Government Financial with Taxes or Inflation · Government Financing with Taxes or In⁄ation...

Government Financing with Taxes or Inflation

Bernardino AdãoBanco de Portugal

André C. SilvaNova School of Business and Economics

XVII Annual Inflation Targeting SeminarBanco Central do Brasil

Rio de JaneiroMay 21-22, 2015

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•

• We calculate the effects of financing an increase in governmentexpenditures in different ways

•

• We focus on two ways of financing government expenditures:• An increase in labor income taxes, τL

• An increase in inflation, π

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Novelty: Financial Frictions and the Demand for Money

• In cash-in-advance models: the frequency of portfolio changes isfixed. For example, one quarter

• Here: the frequency of portfolio changes is a choice. A holdingperiod is from t to t +N, where N is choice. N is endogenous

• Agents decrease their demand for money with higher inflation. Thisbehavior implies costs

• The demand for money is more flexible, which yields• A better fit to the data

• Different predictions

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Findings

• N Endogenous: the welfare cost of financing an increase ingovernment expenditures with inflation is large

• N Fixed: the welfare cost is small• An analyst may conclude that it is optimal to finance an increase ingovernment expenditures with inflation (!)

• N Endogenous• It is optimal to finance an increase in government expenditures withtaxes

• Avoid inflation

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Findings

Table 1. Welfare Cost of an Increase in Government Expenditures (% of income)

Inflation Labor Tax From Tax toInflation

Inflation Labor Tax From Tax toInflation

Transfers,Seigniorage r ×M /P 1.45 0.95 0.50 0.49 0.96 ­0.46

Gov Consumption,Seigniorage r ×M /P

3.03 2.11 0.90 2.01 2.13 ­0.11

Transfers,Seigniorage π×M /P

0.97 1.01 ­0.04 0.51 1.01 ­0.50

Gov Consumption,Seigniorage π×M /P

2.41 2.13 0.28 2.00 2.13 ­0.12

Model and Method of FinancingN  Endogenous N  Fixed

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G increases 5%. G/Y increases from 20% to 21%.

Findings

Table 1. Welfare Cost of an Increase in Government Expenditures (% of income)

Inflation Labor Tax From Tax toInflation

Inflation Labor Tax From Tax toInflation

Transfers,Seigniorage r ×M /P 1.45 0.95 0.50 0.49 0.96 ­0.46

Gov Consumption,Seigniorage r ×M /P

3.03 2.11 0.90 2.01 2.13 ­0.11

Transfers,Seigniorage π×M /P

0.97 1.01 ­0.04 0.51 1.01 ­0.50

Gov Consumption,Seigniorage π×M /P

2.41 2.13 0.28 2.00 2.13 ­0.12

Model and Method of FinancingN  Endogenous N  Fixed

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G increases 5%. G/Y increases from 20% to 21%.

Findings

Table 1. Welfare Cost of an Increase in Government Expenditures (% of income)

Inflation Labor Tax From Tax toInflation

Inflation Labor Tax From Tax toInflation

Transfers,Seigniorage r ×M /P 1.45 0.95 0.50 0.49 0.96 ­0.46

Gov Consumption,Seigniorage r ×M /P

3.03 2.11 0.90 2.01 2.13 ­0.11

Transfers,Seigniorage π×M /P

0.97 1.01 ­0.04 0.51 1.01 ­0.50

Gov Consumption,Seigniorage π×M /P

2.41 2.13 0.28 2.00 2.13 ­0.12

Model and Method of FinancingN  Endogenous N  Fixed

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G increases 5%. G/Y increases from 20% to 21%.

Findings

Table 1. Welfare Cost of an Increase in Government Expenditures (% of income)

Inflation Labor Tax From Tax toInflation

Inflation Labor Tax From Tax toInflation

Transfers,Seigniorage r ×M /P 1.45 0.95 0.50 0.49 0.96 ­0.46

Gov Consumption,Seigniorage r ×M /P

3.03 2.11 0.90 2.01 2.13 ­0.11

Transfers,Seigniorage π×M /P

0.97 1.01 ­0.04 0.51 1.01 ­0.50

Gov Consumption,Seigniorage π×M /P

2.41 2.13 0.28 2.00 2.13 ­0.12

Model and Method of FinancingN  Endogenous N  Fixed

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G increases 5%. G/Y increases from 20% to 21%.

