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Fiscal Policy in an Open Economy

Amit Friedman, Zvi Hercowitz and Jonathan Sidi

February 2012

Abstract

This paper considers macroeconomic implications of a fiscal policy regimewith exogenous tax rates paths and public debt/GDP target in an openeconomy. In this setup, government spending accommodates tax revenuesand target deficits. The analysis is motivated by the Israeli fiscal policyexperience during the 2000s. We use a model where domestic productionrequires imported inputs. The model is calibrated and the effects of pre-announced tax cuts and adoption of a lower debt target are simulated. Theanalysis addresses the dynamics generated by announcements of these pol-icy shifts followed by their actual implementation. The open economy setuphas the property that demand shifts– as government spending being cut tocomply with a lower tax rate or lower debt target– have macroeconomiceffects that are similar to those of productivity shocks.

1. Introduction

This paper focuses on the macroeconomic implications of fiscal policy in a small-open economy when this policy is characterized by (a) an exogenous path of taxrates, generated for example by international tax competition, and (b) a publicdebt/output target, motivated by guidelines as the 60 percent Maastricht bench-mark. Government spending should then accommodate the tax rates and thedebt target. The paper focuses on the interaction of this fiscal setup and the opennature of an economy. In the following paragraphs we elaborate first on the fiscalpolicy setup, then on the implications of the open nature of the economy, andthen on the interaction of these two elements.The analysis in this paper focuses on the effects of exogenous changes in the

tax paths and the public debt target. Note that this fiscal setup reverses the roleof tax rates, government spending and public debt, relative to the usual setup asin Barro’s (1979) classic treatment of tax rates and public debt determination.In that framework, government spending fluctuates exogenously, whereas the taxrates and the public debt are determined endogenously.An example of the present fiscal setup is the fiscal policy in Israel during the

2000s. In 2003, the government announced a multi-year tax-cut program as wellas a commitment to reduce the debt to GDP ratio. Between the years 2003 and2008, the tax-cut program had been fully implemented, and the debt to GDP ratiodecreased from 100 to 76 percent. Accordingly, government consumption droppedfrom 28 percent of GDP in 2003 to 24 percent in 2008. In December 2009, inspite of the world economic crisis, the government renewed its commitment to cuttaxes rates and to further reduce the public debt/GDP ratio to 60 percent– theMaastricht benchmark– within a decade.Compared to a closed economy, the open nature of the economy has distinct

implications for the transmission mechanism of demand changes– as private con-sumption reacting to a tax change or government spending reacting to a tougherdebt target. In the typical closed-economy macroeconomic model, a demand shockraises the interest rate, which in turn induces higher work effort and output bymaking current leisure more expensive. As stressed by Barro and King (1984),this interest rate movement crowds out the other sources of demand, preventingthe positive comovement of private consumption, investment and public spendingas consequence of a shock to one of them.The transmission mechanism of demand changes in the present model is dif-

ferent. First, the interest rate is constant from the world capital market, so that

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the expansionary effect via labor supply does not take place. Instead, becausedomestic production uses imported inputs, an increase in the demand for domes-tic output reduces the relative price of imports in terms of the domestic good– a“real appreciation”. The resulting boost to imported inputs works similarly asthe typical productivity shock in the standard real business cycle models: Thedemand for labor and capital goes up along with production, and this generatesa positive comovement of consumption, investment and labor.There is an important interaction between exogenous changes in tax rates or

in public debt targets and the open-economy nature of the model: Changes in taxrates or public debt targets necessitate government spending adjustment. Thischange in government demand affects macroeconomic activity as described above.To illustrate this interaction, assume a predicted tax cut which for the sim-

plicity of the argument is lump-sum. Realistically, tax changes are predicted inadvance either from announcements or from the public discussion and formal stepsleading to the change. The announcement and later the implementation of the taxchange generates a cycle in economic activity. First, the prediction of a future taxcut has a positive wealth effect on private consumption. As mentioned above, suchincrease in demand causes an appreciation which triggers a positive comovementof imported inputs, labor, investment and output. Subsequently, when the taxcut is implemented, the fiscal rule dictates a reduction in government spendingwhich amounts to an opposite change in demand. Hence, the initial expansion isfollowed by a contraction. Of course, this is a stylized example. The type of fluc-tuation or cycle generated by a policy shift depends on the nature of the policy.If the tax being cut in the previous example is not lump-sum but a tax rate onlabor income, the expansionary effects of the anticipation will remain similar, butthe contractionary impact of reducing government spending when the tax rate isactually cut will be combined with the expansion of labor supply. Hence, if thelatter effect is stronger, the initial expansion will be followed by an additionalexpansion.The paper proceeds as follows. The model is presented in Section 2. Section

3 reports the calibration of the model. The macroeconomic analysis of the fis-cal policy changes is reported in Section 4 using impulse responses. Concludingremarks are given in Section 5.

