents may evade taxes by working in the informal sector, but they are detected with positive probability. Workers are rewarded with government benefits that are proportional to formal (taxed) work. When enforcement is imperfect and collecting taxes is costly, the optimal inflation rate is positive and inflation becomes a second-best tax. Deviations from the Friedman rule are optimal and depend on the tax enforcement policies. Using U.S. data, we compute the quantitative effect of different tax structures on inflation and interest rate. We show that different tax enforcement and government spending (benefits) policies induce different optimal outcomes for inflation and interest rates.