Friedman Rule Research Articles

Foreign Demand for Domestic Currency and the Optimal Rate of Inflation

We characterize the Ramsey optimal rate of inflation in a model with a foreign demand for domestic currency. In the absence of such demand, the model implies that the Friedman rule—deflation at the real rate of interest—is optimal. We show analytically that in the presence of a foreign demand for domestic currency, this result breaks down. Calibrated versions of the model deliver optimal annual rates of inflation between 2% and 10%. The domestically benevolent government imposes an inflation tax to extract resources from the rest of the world in the form of seignorage revenue.

The 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 main message of the paper is that as long as the modified golden rule is attained, the 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 the Friedman rule for a different second‐best environment wherein human capital accumulation is controlled but not physical capital accumulation and (ii) existence of a negative relationship between money growth rate and the economy’s endogenous growth rate.

Money and risk of loss in an asset market segmentation model

A simple asset market segmentation model is constructed to study the relationship between inflation and theft when money is the only medium of exchange. In equilibrium, money is nonneutral and monetary policy has asymmetric effects on theft, real money holding, and consumption. The distributional effects persist over periods and the liquidity effect may arise. Next, given the asymmetric effects of monetary policy, the crime rates differ across economic individuals in order to smooth out consumption fluctuations. Given the conditions of stealing technology, monetary equilibrium would not be always sustainable. Finally, the optimal money growth rate is to minimize theft and the Friedman rule is suboptimal.

Endogenous skill heterogeneity and inflation

This paper examines the implications of ex ante skill heterogeneity for long run inflation. We develop a dynamic general equilibrium model in which there are two types of labor (skilled and unskilled), two types of capital (human and physical), and money is introduced via a cash in advance constraint on consumption purchases. Skill heterogeneity is characterized in terms of (i) a parameter governing the ease with which the two types of labor can be substituted for each other in production; and (ii) the “productivity” of human capital in the production of skill. The model includes the accumulation of human capital which in turn creates skill heterogeneity among workers through an efficiency wage mechanism. Numerical experiments indicate that there is a range of parameter estimates in which the Friedman Rule may not be optimal. Furthermore, our quantitative experiments also indicate that there is a range of parameter values in which a greater degree of skill heterogeneity may be associated with a greater preference for inflation. Empirically, we also find that the inflation and heterogeneity correlation is positive.

Financial market participation, financial intermediation, and monetary policy

It is not uncommon for the Friedman rule to be optimal in neoclassical models with money. Notably, previous studies also find that financial intermediation is not welfare improving when money is costless to hold. This paper departs from previous studies by highlighting the importance of participation costs in financial markets for the participation in financial intermediation and monetary policy. As in previous work, the Friedman rule is optimal. However, I demonstrate that the welfare gains from disinflation are much higher when savings are intermediated if direct participation costs in financial markets are significant. Consequently, financial intermediation can still be optimal at the Friedman rule.

The Simple Analytics of Money and Credit in a Quasi-Linear Environment

For economies in which the real rate of return on money is too low, the standard prescription is to deflate prices 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 agree to honor such obligations ex ante, a lack of commitment (the sine qua non of modern monetary theory) may prevent them from following through on their promises ex post. In such cases, there may exist an incentive-induced limit to deflationary policy.

New probability theory compatible with the new conception of modern thermodynamics. Economics and crisis of debts

We show that G\"odel's negative results concerning arithmetic, which date back to the 1930s, and the ancient "sand pile" paradox (known also as "sorites paradox") pose the questions of the use of fuzzy sets and of the effect of a measuring device on the experiment. The consideration of these facts led, in thermodynamics, to a new one-parameter family of ideal gases. In turn, this leads to a new approach to probability theory (including the new notion of independent events). As applied to economics, this gives the correction, based on Friedman's rule, to Irving Fisher's "Main Law of Economics" and enables us to consider the theory of debt crisis.