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2. The Model

The model has the basic features of the small-open economy framework: Iden-tical households and firms perform dynamic optimization within a competitiveenvironment, while the interest rate is exogenously given from abroad. Hence,the economy is small and open to the world capital markets. However, there is afriction associated with financial transactions which is elaborated below. Capitaland goods are mobile internationally, but labor is not.The main additional feature to the basic framework is that production requires

an imported input which is a different good. Hence, the production functionincludes three factors: Capital, labor, and imports. All imports are treated asintermediate products, as we elaborate below. The productive role of importsimplies that the resulting aggregate supply function is decreasing in their relativeprice.Aggregate demand includes private and public consumption, investment and

exports. The economy’s output does not have a perfect substitute abroad; hence,the economy is not “small”with respect to exports. The world demand for theeconomy’s exports is an increasing function of the price of a substitute abroadrelative to domestic output. We assume that the price of that substitute relativeto imports– two foreign goods– is exogenous. Therefore, given that exogenousrelative price, the foreign demand for exports is an increasing function of therelative price of imports. This relative price coincides with the terms of tradebecause the economy exports domestic output.The relative price of imports is determined so as to clear the goods market:

It equates the aggregate demand to the aggregate supply of domestic output.This equilibrium concept is based on Bruno and Sachs (1985). In this model, thecurrent account is balanced only in the long run.Financial mobility from abroad involves a friction adopted from Schmitt-Grohe

and Uribe (2003): Deviations from a target level of foreign assets are costly.Hence, decreasing the level assets below that level, or borrowing from abroad,has a cost above the foreign interest rate. However, being symmetric, also savingabroad above the target level involves that cost. This mechanism has interestingimplications for the behavior of nondurable and durable consumption, which weanalyze below. As in Schmitt-Grohe and Uribe (2003) the additional implication ofintroducing an assets target is that the model possesses a steady state. Otherwise,given the exogenous foreign interest rate, assets would follow a random walk, and,thus, the long-run variances of assets and other variables would be infinite.

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2.1. Production

The representative firm produces output Qt according to the Cobb-Douglas tech-nology

Qt = Y γt M

1−γt , 0 < γ < 1, (2.1)

where Yt is domestic value added in period t and Mt is imports of intermediateproducts. All imports are treated as intermediate inputs in the production ofdomestic output. This treatment of imports is supported by the observations fromthe Israeli economy that raw materials for production account for about 50 percentof goods imports, and that domestic market prices of the remaining imports–investment and consumption goods– include a large domestic value added sharecomposed of importers’services, domestic transportation and taxation.Because all imports are treated as intermediate products, the degree of open-

ness of the economy, as measured by the ratio of imports to GDP, equals 1 − γ;hence, openness in this model is a function of technology.Value added, or GDP, is produced with capital, K, and labor input, L:

Yt = Kαt L

1−αt , 0 < α < 1. (2.2)

We ignore technological progress, given our focus on fiscal policy effects.Substituting (2.2) into (2.1), we get

Qt = Kαγt L

(1−α)γt M1−γ

t . (2.3)

The capital stock evolves according to

Kt+1 = Kt(1− δk) + It, 0 < δk < 1, (2.4)

where It is gross investment and δk is the depreciation rate of capital.Changing the capital stock involves the adjustment costs of the form

Jkt =ωk

2(Kt+1 −Kt)

2 , ωk > 0, (2.5)

where ωk is a parameter governing the magnitude of these costs.The firm takes prices as given. In terms of domestic output these prices are

the wage, Wt, and the price of imports Pmt .

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The after-tax dividend paid by the firm to the share holders in period t is

Πt = (1−τ ct )[Kαγt L

(1−α)γt M1−γ

t −WtLt − Pmt Mt

]−Jkt −Kt+1+Kt(1−δk), (2.6)

where τ ct is the corporate tax rate. Note that in this case, the depreciation of thecapital stock and it’s adjustment cost are assumed for simplicity not to be taxdeductible. We also assume that firms are fully owned by the domestic households.

2.2. The Firm’s Optimization Problem

The firm maximizes the sum of discounted dividends

Πt +Πt+1

1 + r+

Πt+2

(1 + r)2+ ...,

with r being the real interest rate in period t.The first-order conditions are:

1 + ωk (Kt+1 −Kt) =1

1 + r

[ (1− τ ct+1

)αγQt+1/Kt+1 + 1− δk

+ωk (Kt+2 −Kt+1)

], (2.7)

Wt = (1− α) γKαγt L

(1−α)γ−1t M1−γ

t , (2.8)

Pmt = (1− γ)Kαγ

t L(1−α)γt M−γ

t . (2.9)

In the absence of adjustment costs, (2.7) reduces to the familiar equality(1− τ ct+1

)αγKαγ−1

t+1 L(1−α)γt+1 M1−γ

t+1 = r + δk,

between the marginal productivity of capital and it’s marginal cost, and (2.8),(2.9) equate the marginal productivities of labor and intermediate inputs to theirrelative prices. Solving these two equations for Lt and Mt yields the demands forthese two inputs as functions of the prices:

Lt = ϑlKt (Wt)− 1α (Pm

t )−(1−γ)αγ , (2.10)

Mt = ϑmKt (Wt)− 1−α

α (Pmt )−

1−γ(1−α)αγ , (2.11)

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where ϑl = [(1− α) γ]1αγ

(1−γ

(1−α)γ

) 1−γαγ, ϑm = [(1− α) γ]

1αγ

(1−γ

(1−α)γ

) 1−γ(1−α)αγ

. A keyproperty of these demand functions is the negative effects of the relative price ofimported goods.

