Government Financial with Taxes or Inflation · Government Financing with Taxes or In⁄ation Bernardino Adªo Banco de Portugal AndrØ C. Silva Nova School of Business and Economics

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

André Silva Government Financing 1

•

• 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


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


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


Findings

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

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


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

Findings






3.03 2.11 0.90 2.01 2.13 0.11


0.97 1.01 0.04 0.51 1.01 0.50


2.41 2.13 0.28 2.00 2.13 0.12




Findings






3.03 2.11 0.90 2.01 2.13 0.11


0.97 1.01 0.04 0.51 1.01 0.50


2.41 2.13 0.28 2.00 2.13 0.12




Findings






3.03 2.11 0.90 2.01 2.13 0.11


0.97 1.01 0.04 0.51 1.01 0.50


2.41 2.13 0.28 2.00 2.13 0.12




Findings






3.03 2.11 0.90 2.01 2.13 0.11


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




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


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


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


Model


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)


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


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


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


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


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


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


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


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


Individual Money Holdings, Agents n and n′


Individual Bond Holdings, Agents n and n′


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


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


No Arbitrage

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

r (t)− π (t) = r k (t)− δ


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)


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


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


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


Calibration - Demand for Money in Equilibrium


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


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


Inflation


Welfare Cost


Seigniorage, S = r MP (% of GDP)


Money-Income Ratio, MPY


Size of the Financial Sector, Financing with Inflation


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!


Documents

Government Financial with Taxes or Inflation · Government Financing with Taxes or In⁄ation Bernardino Adªo Banco de Portugal AndrØ C. Silva Nova School of Business and Economics