Optimality of the Friedman rule in economies with distorting taxes

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.     

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: Old and new

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.     

Inflation and Welfare: A Search Approach

This paper uses a search model of monetary exchange to provide new insights for evaluating the welfare costs of inflation. We first show that the search model of money can rationalize the estimates of the welfare cost of inflation based on the "welfare triangle" methodology of Bailey (1956) and Lucas (2000) provided that buyers appropriate the social marginal benefit of their real balances. For other mechanisms, the measure given by the welfare triangle has to be scaled up by a factor that increases with sellers' market power. We introduce capital and endogenous participation decisions and study how the cost of inflation is affected. We provide calibrated examples in which a deviation from the Friedman rule is optimal.     

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.     

Model Uncertainty and Delegation: A Case for Friedman's k-Percent Money Growth Rule?

Model uncertainty affects the monetary policy delegation problem. If there is uncertainty with regards to the determination of the delegated objective variables, the central bank will want robustness against potential model misspecifications. We show that with plausible degree of model uncertainty, delegation of the Friedman rule of increasing the money stock by k percent to the central bank will outperform commitment to the social loss function (flexible inflation targeting). The reason is that the price paid for robustness under flexible inflation targeting outweighs the inefficiency of money growth targeting. Imperfect control of money growth does not change this conclusion.     

In Old Chicago: Simons,Friedman, and the Development of Monetary‐Policy Rules

This paper examines the different policy rules proposed by Henry Simons, who, beginning in the mid‐1930s, advocated a price‐level stabilization rule, and by Milton Friedman, who, beginning in the late‐1950s, advocated a rule that targeted a constant growth rate of the money supply. Although both rules shared the objective of eliminating the policy uncertainty emanating from discretion, they differed because of the different views of Simons and Friedman about the stability of secular relationships. Simons’ rule relates to modern rules that emphasize the pursuit of price stability as representing optimal monetary policy.     

Bargaining and the value of money

Search models of monetary exchange have typically relied on Nash [1950. The bargaining problem. Econometrica 18, 155-162] bargaining, or strategic games that yield an equivalent outcome, to determine the terms of trade. By considering alternative axiomatic bargaining solutions in a search model with divisible money, we show that the properties of the bargaining solutions do matter both qualitatively and quantitatively for questions of first-degree importance in monetary economics such as: (i) the efficiency of monetary equilibrium; (ii) the optimality of the Friedman rule and (iii) the welfare cost of inflation.     

Monetary policy and distribution

A segmented markets model of monetary policy is constructed, in which a novel feature is goods market segmentation, and its relationship to conventional asset market segmentation. The implications of the model for the response of prices, interest rates, consumption, labor supply, and output to monetary policy are determined. As well, optimal monetary policy is studied, as are the costs of inflation. The model features persistent nonneutralities of money, relative price effects of increases in the money supply, persistent liquidity effects, and a negative Fisher effect from a money supply increase. A Friedman rule is in general suboptimal.     

Implications of habit formation for optimal monetary policy

We study the implications for optimal monetary policy of introducing habit formation in consumption into a general equilibrium model with sticky prices. Habit formation affects the model's endogenous dynamics through its effects on both aggregate demand and households’ supply of output. We show that the objective of monetary policy consistent with welfare maximization includes output stabilization, as well as inflation and output gap stabilization. We find that the variance of output increases under optimal policy, even though it acquires a higher implicit weight in the welfare function. We also find that a simple interest rate rule nearly achieves the welfare-optimal allocation, regardless of the degree of habit formation. In this rule, the optimal responses to inflation and the lagged interest rate are both declining in the size of the habit, although super-inertial policies remain optimal.     

习惯形成下的最优货币政策

著名的弗里德曼规则指出,最优货币政策可以通过设置名义利率等于0来实现。本文构造了基于习惯形成的最优货币政策模型,并使用主方法求解了模型。本文的研究表明,当家庭的效用函数偏好具有习惯形成的特点时,弗里德曼规则仍然成立。     

Optimal Constrained Interest-Rate Rules

We show that if policymakers compute the optimal unconstrained interest-rate rule within a Taylor-type class, they may be led to rules that generate indeterminacy and/or instability under learning. This problem is compounded by uncertainty about structural parameters since an optimal rule that is determinate and stable under learning for one calibration may be indeterminate or unstable under learning under a different calibration. We advocate a procedure in which policymakers restrict attention to rules constrained to lie in the determinate learnable region for all plausible calibrations, and that minimize the expected loss, computed using structural parameter priors, subject to this constraint.     