2.3. Preferences and Household’s Constraints

Preferences of the representative household are described by the form proposedby Jaimovich-Rebelo (2009), extended to include durable goods:

∞∑t=0

βt(Ct − ψLϕt Xt)

1−σ

1− σ, 0 < β < 1, ϕ > 1, ψ > 0, σ > 0, (2.12)

Ct = (Cnt )1−θDθ

t , 0 < θ < 1,

Zt = CξtZ

1−ξt−1 , 0 ≤ ξ ≤ 1. (2.13)

where Cnt is nondurable consumption, Dt is the stock of durable goods, and Lt

is labor supply. In the Jaimovich-Rebelo formulation, the parameter ξ in theequation for Xt captures the strength of the income effect on labor supply: Whenξ = 1, Zt = Ct, and then this utility function corresponds to the standard King,Plosser and Rebelo (1988) form, i.e., with full income effect. The other extremeis when ξ = 0, where there is no income effect.A property of this utility function is that as long as ξ > 0, regardless of how

small it is, in the long run Zt = Zt−1 = Ct. Hence, the wealth effect on laborsupply can be very small in the short run, but in the long-run there is a fullincome effect. The motivation for adopting this utility function here is similaras in Jaimovich and Rebelo: To deal with anticipation effects on labor supplyin a realistic manner. Because changes in tax rates are in general announced inadvance, the expectation of a future tax cut is can be consistent with a very smallwealth effect– i.e., this expectation does not cause a large immediate decline inoutput. Over time, however, the wealth effect builds up.Similarly as for productive capital, changes in the stock of durable goods in-

volve adjustment costs of the form

Jdt =ωd

2(Dt+1 −Dt)

2 . (2.14)

This formulation is consistent with the findings in Caballero (1990), who found

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strong support for slow adjustment of durable goods in the U.S.We deviate from the standard permanent income hypothesis by allowing for a

mechanism capturing liquidity effects. Households have an exogenous target levelof assets. Let us denote net financial assets at the beginning of period t with Ft,and the target with F ∗. The cost Jft of being away from target is

Jft =ωf

2(Ft+1 − F ∗)2 , ωf > 0, (2.15)

adopted from Schmitt-Grohe and Uribe (2003). They interpret this formulationas the costs of portfolio adjustment, and focus on the fact that it provides a steadystate to the model of a small open economy.Here, we prefer to see these costs as reflecting too much or too little liquidity

relative to the exogenous F ∗. This formulation produces realistic deviations frompermanent income behavior: Excess sensitivity to temporary income changes,as in Flavin (1985), and excess smoothness to permanent income changes, as inDeaton (1987). We return below to the implications of this specification. As inSchmitt-Grohe and Uribe, the cost of being away from target assets generatesa steady state in the model. This is the element of the model which providesimperfect capital mobility from abroad, in spite of the exogenous world interestrate.Included in F are foreign assets and government bonds. Ownership of firms

and physical capital is already captured by the dividends Πt received from thefirms.The household receives income from labor, dividends and transfers from the

government, Tt. For the household, the relevant tax rates are: τ lt on labor income,τnt on nondurable consumption, and τ dt on durable purchases. We assume forsimplicity that dividends are not taxed. Hence, τ c reflects all capital incometaxation. The one-period household’s budget constraint is given by

(1 + τnt )Cnt +(1 + τ dt

)Cdt +Jdt = (1−τ lt )WtLt+Πt+Tt+(1+r)Ft−Ft+1−Jft , (2.16)

whereCdt = Dt+1 −

(1− δd

)Dt (2.17)

is purchases of durable goods, and 0 < δd < 1 is their depreciation rate.

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2.4. The Household’s Optimization Problem

The household chooses sequences of Cnt , Dt+1, Lt and Ft+1 to maximize the utility

function in (2.12), subject to the sequences of constraints in (2.16), the adjustmentand financial costs functions in (2.14) and (2.15), the evolution of the durable stockin (2.17) and the initial stocks F0 and D0.Defining

St ≡ (Cnt )1−θDθ

t − ψLϕt Zt,

Ucn(t) ≡ S−σt

[(1− θ) (Cn

t )−θDθt

],

Ud(t) ≡ S−σt

[θ (Cn

t )1−θDθ−1t

],

Ul(t) ≡ S−σt[−ψϕLϕ−1t Zt

],

Uz(t) ≡ S−σt (−ψLϕt ) ,

and Υct and Υz

t as the Lagrange multipliers of the budget constraint (2.16) andthe equation for Zt in (2.13), the first-order conditions are:1

0 = Ucn(t)−Υct (1 + τnt )−Υz

t

[(1− θ) ξ (Cn

t )(1−θ)ξ−1Dθξt Z

1−ξt−1

], (2.18)

0 = −Υct

[1 + ωf (Ft+1 − F ∗)