Findings

Table 1. Welfare Cost of an Increase in Government Expenditures (% of income)

Inflation Labor Tax From Tax toInflation

Inflation Labor Tax From Tax toInflation

Transfers,Seigniorage r ×M /P 1.45 0.95 0.50 0.49 0.96 ­0.46

Gov Consumption,Seigniorage r ×M /P

3.03 2.11 0.90 2.01 2.13 ­0.11

Transfers,Seigniorage π×M /P

0.97 1.01 ­0.04 0.51 1.01 ­0.50

Gov Consumption,Seigniorage π×M /P 2.41 2.13 0.28 2.00 2.13 ­0.12

Model and Method of FinancingN  Endogenous N  Fixed

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G increases 5%. G/Y increases from 20% to 21%.

Reasons for the Different Estimates

• N endogenous: decrease in the demand for money when inflationincreases

• The decrease in the demand for money implies smaller seigniorage forthe same rate of inflation as compared with a standard CIA (N fixed)

• Inflation to cover the 5% increase in expenditures:

• N fixed: 5.5% per year

• N endogenous: 12.7% per year

• A model with fixed periods underestimates the impact of inflation

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Seigniorage

• Values within realistic estimates

• Revenues from seigniorage: 1.9 to 2.2% of output

• Sargent et al. (2009): seigniorage higher than 10% of output

• Click (1998): seigniorage 2.5% on average for 90 countries

• Kimbrough (2006): seigniorage between 5 to 15% of output

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Optimal to Finance with Inflation in CIA Models

• Cooley and Hansen (1991, 1992): decreasing inflation from 10% tozero and replacing with taxes

• Welfare losses of 1.02% and 0.87%

• Disutility of decreasing inflation

• Cooley and Hansen (JET 1992): “Controlling for [capital incometaxation], there are likely to be only minor differences associated withhow revenue is raised between labor, inflation, and consumptiontaxation.”

• Existing results from standard cash-in-advance models

• Here: reverse results

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Model

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Agents

• There is a continuum of agents with measure one

• Each agent has a brokerage account and a bank account

• Time is continuous, t ≥ 0

• The agents have different endowments of money, bonds and capital

• Index agents by s = (M0,B0, k0)

• There is a given distribution of agents, F (s)

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Transfer Cost

• The agents pay a cost Γ, in goods, to transfer resources from thebrokerage account to the bank account

• Tj (s), j = 1, 2... : times of the transfers of agent s

• P (t) : price level. π (t) : inflation

• At t = Tj (s), agent s pays P (Tj (s)) Γ to make a transfer betweenthe brokerage account and the bank account

• The holding periods are the intervals [Tj (s) ,Tj+1 (s)), j = 1, 2, ...

• Size of the holding periods: Nj+1 = Tj+1 − Tj

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Money Holdings

• M (t, s) denotes money holdings at time t of agent s

• Cash-in-advance constraint

M (t, s) = −P (t) c (t, s) , t 6= T1,T2, ...

⇒ M+ (Tj (s) , s) =∫ Tj+1

TjP (t) c (t, s) dt +M− (Tj+1 (s) , s) ,

• where M+ (Tj (s) , s) denotes money holdings just after a transfer

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Government Bonds

• Q (t) : price of a bond at time zero

• r (t) ≡ d logQ (t)dt

: nominal interest rate

• B (t, s) : bond holdings at time t of agent s

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Preferences

• King, Plosser, and Rebelo (1988)

∫ ∞

0e−ρt

[c (t, s) (1− h (t, s))α]1−1/η − 1

1− 1/ηdt

• η = 1, ∫ ∞

0e−ρt [log c (t, s) + α log (1− h (t, s))] dt

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Bonds and Claims to Physical Capital

• Law of motion for bonds

B (t, s) = r (t)B (t, s) + (1− τL)P (t)w (t) h (t, s)

•

• Law of motion for claims to physical capital

k (t, s) =(r k (t)− δ

)k (t, s)

•

• limJ→+∞

Q (TJ )B+ (TJ ) = 0 limJ→+∞

Q (TJ )P (TJ ) k+ (TJ ) = 0

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Individual Maximization - Budget Constraint

• At t = Tj (s), agent s is subject to the constraint

•

M+ (Tj ) + B+ (Tj ) + P (Tj ) k+ (Tj ) + P (Tj ) Γ =M− (Tj ) + B− (Tj ) + P (Tj ) k− (Tj ) , j = 1, 2, ...