A model of money with multilateral matching

We develop a model of decentralized monetary exchange to examine the distributional effects of inflation across heterogeneous agents. The agents have private information about their productivity, preferences, or money holdings. Matching is multilateral and each seller is visited by a stochastic number of buyers. The good is allocated according to a second-price auction in money. In equilibrium, homogeneous buyers hold different amounts of money leading to price dispersion. We find the closed-form solution for the distribution of money holdings. Entry of sellers is suboptimal except at the Friedman rule. Inflation acts as a regressive tax.     

Optimal monetary policy in an economy with incomplete markets and idiosyncratic risk

This study investigates an incomplete markets economy in which the saving behavior of a continuum of infinitely lived agents is influenced by precautionary saving motives and borrowing constraints. Agents can use two types of assets (interest bearing IOUS and money) to smooth consumption. Money is valued because of a timing friction in the bond market. In particular, the bond market closes before agents observe their idiosyncratic productivity shock. I find that the Friedman rule is not optimal for this economy. The results indicate that the optimal allocation has a rate of inflation of 10%, and a positive amount of private credit held by the government. A positive inflation rate transfers resources from agents with big endowments to those holding bonds which improves risk sharing, and therefore, welfare. However, for higher rates of inflation, agents economize on money holdings, offsetting the insurance effects, and causing a reduction in welfare. Furthermore, higher rates of inflation discourage agents from borrowing, and the endogenous lower bound on bond holdings is higher than the exogenous borrowing limit. High rates of inflation, therefore, exacerbate frictions in the bond market.     

Robust monetary policy with imperfect knowledge

We examine the performance and robustness properties of monetary policy rules in an estimated macroeconomic model in which the economy undergoes structural change and where private agents and the central bank possess imperfect knowledge about the true structure of the economy. Policymakers follow an interest rate rule aiming to maintain price stability and to minimize fluctuations of unemployment around its natural rate but are uncertain about the economy's natural rates of interest and unemployment and how private agents form expectations. In particular, we consider two models of expectations formation: rational expectations (RE) and learning. We show that in this environment the ability to stabilize the real side of the economy is significantly reduced relative to an economy under RE with perfect knowledge. Furthermore, policies that would be optimal under perfect knowledge can perform very poorly if knowledge is imperfect. Efficient policies that take account of private learning and misperceptions of natural rates call for greater policy inertia, a more aggressive response to inflation, and a smaller response to the perceived unemployment gap than would be optimal if everyone had perfect knowledge of the economy. We show that such policies are quite robust to potential misspecification of private sector learning and the magnitude of variation in natural rates.     

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.     

Quantifying and sustaining welfare gains from monetary commitment

Our objectives are: to quantify the stabilization welfare gains from commitment; to examine how commitment to an optimal rule can be sustained as an equilibrium; to find a simple interest rate rule that approximates the optimal commitment one. We utilize an empirical micro-founded euro-area DSGE model, a quadratic approximation of household utility as the welfare criterion, employing a nominal interest rate lower bound. In contrast to previous studies, we find significant commitment stabilization gains of around a 0.4-0.5% equivalent permanent consumption increase, and with higher price stickiness gains over 2%. We find that a simple optimized commitment rule responding to inflation and the real wage mimics the optimal one.     

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 nonzero 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‐Grohè and Uribe (2004a) —follow from the violation of the Diamond and Mirrlees (1971) principle on production efficiency.     

Monetary policy under model and data-parameter uncertainty

Empirical Taylor rules are much less aggressive than those derived from optimization-based models. This paper analyzes whether accounting for uncertainty across competing models and (or) real-time data considerations can explain this discrepancy. It considers a central bank that chooses a Taylor rule in a framework that allows for an aversion to the second-order risk associated with facing multiple models and measurement-error configurations. The paper finds that if the central bank cares strongly enough about stabilizing the output gap, this aversion leads to significant declines in the coefficients of the Taylor rule even if the central bank's loss function assigns little weight to reducing interest rate variability. Furthermore, a small degree of aversion can generate an optimal rule that matches the empirical Taylor rule.