]+ βΥc

t+1(1 + r), (2.19)

0 = −Υct

[1 + τ dt + ωd (Dt+1 −Dt)

]+ βUd(t+ 1)

+ βΥct+1

[(1 + τ dt+1

) (1− δd

)+ ωd (Dt+2 −Dt+1)

]− βΥz

t+1

[θξ(Cnt+1

)(1−θ)ξDθξ−1t+1 Z

1−ξt+1

], (2.20)

0 = Ul(t) + Υct(1− τ lt )Wt, (2.21)

0 = Uz(t) + Υzt − βΥz

t+1

(Cnt+1

)(1−θ)ξDθξt+1 (1− ξ)Z−ξt . (2.22)

To provide intuition on these optimality conditions, we concentrate now onthe case where the utility function is standard, i.e., ξ = 1 (or Zt = Ct), tax ratesin periods t and t+ 1 are equal, β(1 + r) = 1 and there are no adjustment costs.

1For each period t, there are 7 unknowns: Cnt , Ft+1, Dt, Lt, Zt,Υct ,Υ

zt and 7 equations (the

5 first-order conditions, the budget constraint and the equation for Zt.

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In this case, the first-order conditions can be written as:

Ucn(t)[1 + ωf (Ft+1 − F ∗)

]= Ucn(t+ 1), (2.23)

Ucn(t) = βUd(t+ 1)

(1 + τn

1 + τ d

)+ βUcn(t+ 1)

(1− δd

),

(2.24)

−Ul(t) = Ucn(t)

(1− τ l

1 + τn

)Wt. (2.25)

Equation (2.23) is the Euler equation on savings which leads to consumptionsmoothing when ωf = 0, (2.24) equates the purchasing cost of the durable goodto it’s marginal utility plus it’s discounted resale value, and (2.25) determinesoptimal labor supply.The nonstandard element here appears in (2.23). As mentioned above, the

costs of deviating from the assets target F ∗ generate excess sensitivity to tempo-rary income changes, as in Flavin (1985), and excess smoothness to permanentincome changes, as in Deaton (1987).2 To illustrate this, consider first a temporaryincrease in the wage, dividends or transfers from the government starting from asteady state situation of Ft = F ∗. The desire to save to smoothen consumptionover time increases Ft+1. According to (2.23), this implies that Ucn(t)/Ucn(t + 1)falls, and thus current consumption reacts more than predicted by permanentincome theory. This is the excess sensitivity property.Consider now the anticipation of a future transfer or tax cut (beyond t + 1).

The desire to upscale nondurable consumption and the durable stock to the newoptimal levels requires borrowing– a reduction of Ft+1– counting on higher netincome in the future. In (2.23) this implies that Ucn(t)/Ucn(t+ 1) goes up ratherthan remain equal to one as permanent income theory predicts. Hence, nondurableconsumption adjusts upwards gradually rather than immediately. This is theexcess smoothness property, which follows from the liquidity shortage. Note inequation (2.24), that Ud(t+ 1)/Ucn(t+ 1) must also go up. This implies that alsothe durable stock adjusts gradually.In terms of labor supply, the wealth effect that reduces the willingness to

work, encounters an opposite effect via the liquidity shortage. As assets decline,the gradual adjustment of nondurable consumption reduces the wealth effect onlabor supply. Quantitatively, however, it turns out that the wealth effect on labor

2Campbell and Hercowitz (2009) show that both phenomena can be explained by liquidityconstraints.

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supply with ξ = 1 is still very strong.

2.5. Government

The modelling of the public sector captures it’s behavior in Israel since 2003. Inthat year, the government announced simultaneously a multi-year tax-cut programand a commitment to reduce the public debt to GDP ratio. Between the years2003 and 2008, the tax-cut program had been fully implemented, while the publicdebt decreased from 100 percent of GDP to 76 percent. Accordingly, governmentconsumption dropped from 27.8 percent of GDP in 2003 to 23.8 percent in 2008. InDecember 2009, in spite of the world crisis, the government renewed its committedto cut tax rates according to the plan and further reduce the public debt/GDPratio to 0.6– the Maastricht Accord benchmark– in about a decade. Along theselines, we model government expenditures as endogenous to the path for the debt,exogenous tax rates, and expected tax revenues.The government has an exogenous target for the public debt to GDP ratio

and a rate of convergence towards that target. Defining η as the target ratio ofgovernment debt to GDP, the target debt is

B∗∗t+1 = ηEt (Yt+1) . (2.26)

The government plans to achieve this target gradually. The intermediate target,i.e., the target for the debt next period, is

B∗t+1 = B∗t(B∗∗t+1/B

∗t

)λb, 0 < λb < 1, (2.27)

where λb govern the speed of adjustment to the final target.Total revenue from taxation is

Rt = τ ltWtLt + τ ct (Qt −WtLt − Pmt Mt) + τnt C

nt + τ dt C

dt . (2.28)

The government spends Gt in goods and services, Tt in transfers to the public,and (1 + r)Bt in debt servicing and repayment. Given tax revenues, transfers, theoutstanding debt and the intermediate debt target, the amount the governmentcan spend in in goods and services should satisfy

