Keywords:Macroeconomic stabilizationValue added taxInterest rateEconomic costs of taxation
The value added tax (VAT) has been proposed as a macroeconomic stabilization instrument. This paper con-siders some practical implications of a variable VAT. It then develops a dynamic general equilibrium model toassess its usefulness as a stabilization instrument. A variable rate VAT would no longer be less distortionarythan other taxes. It would distort between current and future consumption, i.e. savings and investmentdecisions, and hence raise the economic costs of taxation. Moreover, a variable VAT would be less effectivein dampening business cycles than the conventional stabilization tool, an interest rate. This is because of theadditional adverse supply effects. A change in the interest rate affects this period's savings and investmentdecisions, whereas a variable VAT rate would influence savings and investment decisions over time. A variableVAT rate is therefore unlikely to be a useful stabilization instrument.
The 2008 global financial crisis and subsequent worldwide eco-nomic recession led to a recourse by governments to fiscal policy asa tool for macroeconomic stabilization (e.g. Feldstein, 2009). Countriesimplemented various stimulative fiscal measures. These included in-creases in public consumption and infrastructure investment, andmea-sures to boost household disposable income through cutting incometaxes and increasing benefits and subsidies, as well as tax reductionsfor businesses. Moreover, the United Kingdom temporarily reducedits value added tax (VAT) to stimulate consumer spending. The ratereduction took effect on 1 December 2008 and temporarily loweredthe VAT rate from17.5% to 15% until 31December 2009. Further tempo-rary VAT rate cuts have been suggested by the International MonetaryFund (2012) as economic growth has remained sluggish in the UnitedKingdom and worldwide.
A more active countercyclical use of the value added tax has alsobeen proposed in New Zealand. For example, the New Zealand centralbank suggested that “the (VAT) rate could be raised during periods ofintense pressures on resources and lowered when inflationary pres-sures were very weak” (Reserve Bank of New Zealand, 2007).1
The purpose of this paper is to investigate the economic effects ofa variable value added tax and its usefulness as a stabilization instru-ment. The paper considers some practical implications of a variableVAT. It then develops a dynamic general equilibrium model to assess
ation instrument for monetary(2006).
rights reserved.
its effectiveness in reducing business cycle fluctuations. The frame-work of analysis is a small open economy that operates under aflexible exchange rate with imperfect competition and sticky prices.The model is calibrated for New Zealand, a small open economy witha comprehensive and broad base value added tax.
The paper proceeds as follows. Section 2 briefly discusses NewZealand's value added tax and the features that make a VAT lessdistortionary than other taxes. It then considers some practical impli-cations of a variable VAT rate. Section 3 derives the theoretical modeland discusses the economic costs of a variable VAT rate. The effective-ness of a variable VAT as a stabilization tool compared to an interestrate is evaluated in Section 4 and the last section summarizes andconcludes.
2. Practical considerations
This section briefly discusses New Zealand's value added tax andthe economic costs of taxation. It then considers some practicalimplications of using a variable value added tax rate as a stabilizationtool.
2.1. New Zealand's value added tax
New Zealand's value added tax is charged at 15% and applies to acomprehensive and broad base. It is designed to collect tax revenuefrom the final consumption of goods and services in New Zealand.In line with international practice, it is based on the destinationprinciple. That is, tax is charged according to the destination ofgoods and services rather than the source of that supply. Under thedestination principle, supplies of goods and services are taxed inthe jurisdiction in which the goods and services are consumed. This
means that exports are zero-rated, while imports are taxed. VATapplies at all stages of production, including imports. However, asa value added tax, VAT paid on intermediate goods and services canbe reclaimed.
2.2. Economic costs of taxation
Taxes are needed to finance government expenditure. But raisingtaxes creates administration and compliance costs. Moreover, taxa-tion has economic costs because it distorts economic behavior.2
A value added tax is less distortionary than other taxes for severalreasons (Auerbach, 2008; Banks and Diamond, 2010). First, VAT istypically charged at a uniform, relatively low rate to a (more orless) comprehensive and broad base. This lowers the economic costsof taxation, which tend to increase the higher the tax rate and thenarrower the base. Second, in theory VAT does not distort businessor export decisions. This is because the tax paid on production inputsand exports is deductible. Third, VAT does not distort between cur-rent and future consumption, i.e. savings and investment decisions.
The remainder of this paper argues that the features that make thevalue added tax less distortionary than other taxes would no longerhold with a variable rate.
2.3. Practical implications of a variable VAT rate
A variable VAT would disproportionately distort business deci-sions of certain sectors of the economy. For example, changes in therate of VAT would have a material impact for businesses that areunable to deduct VAT input tax because they make supplies ofexempt goods and services, like the financial services sector.
A variable VAT would increase compliance costs as businesseswould need to change prices more frequently. In response to ratechanges, businesses would have to conduct physical stock-takes andvalue work-in-progress to re-price goods and services. Frequentlyvarying the tax rate could make collecting VAT unworkable for somegoods and services, such as insurance premiums, telecommunicationsor power, which are usually invoiced at one point in time but suppliedover a number of periods.
Tax administration costs would increase. With a variable VAT thegovernment would need to revise transfer payments to ensure thattax related consumer price movements do not affect the value ofsuch transfers.
A variable VAT rate may also lead to pressures for differential ratesacross commodities and exemptions. Exemptions and differentialrates would raise the distortionary costs of taxation (Atkinson andStiglitz, 1976; Kaplow, 2007) and impact on the effectiveness of VATas a stabilization tool. Its usefulness as a policy instrument would bereduced further if consumers tried to mitigate the impact of tax ratechanges by “panic buying” or “consumer strikes”.