HYPERBOLIC DISCOUNTING AND POSITIVE OPTIMAL INFLATION

The Friedman rule states that steady-state welfare is maximized when there is deflation at the real rate of interest. Recent work by Khan, King, and Wolman [Review of Economic Studies10 (4), 825–860] uses a richer model but still finds deflation optimal. In an otherwise standard New Keynesian model we show that, if households have hyperbolic discounting, small positive rates of inflation can be optimal. In our baseline calibration, the optimal rate of inflation is 2.1% and remains positive across a wide range of calibrations.

Monetary and Fiscal Policies in a Heterogeneous-Agent Economy

I study the effects of long-run inflation and income taxation in an economy where households face uninsurable idiosyncratic risks. I construct a tractable competitive search framework that generates dispersion of prices, income and wealth. I analytically characterize the stationary equilibrium and the policy effects on individual choices. Quantitative analysis finds that monetary and fiscal policies have distinctive effects on macro aggregates, such as output, savings, wealth dispersion, income and consumption inequalities. There can be a hump-shape relationship between welfare and the respective policies. Overall, welfare can be maximized by a deviation from the Friedman rule, paired with distortionary income taxation.

Credit, Externalities, and Nonoptimality of the Friedman Rule

We construct a cash-credit model with positive externalities in the production of credit goods. It is shown that under suitable conditions, the Friedman rule is not optimal and there exists an optimal nominal interest rate that maximizes the social welfare and output. This is because increasing the nominal interest rate improves sectoral misallocations caused by externalities in our economy.

Anticipation of Future Consumption: A Monetary Perspective

We adapt the (Sidrauski, 1967) monetary model 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 wellbeing 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.

Liquidity, welfare and distribution

This work presents a dynamic general equilibrium model where wealth distribution is endogenous. I provide channels of causality that suggest a complex relationship between financial markets and the real activity which breaks down the classical dichotomy. As a consequence, the Friedman rule does not hold. In terms of the current events taking place in the world economy, this paper provides a rationale to advert against the perils of an economy satiated with liquidity. Efficiency and distribution cannot thus be considered as separate attributes once we account for the interactions between financial markets and the economic performance.

Welfare Costs of Inflation and the Circulation of US Currency Abroad

Empirical studies of the shoe-leather costs of inflation are typically computed using M1 as a measure of money. Yet, official data on M1 includes all currency issued, regardless of the country of residence of the holder. Using adjusted monetary data, we show that the failure to control for currency held by non residents may lead to significantly overestimating the welfare costs for the domestic economy. In particular, our estimates of shoe-leather costs are minimized for a positive but moderate value of the inflation rate, thereby justifying a deviation from the Friedman rule in favor of the Fed’s current policy.

On the Limitations of Monetary Policy

This paper argues that in a homogeneous monetary Real Business Cycle economy where a complete set of nominal contingent claims exist, the requirement to collateralize loans, alone, does not affect the equilibrium allocation when monetary policy is chosen optimally: the Pareto optimal allocation can be supported. Rather, it is the presence of additional inefficiencies such as market incompleteness or heterogeneity of agents that limits the ability of optimal monetary policy, and more precisely, inflation, to support the first best allocation. In our model policy is non-Ricardian or equivalently outside money exists, and the Central Bank trades only in short-term nominally risk-free bonds: as a consequence monetary policy that sets rates of interest and accommodates money demand effectively determines the allocation of prices at equilibrium. A Friedman rule (r=0), which would be optimal in the absence of collateral constraints, here it is not: at the resulting prices collateral constraints bind. A path of prices that avoids binding collateral constraints necessarily involves a non-zero interest rate. The path of prices that supports the Pareto optimal allocation occurs when the collateral constraint binds: a positive inflation tax on money balances is efficient. For interest rates that permit the collateral constraint to bind, a policy of stable inflation (alternatively, money growth) implies that the collateral constraint binds after a sequence of positive (respectively negative) productivity shocks followed by a negative (respectively positive) productivity shock.