Gt ≤ Rt +B∗t+1 − Tt − (1 + r)Bt. (2.29)

We assume that this constraint always binds, and hence actual debt at the end

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of every period isBt+1 = B∗t+1. (2.30)

2.6. Rest of the World

The rest of the world demands the domestic good according to the function

Xt = X0 (P xt )χ , χ > 0, (2.31)

where X0 is a scale parameter reflecting the volume of the world trade and P xt is

the price of a foreign substitute of the domestic good relative to the price of thedomestic good.The price of the foreign substitute to the domestic good relative to the price

of imports is

P xmt =

P xt

Pmt

, (2.32)

which is exogenously given from the world markets.The interest rate is given from the world financial market, and equals the rate

of time preference. Hence,

r =1− β

β(2.33)

for all t. In other words, foreign financial traders have the same time preferenceas the domestic households.

2.7. Equilibrium

The dynamic nature of the model implies that equilibrium involves the simulta-neous computation of the expected future paths of the economy. However, as aversion of the Bruno and Sachs’(1985) framework, the equilibrium in this modelcan be given the following heuristic aggregate demand-aggregate supply interpre-tation by holding expectations of future variables constant.In the equilibrium condition in the output market

Qt = Cnt + Cd

t + It +Gt +Xt + Jkt + Jdt + Jft , (2.34)

the left-hand side and the right-hand side represent aggregate supply and aggre-gate demand in the space of Qt and 1/Pm

t – the relative price of domestic output

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in terms of foreign goods. Aggregate supply follows from substituting labor de-mand from (2.10) and imports demand (2.11) into the production function (2.3),while the wage equals the households rate of substitution between consumptionand leisure as in (2.21), which describes labor supply. Therefore, this implies equi-librium in the labor market. Because of the negative effect of Pm

t on the demandfor intermediate inputs and labor, output supply can be visualized as an upwardsloping curve with 1/Pm

t as the price. Regarding aggregate demand, the positivelink between exports and Pm

t from (2.31) implies that aggregate demand can berepresented by a downward sloping curve. Hence, the equilibrium values of Qt

and 1/Pmt are positively affected by demand positive shifts– higher economic ac-

tivity accompanied by a appreciation– while a supply positive shift causes highereconomic activity and a depreciation. This is a basic intuition that will be usedto interpret the simulations of the model.

2.8. The Trade and the Current Account

The current account balance, CAt, and the corresponding capital flows follow from(2.34) by adding r (Ft −Bt)− Pm

t Mt on both sides:

Qt+r (Ft −Bt)−Pmt Mt = Cn

t +Cdt +It+Gt+Xt+J

kt +Jdt +Jft +r (Ft −Bt)−Pm

t Mt,

or, rearranging,

CAt ≡ Xt+r (Ft −Bt)−Pmt Mt = Qt+r (Ft −Bt)−Pm

t Mt−Cnt −Cd

t−It−Gt−Jkt −Jdt −Jft .

(2.35)The current account balance equals the difference between receipts from abroad

from exports and assets less payments abroad from imports and debt, or alterna-tively, total income less total expenditures.The trade balance is

TBt ≡ Xt − Pmt Mt.

2.9. Conversion of Variables from Output Units to GDP Units

The usual macroeconomic analysis as well as the national income accounts em-phasize GDP, or domestic product, rather than domestic output. In particular,relative prices of imports and exports are computed using GDP price indices, andnot output price indices– as the model naturally involves. Hence, prior to report-

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ing the results from the model’s simulations, we derive the theoretical counterpartsof variables as they are usually measured.From equation (2.1), effi cient production implies that the relative price of value

added in terms of output equals

P yt = γ

Qt

Yt.

Substituting Y in terms of Q from (2.1) we get

P yt = γ

QtM1−γγ

t

Q1γ

t

= γ

(Mt

Qt

) 1−γγ

. (2.36)

Then, to convert variables expressed in terms of output to GDP terms we divideby P y

t .In particular, the relative price of imports in terms of GDP, or the “real ex-

change rate”is

Rert =Pmt

P yt

= Pmt

1

γ

(Qt

Mt

) 1−γγ

, (2.37)

i.e., equals the relative price of imports in terms of output divided by the relativeprice of GDP in terms of output.

3. Parameter Values

Most of the parameter values are taken from Friedman and Hercowitz (2010),which were computed based on Israeli data for the 2000s. Parameters of the utilityfunction are from Jaimovich and Rebelo (2009). The details of the calibration canbe found in those papers. Here, we present only a summary of the procedureregarding the main parameters.The unit of time is defined as one quarter. The calibrated parameter values

are listed in Table 1.

