Friedman Rule Research Articles

Endogenous innovation scale and patent policy in a monetary schumpeterian growth model

Abstract This paper develops a monetary R&D-driven endogenous growth model featuring endogenous innovation scales and the price-marginal cost markup. To endogenize the step size of quality improvement, we propose a tradeoff mechanism between the risk of innovation failure and the benefit of innovation success in R&D firms. Several findings emerge from the analysis. First, a rise in the nominal interest rate decreases economic growth; however, its relationship with social welfare is ambiguous. Second, either strengthening patent protection or raising the professional knowledge of R&D firms leads to an ambiguous effect on economic growth. Third, the Friedman rule of a zero nominal interest rate fails to be optimal in view of the social welfare maximum. Finally, our numerical analysis indicates that the extent of patent protection and the level of an R&D firm’s professional knowledge play a crucial role in determining the optimal interest rate.

Monetary policy in a Schumpeterian economy with endogenous fertility and human capital accumulation

This study investigates the growth and welfare effects of monetary policy in a Schumpeterian economy featuring cash-in-advance (CIA) constraints and two engines of growth: innovation from R&D and human capital accumulation from endogenous fertility. Our theoretical analysis considers the cases of various CIA constraints. When the CIA constraint is only on consumption, higher inflation retards economic growth by weakening human capital accumulation. When the CIA constraint is only on R&D, higher inflation would generate a negative or U-shaped effect on economic growth, depending on the interplay between inflationary effects on innovation and human capital accumulation. When the CIA constraint is only on manufacturing, the growth effect of inflation could be positive (negative) if the positive growth effect from technological progress dominates (is dominated by) the negative effect from human capital accumulation. Our quantitative analysis finds a generally negative inflation-growth relationship in the calibrated economy. Moreover, the welfare effect of inflation is also negative, implying that the Friedman rule is optimal.

Naïve agents with non-unitary discounting rate in a monetary economy

We incorporate naïve agents with a non-unitary discounting rate into a cash-in-advance (CIA) model. Through this extension, we obtain the following results. First, we show that there exists an equilibrium in which the CIA constraint does not bind when individuals discount their utilities from future consumption lower than their utilities from future leisure time. Notably, this non-binding equilibrium exists even if the nominal interest rate takes a positive value. Second, we demonstrate that increases in the money supply growth rate decrease individuals’ saving rates in equilibrium, where the CIA constraint does not bind. Third, we exhibit that when the equilibrium where the CIA constraint does not bind exists, the welfare level of this equilibrium can be higher than that of the equilibrium in which the CIA constraint binds. Moreover, we deduce that the Friedman rule cannot be optimal in the equilibrium in which the CIA constraint binds and present the result that the optimal level of the optimal nominal interest rate is affected by the difference in the discount rates.

Coexistence of money and interest-bearing bonds

I construct a monetary model with agents that face idiosyncratic shocks to how they discount future utility. Once shocks are revealed, agents trade money for bonds in a financial market, then money for goods in a goods market, and finally move into the next time period. Away from the Friedman rule, money is scarce so that those who turn out to care little about the future, sell bonds at a discount to obtain money for immediate consumption—in the financial market, they reduce the savings value of their asset portfolio to obtain more liquid asset positions. This generates a net re-distribution of savings from agents that attach a low value to the future, to agents that attach a high value to the future. Ex-ante utility increases because losing savings when the future has low value, is dominated by receiving savings when the future has high value. The scarcity of money, however, leads to binding liquidity constraints in the goods market, which reduces ex-ante utility. The financial-market effect can dominate the goods-market effect, in which case the coexistence of money and interest-bearing bonds arises for an optimal policy.

Liquidity, the Mundell–Tobin Effect, and the Friedman Rule

AbstractWe investigate how a positive relation between inflation and capital investment (the Mundell–Tobin effect, MT‐E) affects optimal monetary policy in a framework that combines overlapping generations and new Monetarist models. We find that inflation rates above the Friedman rule are optimal if and only if there is an MT‐E. In the absence of the MT‐E, the Friedman rule is optimal. With an MT‐E, increasing inflation above the Friedman rule leads to a first‐order welfare gain from increasing capital investment, and only to a second‐order welfare loss from reducing consumption in markets where liquidity matters.