The payment mechanisms and liquidity effects

A general equilibrium model with multiple means of payment in segmented markets is constructed to study the liquidity effects. It is shown that, under certain conditions, stored value – money issued by private entrepreneurs weakens, but does not completely eliminate the liquidity effects that exist when stored value is prohibited. The Friedman rule can be optimal in the regime with floating stored value. The impact of monetary policy now depends not only on the monetary intervention of the central bank, but also on the quantity of the outstanding private money and its velocity.

SEARCH, WELFARE, AND THE “HOT POTATO” EFFECT OF INFLATION

An increase in inflation causes people to hold smaller real balances and to speed up their spending. Virtually all monetary models capture the first—inflation tax—effect. Few capture the second—hot potato—effect. Those that do associate negative welfare consequences with the hot potato effect. Because both the inflation tax and the hot potato effect imply that inflation has negative effects on welfare, an optimal monetary policy is characterized by the Friedman rule. In the model presented here, there is a hot potato effect, but—all else held constant—the hot potato effect has positive consequences for welfare. As a result, a departure from the Friedman rule can be socially desirable.

Monetary policy when wages are downwardly rigid: Friedman meets Tobin

Monetary policy in an economy with both downwardly rigid wages and a transaction motive for money demand is studied using a dynamic stochastic general equilibrium model. The two key features of the model imply that both Tobin's “inflation grease” argument and Friedman's rule are operative, and so optimal inflation may be positive or negative. The Simulated Method of Moments is used to estimate the nonlinear model based on its second-order approximation. Results indicate that the Ramsey policy that maximizes social welfare involves an average inflation rate of about 0.4% per year. In the more realistic case where a central banker follows a simple targeting policy, the optimal inflation target is about 1% per year. We view this result as providing support for the low, but strictly positive, inflation targets used in many countries.

Financial market imperfections and monetary policy strategy

In a model with imperfect money, credit and reserve markets, we examine if an inflation-targeting central bank applying the funds rate operating procedure to indirectly control market interest rates also needs a monetary aggregate as policy instrument. We show that if private agents use information extracted from money and financial markets to form inflation expectations and if interest rate pass-through is incomplete, the central bank can use a narrow monetary aggregate and the discount interest rate as independent and complementary policy instruments to reinforce the credibility of its announcements and the role of inflation target as a nominal anchor for inflation expectations. This study shows how a monetary policy strategy combining inflation targeting and monetary targeting can be conceived to guarantee macroeconomic stability and the credibility of monetary policy. Friedman's k-percent money growth rule, which can generate dynamic instability, and two alternative stabilizing feedback monetary targeting rules are examined.

Monetary Policy and Banking Structure

In this paper, I examine the differences in optimal monetary policy in various banking systems. In particular, I compare two monetary economies: one with a competitive banking system and the other with a monopolistic one. In addition, the optimality of the discount window policy is considered. It is shown that the Friedman rule is the optimal monetary policy in a monopolistic banking economy, and the zero-inflation policy is optimal in a competitive banking economy under appropriate parameters. In addition, the combination of the Friedman rule and the discount window policy can achieve efficient allocation in both banking systems.

Friedman meets Becker and Mulligan in a monetary neoclassical growth model

We study a neoclassical growth model with the time preference determined by resources spent on imagining future pleasures along the line of Becker and Mulligan (Q J Econ 112:729–758, 1997). We introduce money into the economy via a cash-in-advance constraint and study the effect of higher seignorage taxes or higher monetary growth rates on capital, consumption and welfare in the long run. We find that if the fraction of investment constrained by cash is smaller than a threshold, the negative-monetary-growth Friedman (The Optimum Quantity of Money and Other Essays, 1969) rule does not hold and the optimal inflation rate is positive. Calibrating our model yields a mild optimal inflation rate per annum with a switch from zero inflation to optimal inflation creating a sizable welfare gain in terms of consumption equivalence.