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Table 1: Parameters ValuesProduction and Utility Functions

GDP share in output γ 0.7Capital share in GDP α 0.3Depreciation rate of capital δk 0.02Utility function parameter θ 0.165Depreciation rate of durables δd 0.025Discount rate β 0.99Utility curvature σ 1

Jaimovich-Rebeloξϕψ

0.0011.51

Fiscal PolicyDebt to GDP ratio target η 0.6Public debt convergence λb 0.025Effective corporate tax τ c 0.15Average tax on labor τ l 0.15Tax on nondurables (VAT) τn 0.165Tax on durables (VAT + purchase) τ d 0.50

Other ParametersAdjustment costs of capital ωk 0.25Adjustment costs of durable goods ωd 0.25Financial costs ωf 0.01Exports elasticity χ 0.2Real interest rate r 0.01Net portfolio position F ∗ 0Unilateral transfers (% of GDP) T 0

The technology parameters γ and α were calibrated using the relevant sharesduring the 2000s. The parameter γ was set equal to the average ratio of imports tooutput, and the value of α equals the average nonlabor income share in GDP. Thedepreciation rate of productive capital δk is 2 percent, the average of the quarterlydepreciation rates across capital goods.3 The depreciation rate of durable goods,δd, was set at 2.5 percent. Note that durable goods do not include housing; thus,

3This is the average depreciation rate from the detailed perpetual capital stock system at theBank of Israel.

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the depreciation of these goods is higher than that of productive capital whichincludes structures– the productive counterpart of housing.The value of the financial costs parameter, ωf = 0.01, estimated in Friedman

and Hercowitz (2010), indicates a nonnegligible friction in the financial market.Hence, consumption decisions in the model will be affected by fluctuations inhouseholds’available liquidity. The value of the elasticity of exports to the relativeprice of the domestic good, χ = 0.2 is from Friedman and Lavi (2006).For the utility function, the value of the parameter θ was based on the average

ratio Cd/Cn = 0.141 during the 2000s (excluding housing services in Cn). Thediscount rate β was set such that the steady state level of the real interest rate(1/β − 1) equals one percent, or 4 percent annualized. As stressed by Jaimovichand Rebelo in a similar context, setting ξ = 0.001 implies that there is very littleincome effect on labor supply in the short run. Setting ϕ = 1.5 implies that theelasticity of labor supply to the real wage in the case of ξ = 0, is 2.The target ratio of fiscal debt to GDP, η, was set equal to the Maastricht

Treaty required ratio, 0.6, adopted by the Israeli government as well. The rate ofconvergence of B to B∗∗ is determined by λb. According to the rule adopted bythe Israeli government in December 2009, this target should be met by the end ofthe decade (2020). The decline in B∗ when starting from a debt of 80% of GDPimplies that, approximately, λb = 0.025 (40 quarters).4 Note this applies to anytax schedule, because the assumption is that G adjusts to tax revenues given thepath for the debt. The tax rates were calibrated using the average effective ratesduring the 2000s.The net portfolio position of the private sector F ∗ is calibrated to zero. Note

that under this value for private net assets, government debt is held abroad.

4. Policy Analysis

In this section we present results from the analysis of fiscal policies similar tothose in Israel in the 2000s: Pre-announced tax rate cuts and the adoption of alower public debt/GDP target. For this analysis we simulate and discuss impulseresponses from the model. These responses are plotted in percentage deviationsfrom the initial steady state along periods of time expressed in quarters since theannouncement.

4The approximation follows from looking at achieving the middle range ratio 0.7 in half thetime, 20 quarters.

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4.1. Expected Tax Changes

We address reductions in three tax rates: the labor income tax, τ l, the corporatetax, τ c, and the tax on durable goods purchases, τ d. Changes in the tax rate onnondurable consumption have similar effects as those for the labor tax.5 Thesetax cuts are permanent and announced 10 quarters in advance. We follow theeffects from the time of the announcement to the time of implementation, andfrom then onwards.Figure 4.1 shows the effects of a one percentage point reduction of τ l; from 0.15

to 0.14. The response of Y summarizes the effects of this policy: GDP expandsto some extent prior to the actual tax decline, and then it increases further atthe time of implementation. The early expansion is demand driven, and thetransmission mechanism, as discussed earlier is a basic feature of the present openeconomy model. Demand for investment and for consumption of both types goup with the announcement, as shown in the K, CN and CD panels. This demandincrease is reinforced by higher government spending, as shown in the G panel,which is fueled by the higher tax revenues generated by the additional economicactivity; the tax rate is unchanged yet.The demand increase following the announcement causes an appreciation, as

it can be seen in the RER panel. The decline in the relative price of importedinputs induces higher imports– and thus a trade balance deficit shown in the TBpanel– which increase the marginal productivities of capital and labor. This is themechanism expanding investment and labor demand before the actual lowering ofthe tax rate. The initial increase in the wage rate in panel W is a result from thehigher labor demand. At the time of implementation, the wage goes down due tothe labor supply surge as the labor income tax is cut. This is the force behind thefurther increase in the domestic product, which this time it can be described assupply driven. The depreciation at that time, and the trade balance turning fromdeficit to surplus, is consistent with this interpretation. The hike in consumptionof both types at that time is due partly to the complementarity of labor supply andconsumption in utility, and partly to the increased available liquidity. Over time,domestic product, the capital stock and labor input converge to higher steady-state values, while government spending converges to a lower steady state valuegiven the decline in tax revenues.

