Foreign Demand for Domestic Currency and Optimal Rate of Inflation v1

8/8/2019 Foreign Demand for Domestic Currency and Optimal Rate of Inflation v1

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Introduction

More than half of US Currency circulates abroad. As of December 2005, about $450 billion

of the $760 billion of US banknotes were held in other countries.

In absence of a foreign demand for local currency, the welfare maximizing optimal rate of

inflation follows the Friedman rule. Friedman rule is based on the idea that in the long run

inflation is a monetary phenomenon. The opportunity cost of holding money should equal

the social cost of creating additional fiat money. It is assumed that, since the marginal cost

of creating additional money is approximately zero, this opportunity cost; also the nominal

rates of interest should be zero.

Fishers rule says:

Nominal Interest rate = Real Interest Rate + Expected Inflation

if Nominal Interest Rate is 0,

Expected inflation = - Real Interest Rate

Analytically, this can be shown to be optimal in the absence of foreign demand for

domestic currency. However, the results are different when there is a substantial foreign

demand. Optimal rates of Inflation have been observed to be anywhere from 2-10%.

In this paper, the authors first present a dynamic monetary model with a foreign demand for

domestic currency, and then establish the optimality and failure of Friedman rule in the

corresponding absence and presence of the foreign demand of domestic currency. They

further go on to show that under plausible conditions, sizable (2-10%) deviation can bejustified from the inflation associated with Friedmans rule.

USDCirculation

In 2005, $450 billion

of the $760 billion of

US banknotes were

held in other

countries.

FriedmansRule

Central bank should

seek a rate of

deflation equal to

the real interest

rate on government

bonds and other safe

assets, to make the

nominal interest rate

zero.

Foreign Demand for Domestic Currency and Optimal rateof inflation

About the following paper

Summarized By: Anoj Ramasamy Sundar (HT094307J)

NBER Working Paper: 15494

Authors: Stephanie Schmitt-Grohe and Martin Uribe

Paper title: Foreign Demand for domestic Currency and Optimal Rate of Inflation

Published on: November 2009

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The Model and the Dynamic Ramsey Equilibrium

Consider an economy populated by large number of identical households. Each household

has preferences defined over sequences of consumption (ct) and effort (ht) choices in a

time discounted aggregate utility function, over an infinite time horizon.

The single period utility, U is increasing in consumption and decreasing in effort (more

work, less leisure), and strictly concave. Nominal money holdings Mtd

is also the money

supply that facilitates domestic consumption purchases in the economy at any time period.

Since money can be reused for transactions, we will also define Money velocity (vtd) and

transaction cost s(vt) that decreases with increasing money velocity.

Households invest in one-period nominal bonds Bt at a nominal interest rate of Rt.Households supply labor at a real wage rate (wt), and receive profit t from ownership of

firms, and pay income taxes at flat rate of t. To prevent households from engaging in

Ponzi-type schemes, a restriction is placed such that in long run, net nominal liabilities grow

at a rate smaller than the nominal interest rate. Thus, households cannot roll over their

debts forever.

In this model, Households have to choose sequences of choices {consumption, work hours,

money velocity, Nominal money supply and Bonds} at each time period, given sequences

of {Prices, Taxes, Interest Rates, Profits}

Final good are assumed to be produced by competitive firms using the Technology F(h t) i.e.

only labor as the factor of production. Firms will choose labor input to maximize their profit.

Now, let us bring in foreign demand for domestic money (Mtf) and Government actions.

Government prints money (for Domestic Mtd

and Foreign Mtfdemand), issues nominal, one-

period bonds and levies taxes to finance an exogenous stream of public consumption g t

and interest obligations on outstanding public debts.

A competitive Ramsey equilibrium is thus a set of sequences of choices {money velocities

domestic and foreign use, wages, consumption, work hours, domestic and foreign

demand for local money, Bonds issued by govt. and Prices} over an infinite time horizon.

Combining households and governments sequential budget constraints (described above)

also makes it clear that domestic economy collects seignorage revenue from foreigners

whenever nominal balances held by foreigners increase.

MoneyVelocity

Average frequency

with which a unit of

money is spent in a

specific period of time

SeignorageRevenue

Difference between

interests earned on

securities acquired in

exchange for bank

notes and the actual

costs of producing

and distributing those

notes

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Solving the Dynamic Ramsey Problem

The government is assumed to be benevolent towards domestic residents. This means that

welfare function of government coincides with the welfare function of the domestic

households and is independent of the interests and preferences of foreign residents. We fix

the initial price level arbitrarily. Ramsey problem consists in choosing a set of sequences of

{consumption, work hours and money velocity} to maximize households utility function

subject to constraints defined in the primal form.

Solving the maximization problem, we can conclude that in case of no foreign demand for

domestic currency, if Ramsey equilibrium exists, it is at zero nominal interest rate.

Failure of Friedman Rule

Without going into the technical aspects of the derivation, let us try to think why, in presence

of foreign demand for domestic currency (Mf> 0), Friedman rule ceases to be Ramsey

optimal. The intuition is based on the fact that at negative inflation (consistent with

Friedmans rule), foreign money holdings increase in real value as price levels fall, resulting

in welfare transfer from domestic to foreign consumers. Levying a positive inflation to tax

these foreign money holdings, also taxes domestic consumers with a domestic welfare loss

due to increased transaction costs. Thus the Ramsey planner faces this tradeoff of setting an

inflation rate above Friedmans rule and still maximizing domestic welfare.

Quantifying Deviation from Friedmans rule

Schmitt-Grohe and Uribe, developed a numerical algorithm that delivers the exact solutions

to the steady state of Ramsey equilibrium which addresses the planners tradeoffs. In this

calibrated model, when foreign demand is nil, inflation is -3.85, income tax rate is 18% and

nominal interest rate is 0, consistent with Friedmans rule. As foreign demand increases,

Friedmans rule is no longer optimum. For a foreign demand of 22% of total money, inflation

is 2.1% and nominal interest rate is 6.18%. As foreign demand rises as high as 32%, Inflation

targets reach 10.5% with a corresponding reduction in income tax rates.

This optimality solution suggests that benefit from collecting an inflation tax appears to

strongly dominate inflation costs to domestic agents.

Optimal Rateof Inflation

In absence of Foreign

Demand, follows

Friedmans rule

In presence of

significant Foreign

demand, is observed

to be 2-10%

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Conclusion

A significant foreign demand for domestic currency, as seen for the U.S. dollar, can

incentivize monetary authority to generate positive rates of inflation. This acts as a tax to

extract real resources from rest of the world towards domestic consumption. In our model, the

Ramsey planner weights this incentive against the cost that inflation causes to domestichouseholds. In absence of a foreign demand, Ramsey-optimal policy calls for adopting

Friedmans rule i.e. deflating at the real rate of interest. For plausible calibrations of our

model, this tradeoff is resolved in favor of taxing foreign holdings of domestic currency at

rates ranging from 2-10% per year

Word Count

[Submission details] 36 words[Article] 1050 words[Side bars] 90 words

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Foreign Demand for Domestic Currency and Optimal Rate of Inflation v1