• It simplifies the problem if we write the constraint of the brokerageaccount in present value

• Use the law of motion of bonds and physical capital

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Individual Maximization - Budget Constraint

• At t = 0, agent s is subject to

∞

∑j=1Q (Tj )

Transfer Amount︷ ︸︸ ︷M+ (Tj ) +

Transfer Cost︷ ︸︸ ︷P (Tj ) Γ

≤ ∞

∑j=1Q (Tj )M− (Tj ) +W0 (s) ,

where

W0 (s) = B0 + P0k0 +∫ ∞

0Q (t) (1− τ)P (t)w (t) h (t, s) dt

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Individual Maximization Problem

• Agents choose transfer times, consumption, money, and hours of work

maxc ,h,Tj ,M

∑∞j=0

∫ Tj+1(s)Tj (s)

e−ρtu (c (t, s) , h (t, s)) dt

subject to

∞

∑j=1Q (Tj )

Transfer Amount︷ ︸︸ ︷M+ (Tj ) +

Transfer Cost︷ ︸︸ ︷P (Tj ) Γ

≤ ∞

∑j=1Q (Tj )M− (Tj ) +W0 (s)

M (t, s) = −P (t) c (t, s), t 6= T1,T2, ... M0 ≥ 0 given

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Individual Money Holdings, Agents n and n′

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Individual Bond Holdings, Agents n and n′

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Production

Y (t) = Y0K (t)θ H (t)1−θ

• K (t) : aggregate capital

• H (t) : aggregate hours of work

• Capital depreciates at the rate δ

• k (t, s) and h (t, s) : individual capital and hours of work

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Interest Rates and Wages

• From profit maximization,

•

•

r k (t) = FK (K ,H)⇒ r k (t) = θY0

(K (t)H (t)

)−(1−θ)

•

•

w (t) = FH (K ,H)⇒ w (t) = (1− θ)Y0

(K (t)H (t)

)θ

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No Arbitrage

• To avoid arbitrage between bonds and capital, we must have

r (t)− π (t) = r k (t)− δ

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From the First Order Conditions

•αc (t, s)1− h (t, s) = (1− τL)w (t) e

−r (t−Tj ), t ∈ [Tj ,Tj+1)

•

•c (t, s)c (t, s)

= −r

•

•h (t, s)h (t, s)

= 0 : constant hours of work (h)

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Optimal Consumption

• Individual consumption

c (t, s) = c0e−r (t−Tj (s))

• Aggregate consumption

C (t) = c01− e−rNrN

e(r−ρ−π)t

• Equilibriumr = ρ+ π,

r k = ρ+ δ

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System of Equations

5 equations, 5 unknowns: N, h, c0, MP , τL

N : c0rN(1− 1−e−ρN

ρN

)= ρΓ

h : h = 1− αc0(1−τL)(1−θ)Y0( KH )

θ

c0 : c0 1−e−rN

rN + δ(KH

)h+ G

>0 or =0+ 1

N Γ = Y0(KH

)θh

MP : M

P =c0e−rN

ρ

[e rN−1rN − e (r−ρ)N−1

(r−ρ)N

]GBC : G = τLwH + r MP or G = τLwH + πM

P

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Calibration

• Find γ, α, τL and G such that

• m = mAvg . mAvg = 0.257 year. (Money-Income ratio, MPY )

• h = 0.3. (Hours of work)

• r = rAvg . rAvg = 3.64% p.a.

• Government Budget Constraint holds (G = τLwH + rMP )

• GY= v , such as v = 20%

• To facilitate comparison: same dataset used by Lucas (2000), Lagosand Wright (2005), Ireland (2009), Silva (2012), and others

• θ and δ taken from Cooley and Hansen (1989). Y = Y0K θH1−θ

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Calibration - Demand for Money in Equilibrium

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Financing with Inflation

• Inflation distorts the decision on consumption and labor

• Moreover, it distorts the decision on the demand for money

• N Fixed: the demand for money changes little• The results are similar as obtained with financing with taxes

• N Endogenous: the effects on the demand for money are taken intoaccount

• Predictions change substantially

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In the Simulations that Follow

• Initial government expenditures such that GY = 20%. Increase G untilGY = 21% (G increases 5%)

• G stands for transfers. Rebated to agents

• Seigniorage: S = r MP

• Initial nominal interest rate: r = 3.64% p.a.

• The increase in G is financed either with taxes on labor or withinflation

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Inflation

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Welfare Cost

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Seigniorage, S = r MP (% of GDP)

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Money-Income Ratio, MPY

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Size of the Financial Sector, Financing with Inflation

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The financialsector to GDPratio increasesabout 1%point.

The predictionsagree with theestimates ofEnglish (1999).

Conclusions

• Effects of financing an increase in government expenditures withtaxes or inflation

• We take into account changes in the demand for money

• Letting the frequency of trades change has strong implications:• It improves the match of the demand for money to the data

• The magnitude and the direction of the predictions change

• Financing the government with taxes or inflation has larger differencesthan previously predicted

• CIA model with fixed frequency: rely on inflation for plausible cases

• Here: do not use inflation!

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