5In terms of labor supply, both taxes have identical roles– as it can be seen in equation (2.25).Regarding savings, only in the period prior to the implementation, τ ct differs from τ ct+1, and thusthe consumption tax does not cancel out from the savings conditions only in this period. Hence,reducing the labor income tax and the consumption tax have similar but not identical effects.

17

Figure 4.1: Future Labor Income Tax Cut

1 100 2000

0.2

0.4

0.6

0.8GDP (Y)

1 100 2000

0.1

0.2

0.3

0.4Capital  Stock (K)

1 100 200­1

­0.5

0

0.5Hourly Wage (W)

1 100 2000

0.5

1Labor Input (L)

1 100 2000

0.5

1

1.5Nondurable Consumption (CN)

1 100 2000

1

2

3Durable Purchases (CD)

1 100 200­1

0

1

2Real Exchange Rate (RER)

1 100 200­40

­20

0

20Trade Balance (TB)

1 100 200­3

­2

­1

0

1Government Consumption (G)

18

Figure 4.2 addresses a reduction in the corporate income tax τ c from 0.15 to0.14. Here, the tax cut announcement impacts the economy mainly by increas-ing the optimal capital stock. Higher investment demand causes an appreciationwhich has the expansionary effect discussed earlier. Consumption, in contrast,declines due to the liquidity effects of high investment expenses by firms: Div-idends are temporarily cut and thus households wish to borrow to smooth con-sumption. However, lowering F below F ∗ is costly. As discussed in Section 2.4,this reduces liquidity, which in turn depresses consumption of both types.The employment cycle– in panel L– is an illustration of the typical effects of

the present fiscal rule in an open economy. The announced tax cut generatesa demand driven boom. Later, when the tax cut is implemented, governmentexpenditures need to be cut, and this generates a demand driven contraction.This cycle is present also in output– as it can be seen in the Y panel– but thelarge capital accumulation due to the corporate tax cut reduces the amplitudeof the cycle as the economy experiences a strong upward trend for large numberof years. In other words, the contraction due to the government spending cut isobscured by the supply driven expansion at the time of implementation– whichappeared above also in the case of the cut in τ l.Over time, the economy approaches a new steady state with higher capital and

inputs. The long-run depreciation is due to the expansionary effect of the lowertax rate on output supply.Figure 4.3 shows the responses to a five percentage points reduction in the tax

rate on durable goods purchases. This policy generates a cycle associated with thedemand for durable goods. This case differs from the previous tax cuts becauseof the sensitivity of investment– in this case in durable consumption goods– tochanges in factors determining the optimal stock. The swings in the demand fordurable goods purchases dominate here the other effects stressed earlier.As it can be expected, durable purchases decline sharply at the time of the

announcement– as the price to the consumer is expected to go down. Demand fordurable goods declines even further till implementation, as the time left to forgoutility from durable goods becomes shorter– and then it soars. This is reflected incorresponding fluctuations of the real exchange rate, and thus in production andemployment. In the long run, the lower tax rate keeps total consumption demandhigher than in the old steady state, leading to a higher level of output, in spite ofthe reduction in government demand.

19

Figure 4.2: Future Corporate Tax Cut

1 100 2000

0.2

0.4

0.6

0.8GDP (Y)

1 100 2000

0.5

1

1.5Capital  Stock (K)

1 100 2000

0.05

0.1

0.15

0.2Hourly Wage (W)

1 100 200­0.1

0

0.1

0.2

0.3Labor Input (L)

1 100 200­0.2

0

0.2

0.4

0.6Nondurable Consumption (CN)

1 100 200­3

­2

­1

0

1Durable Purchases (CD)

1 100 200­0.5

0

0.5

1

1.5Real Exchange Rate (RER)

1 100 200­30

­20

­10

0

10Trade Balance (TB)

1 100 200­1.5

­1

­0.5

0Government Consumption (G)

20

Figure 4.3: Future Tax Cut on Durable Goods Purchases

1 100 200­4

­2

0

2

4GDP (Y)

1 100 200­0.2

0

0.2

0.4

0.6Capital  Stock (K)

1 100 200­2

0

2

4Hourly Wage (W)

1 100 200­5

0

5Labor Input (L)

1 100 200­5

0

5Nondurable Consumption (CN)

1 100 200­300

­200

­100

0

100Durable Purchases (CD)

1 100 200­20

­10

0

10Real Exchange Rate (RER)

1 100 200­200

­100

0

100

200Trade Balance (TB)

1 100 200­20

­10

0

10

20Government Consumption (G)

21

4.2. Lowering the Public Debt Target

Figure 4.4 shows the responses to the adoption of a public debt/GDP target of 0.6when the current ratio is 0.8. The initial effect is quite contractionary, due to thegovernment spending cut and the resulting depreciation– GDP and employmentdecline substantially.Interestingly, the long-run effects are expansionary due to the decline in the

government interest payments. This induces a shift of public expenditure towardsa higher G, which in turn causes a long-run appreciation. The resulting largerimports increase the optimal size of capital and labor demand, leading to a higherlevel of production. This cycle is, however, quite long. Given the current calibra-tion, GDP becomes higher than the initial level after about 15 years.