Milton Friedman and the Road to Monetarism: A Review Essay

Milton Friedman and the Road to Monetarism: A Review Essay

Optimal long-run money growth rate in a cash-in-advance economy with labor-market frictions

AbstractWe revisit the Friedman rule in a labor search model and extend Heer (2003), Cooley and Quadrini (2004), and Wang and Xie (2013) to one that allows for endogenous growth. We show that, even without a liquidity effect or a CIA constraint on firms’ wage payment, our model offers a different channel for moderate money growth to increase welfare. Intuitively, in a one-sector endogenous growth economy, the technology is of constant returns with respect to capital. When the labor market is frictional, a moderate increase in money growth induces an expansion in vacancy and employment. Labor and capital are complements in production. With an increase in employment, when the technology is neoclassical, the decreasing return in capital leads to a lower marginal product of labor. However, in an endogenous growth framework wherein the technology exhibits socially constant returns in capital, the marginal product of labor is constant. Due to a constant marginal product of labor, modest inflation raises employment, enlarges economic growth, and increases welfare. Moreover, the optimal long-run inflation rate departs from the Friedman rule, even when the Hosios rule holds. Finally, we find that our model with sustainable growth fits the data better than that without sustainable growth.

Optimal Taxes under Private Information: The Role of Inflation

AbstractOnce explicit information available to the taxing authority and incentives associated with private information problems are explicitly taken into account, only a limited set of policy instruments are consistent with agents not engaging in side trades. Within this spirit, we study the role of taxes and inflation in minimizing the dead‐weight loss associated with the provision of good incentives and other market imperfections when fiat money is essential. When the government has a rich information set and can observe savings, effort, and consumption in frictionless markets, the constrained efficient allocation can be achieved with affine history‐dependent consumption taxes. Thus, monetary policy is redundant. In contrast, when the government observes sales, rather than actual consumption, a tax arbitrage exists. Uniform affine consumption taxes prevent side trades. We also find that a deviation from the Friedman rule is optimal as it helps induce truth‐telling and alleviate a pecuniary externality. However, optimal monetary and fiscal policies in this setting cannot implement the constrained efficient allocation.

Monetary Policy in a Schumpeterian Growth Model with Vertical R&D Sectors

AbstractWe explore the growth and welfare effects of monetary policy in a Schumpeterian economy with cash‐in‐advance (CIA)‐constrained research and development (R&D) investment in both the upstream and downstream sectors. We show that the nominal interest rate can have an inverted‐U relation with economic growth due to its effects on labor allocations between manufacturing and R&D and between the R&D sectors. Furthermore, aggregate R&D overinvestment is generally sufficient but not necessary for the Friedman rule of zero nominal interest rates to be suboptimal. Calibrated using data from U.S. manufacturing firms, our model features a positive welfare‐maximizing nominal interest rate despite aggregate R&D underinvestment.

Tax smoothing and optimal inflation persistence in RBC monetary models revisited

This article re-examines the optimality of tax smoothing and optimal inflation persistence in the context of monetary models with cash constraints where the Friedman rule is not optimal. I consider distortionary taxes on either consumption or labor income. As a consequence of the non-optimality of the Friedman rule, the Ramsey-optimal policy features a tax rate volatility that is orders of magnitude larger than the cornerstone tax-smoothing result of the standard Ramsey literature. The Ramsey results also imply an optimal inflation rate that is much more persistent than the existing results. When all consumption goods are subject to a cash constraint, purposeful tax and interest rate volatilities are used to smooth wedges. Therefore, in contrast to the widely accepted view in the literature that in RBC models wedge smoothing implies tax smoothing, this paper shows that this is not necessarily true. I also discuss the Ramsey problem in the context of the cash-credit goods framework with non-homothetic preferences where neither tax-smoothing nor wedge smoothing result necessarily holds when the Friedman rule ceases to be optimal.