5. Concluding Remarks

We use an open-economy model to analyze fiscal policy based on exogenouschanges in tax rates and in the public debt target. The model is an updatedversion of the Bruno-Sachs framework, where the relative price of the domesticgood in terms of foreign goods clears the output market. The demand for goodsdepends negatively on the relative price of the domestic good through exports.The supply of goods depends positively on this relative because a higher relativeprice implies a relatively lower cost of imported inputs. The model has the Key-nesian feature that aggregate demand shocks can generate positive comovementsof production, labor input, consumption and investment, similarly as productivityshocks do in the neoclassical closed-economy model.The analysis concentrates first on tax cuts. We trace their macroeconomic

effects from the announcement through the implementation to convergence tothe long-run levels. Specifically, we deal with cuts in the tax rates on labor in-come, corporations, and durable goods purchases. The dynamic effects of the taxcuts on labor income and corporations have similarities: Both generate: (a) realexchange rate appreciation from announcement to implementation– as consump-tion and investment demand increase due to wealth effects and higher profitabilityof investing– and (b) real exchange depreciation from implementation onwards.The latter is due to the expansion in labor input and the capital stock as thecorresponding tax rates decline. The tax cut on durable goods purchases differsbecause it generates a cycle dominated by the swings in the demand for durablegoods. The announcement reduces the demand for durables sharply, and thus it

22

Figure 4.4: Lowering the Public Debt/GDP Target

1 100 200­1

­0.5

0

0.5GDP (Y)

1 100 200­0.5

0

0.5Capital  Stock (K)

1 100 200­1

­0.5

0

0.5Hourly Wage (W)

1 100 200­1.5

­1

­0.5

0

0.5Labor Input (L)

1 100 200­1.5

­1

­0.5

0

0.5Nondurable Consumption (CN)

1 100 200­6

­4

­2

0

2Durable Purchases (CD)

1 100 200­2

0

2

4

6Real Exchange Rate (RER)

1 100 200­50

0

50

100Trade Balance (TB)

1 100 200­10

­5

0

5Government Consumption (G)

23

has a strong contractionary effect. The implementation affects the economy inthe opposite direction.The adoption of a lower public-debt/GDP target has a contractionary effect in

the short run, as government spending has to be reduced. In the long-run, how-ever, the lower level of interest payments on the public debt allows the governmentto spend more on goods. This expands the economy, and the new steady state ischaracterized by higher levels of output, investment and private consumption.The present analysis of expected tax rate changes is related to the literature

on the cyclical effects of news about the future as Beaudry and Portier (2007) andJaimovich and Rebelo (2009). The open-economy nature of the current analysisdiffers from their closed-economy setup. Here, good news about the future causesan appreciation, which works similarly as a productivity shock. Hence, laborsupply reacts to two opposite forces: The wealth effect which reduces work effort,and the increased demand for labor which increases it by higher wages. The lattereffect is absent in the closed-economy setup.

24

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[3] Beaudry, Paul and Franck Portier (2007) “When Can Changes in Expecta-tions Cause Business Cycle Fluctuations in Neo-Classical Settings?”Journalof Economic Theory, 135(1), pp 458-477.

[4] Bruno, Michael and Jeffrey Sachs (1985) “Economics of Worldwide Stagfla-tion”, Harvard University Press, Cambridge, MA.

[5] Caballero, Ricardo J. (1990) “A Case for Slow Adjustment”The QuarterlyJournal of Economics, 105(3), pp. 727-743.

[6] Campbell, Jeffery R. and Zvi Hercowitz (2009) “Liquidity Constraints of theMiddle Class”, discussion paper.

[7] Deaton, Angus (1987) “Life-Cycle Models of Consumption: Is the EvidenceConsistent with the Theory?”, in T. Bewley, ed. Advances in Econometrics,Fifth Wold Congress, Vol 2, Cambridge University Press.

[8] Flavin, Marjorie (1985) “Excess Sensitivity of Consumption to Current In-come: Liquidity Constraints or Myopia?”Canadian Journal of Economics18, pp. 117—136.

[9] Friedman, Amit and Yaacov Lavi (2006) “The Real Exchange Rate and For-eign Trade in Israel”Bank of Israel Review 79, pp.37-86 (Hebrew).

[10] Friedman, Amit and Zvi Hercowitz (2010) “A Real Model of the Israeli Econ-omy”Discussion Paper No. 2010.13, Bank of Israel.

[11] Jaimovich, Nir and Sergio Rebelo (2009) “Can News about the Future Drivethe Business Cycle?”American Economic Review, (99)4, pp. 1097-1118. 1

[12] King, Robert G., Charles I. Plosser and Sergio Rebelo (1988) (1988) “Produc-tion, Growth and Business Cycles: I. The Basic Neoclassical Model”Journalof Monetary Economics, 21(2-3), pp. 195-232.

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[13] Schmitt-Grohe, Stephanie and Martin Uribe (2003) “Closing Small OpenEconomy Models”Journal of International Economics (61), pp. 163-185.

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