Coexistence of Money and Interest-Bearing Bonds

This paper revisits how coexistence of money and bonds can make a society better off. For this purpose, a model is constructed in which payment instruments matter for settling real transactions and savings instruments matter because agents differ in how they discount future utility. Because bonds and money differ in their characteristics as payment and savings instruments, the model is able to explain the coexistence puzzle for an optimally chosen monetary policy. Such a policy trades-offs efficiency in financial markets, in which money is traded for bonds, with efficiency in goods markets, in which money is traded for a real good. Financial markets can achieve a better distribution of savings when agents are constrained by their money holdings, but this is bad for efficiency in goods markets. The former effect can dominate the latter so that optimal policy deviates from the Friedman rule.

Time Consistency and Counterproductive Monetary Policy Cooperation in a Two‐Country New Keynesian Model

AbstractWe use a two‐country New Keynesian model to revisit the issue of counterproductive monetary policy cooperation. By analyzing the optimal commitment, discretionary, and sustainable policies, we show how counterproductive cooperation and governments' commitment ability are linked. The global Friedman rule, whereby both countries always adopt the Friedman rule, maximizes the joint welfare for a wide range of parameters. However, cooperation makes the global Friedman rule unimplementable under discretionary policies and harder to sustain under sustainable policies. Counterproductive cooperation therefore arises naturally when governments lack commitment ability and some stronger commitment device than reputation is necessary to achieve gains from cooperation.

THE FRIEDMAN RULE: EXPERIMENTAL EVIDENCE

AbstractWe evaluate the Friedman rule for optimal monetary policy in a laboratory economy based on Lagos–Wright (Journal of Economic Theory 145 (2010), 1508–24). We explore two implementations of Friedman's rule: one involving deflationary monetary policy and another where interest is paid on money. We compare the welfare consequences of the Friedman rule with two other policies: a constant money supply regime and a regime where the money supply grows at a constant k%. Counter to theory, we find that the Friedman rule is not welfare‐improving, performing no better than the constant money regime. By one welfare measure, the k% money growth rate regime performs best.

Interest on reserves, helicopter money and new monetary policy.

We build a nonlinear dynamic model with currency, demand deposits and bank reserves. Monetary base is controlled by central bank, while money supply is determined by the interactions between central bank, commercial banks and public. In economic crises when banks cut loans, monetary policy following a Taylor rule is not efficient. Negative interest on reserves or forward guidance is effective, but deflation is still likely to be persistent. If central bank simultaneously targets both interest rate and money supply by a Taylor rule and a Friedman's k-percent rule, inflation and output are stabilized. An interest rate rule policy is just a subset of a more general monetary policy framework in which central bank can move interest rate and money supply in every direction.

International outsourcing, exchange rates, and monetary policy☆

Firms’ decisions to outsource the production of intermediate inputs abroad depend on the macroeconomic environment set by governments’ monetary and foreign exchange policies, while the relocations of production change liquidity demands in the financial markets and affect policy effectiveness. This paper studies theoretically the interdependence of firms’ sourcing decisions and governments’ conducts of policies. By constructing a two-country, monetary model with segmented financial markets to incorporate the microeconomic foundations of firms’ make-or-buy decisions and highlight the working capital needs of both buyers and suppliers of intermediate inputs, the endogenous adjustments of international outsourcing at both the extensive and intensive margins are examined. It shows that the adjustments at the intensive margin of firms’ sourcing decisions will dampen the effects of temporary monetary shocks under a fixed exchange rate if the firms face low upfront payments to their foreign suppliers. The adjustments at the extensive margin can alter qualitatively the impacts of a currency revaluation and help explain the perverse effect on the trade balance. Implementing the Friedman rule and a fixed exchange rate regime can address both margins so that the socially optimal allocation can be achieved.

Shadow banks, banking policies and China’s macroeconomic fluctuations

This paper develops a model of the Chinese economy using a DSGE framework that accommodates a banking sector and money. The model is used to shed light on the period of the Global Financial Crisis. It differs from other applications in the use of Indirect Inference to estimate and test the model. Officially mandated bank lending and government spending were used to supplement monetary policy to aggressively offset shocks to demand. This paper examines the efficacy of monetary policy in terms of the reduction in the frequency of severe economic slowdowns. We find that monetary policy can be used more vigorously to stabilise the economy, making direct banking controls and fiscal activism unnecessary. A nominal GDP targeting monetary policy is the most efficient, compared with a conventional Taylor Rule, a Friedman rule or a price level targeting rule.

The Nature of Money in a Convertible Currency World

In a world where the means of exchange is convertible into the numeraire consumption good at a fixed rate, no one wants to hold money over time – and due to convertibility there is no means by which the Friedman rule can generate deflation. This is the environment we study in this paper in order to demonstrate that there is still a way to reach the first-best: institutionalize the naked shorting of the unit of account, or in other words establish a banking system.
 To motivate the benefits of a banking system, the environment has real productivity shocks that are constantly changing the optimal level of economic activity, so the optimal quantity of money is inherently stochastic. Efficiency in such an environment requires the capacity to expand the money supply on an “as needed” basis. We show how a debt-based payments system that relies on banks to certify the individual debtors’ IOUs addresses the monetary problem.
 This model explains (i) central bank monetary policy as a means of stabilizing the banking system and (ii) usury laws as means of promoting equilibria that favor non-banks over those that favor banks. Furthermore, by modeling a commercial bank-based monetary system as an efficient solution to a payments problem this paper develops a theoretic framework that may be used to evaluate central bank digital currency proposals.

Relationship finance, informed liquidity, and monetary policy

We study the aggregate effects of credit relationships in an economy where lenders provide liquidity and expertise to firms in distress. Lenders' effort in the restructuring of firms' investments endogenously depends on their financial involvement in investments. Firms trade off the benefits of precautionary internal liquidity with the need to incentivize lenders' restructuring effort through their financial involvement. We find that, through these intensive margin effects, credit relationships can induce overinvestment, calling for a positive interest rate policy that departs from the Friedman rule. Credit relationships, however, can enhance the resilience of investment to economic conditions. Unconventional monetary policies that inject liquidity into the lending sector enhance the stabilizing effects of credit relationships but have ambiguous welfare consequences.

Coexistence of Money and Interest-Bearing Bonds

This paper revisits how coexistence of money and bonds can make a society better off. For this purpose, a model is constructed in which payment instruments matter for settling real transactions and savings instruments matter because agents differ in how they discount future utility. Because bonds and money differ in their characteristics as payment and savings instruments, the model is able to explain the coexistence puzzle for an optimally chosen monetary policy. Such a policy trades-offs efficiency in financial markets, in which money is traded for bonds, with efficiency in goods markets, in which money is traded for a real good. Financial markets can achieve a better distribution of savings when agents are constrained by their money holdings, but this is bad for efficiency in goods markets. The former effect can dominate the latter so that optimal policy deviates from the Friedman rule.

Monetary Policy in a Schumpeterian Growth Model with Two R&D Sectors

We explore the growth and welfare effects of monetary policy in a two-sector Schumpeterian economy with cash-in-advance (CIA) constrained R&D investment in both sectors. We show that a nominal interest rate increase generates two effects on equilibrium labor allocation: a manufacturing-R&D-reallocation effect and a cross-R&D-sector effect. The former reduces economic growth by shifting labor from R&D to production, whereas the latter can enhance it by shifting labor from the less productive R&D sector to the more productive one. From the welfare perspective, we show that unless the high productivity R&D sector is severely more CIA-constrained than the low productivity one, aggregate R&D overinvestment is sufficient but not necessary for the Friedman rule of monetary policy to be suboptimal. Our benchmark parameterization suggests that a positive nominal interest rate is optimal despite that it exacerbates the aggregate R&D underinvestment problem.