3. Theoretical model
To illustrate the adverse effect of a variable VAT on investmentand savings, this section develops a dynamic general equilibriummodel, which is calibrated to New Zealand. There are four agentsin the economy: households, firms, a government and a monetaryauthority.
2 Taxes affect people's decisions on howmuch education to obtain, whether or not toenter market paid employment, how much to work, whether or not to apply for pro-motion, when to retire. They impact on the amount people save and how they save ifdifferent tax rates apply to different savings instruments. Taxes also influence risk tak-ing and entrepreneurship and provide incentives for tax planning.
3.1. Households
Households are infinitely lived and a typical household valuesstreams of consumption and leisure according to
EtX∞k¼0
βk ln Ctþk
� �þ γ 1−Ntþk
� �� � ð1Þ
where γ>0 is a parameter, β∈(0,1) is the household's discount fac-tor, Et is a conditional expectations operator with respect to informa-tion available at time t and consumption is given by Ct. Households'time is normalized to one, and Nt and (1−Nt) denote the proportionsof time spent in work and in leisure with Nt∈(0,1). The period utilityfunction, U(Ct, Nt), is given by
U Ct ;Ntð Þ ¼ ln Ctð Þ þ γ 1−Ntð Þ ð2Þ
Each household consumes many goods, all of which are domesti-cally produced. Ct is the quantity consumed in period t of an index
of these goods with Ct=[∫01Ct(j)(θ−1)/θdj]θ/(θ−1), where Ct (j) denotes
the household's period t consumption of good j and θ>0 is the priceelasticity of demand.3 The price of consumption good j is given byPt (j) and the aggregate price level, Pt, is an index given by Pt=[∫0
1Pt(j)1−θdj]1/(1−θ).Households earn income from supplying labor, Nt, at wage rate Wt
and by renting physical capital, Kt-1, accumulated last period, to firmsat rate Rt. All physical capital is imported. Moreover, householdsreceive dividend payments, Ωt, from firms and earn income fromholding domestic bonds issued by the government, Btg, and foreignbonds, Bt∗. Bt+1
g and Bt+1∗ are the amounts of the nominal government
and foreign bonds held by the household at the end of period t withBtg≧0 and Bt
∗>0 for all t.4 Domestic bonds, Btg, earn a nominal return(in terms of domestic currency) of It and the nominal rate of interestpaid on foreign bonds, Bt∗, is given by It
∗. Households also hold money,Mt, as a medium of exchange to purchase consumption and capitalgoods, where Mt+1 is the amount of domestic currency held at theend of period t. Households pay taxes on their earned income. Thetax rate on their wage, rental, interest and dividend income is givenby τ. Capital gains from exchange rate movements are not taxed.The government also imposes a value added tax, τtVAT. The VAT rateis fixed when the nominal interest rate is used as the stabilizationtool. It is variable when VAT is the stabilization instrument.
The typical household's budget constraint in nominal terms isgiven by
where δ∈(0,1) is the economic depreciation rate of capital. St denotesthe nominal exchange rate and Pt
∗ is the foreign price level.5 The priceof capital, which is imported, is given by StPt
∗ and the net VAT is zeroas the tax paid on production inputs is fully deductible. Households'budget constraint can be interpreted as follows. Each period, house-holds earn income. They then sell their domestic and foreign bondsand physical capital to purchase consumption goods and new finan-cial and real assets. Households' budget constraint is binding andtheir expenditure is equal to their income.
3 The government's consumption index (discussed below) is given accordingly.4 The supply of foreign bonds is infinite and households' demand is always met.5 The nominal exchange rate, St, is measured as the price of foreign currency in units
of domestic currency, i.e. an increase in St indicates a depreciation of the domesticcurrency.
7 The exchange rate cancels out in the relative price term.
368 I. Claus / Economic Modelling 30 (2013) 366–374
The household's cash-in-advance constraint is given by
1þ τVATt
� �PtCt þ StP
�t Kt− 1−δð ÞStP�
t Kt−1≤Mt ð4Þ
It holds as an equality at an optimum if It>0.Inflation is positive in steady state and nominal variables are
trending. Let Wt=Pt ¼ W t , Rt=Pt ¼ Rt , Bgtþ1=Pt ¼ B
gtþ1, B
�tþ1=P
�t ¼ B
�tþ1
and Ωt=Pt ¼ Ωt . Using Eq. (4), the household's budget constraint canthen be re-written in real terms as
1−τð ÞW tNt þ 1−τð ÞRtKt−1 þ 1þ 1−τð ÞItð ÞBgt
1þΠtþ 1þ 1−τð ÞI�t� �
QtB�t
1þΠ�t
þ 1−τð ÞΩt−Bgtþ1−QtB
�tþ1− 1þΠtþ1
� ��1þ τVATtþ1
� �Ctþ1
þQtþ1Ktþ1− 1−δð ÞQtþ1KtÞ ¼ 0
ð5Þwhere Qt=StPt
∗/Pt denotes the real exchange rate, Πt=Pt/Pt−1−1 isthe domestic inflation rate and the foreign inflation rate is given byΠt
∗=Pt∗/Pt−1
∗ −1.The household's optimization problem consists of choosing
Ct ;Nt ;Kt ; Bgtþ1; B
�tþ1
n ofor all t∈ [0, ∞) to maximize utility (Eq. (2))
subject to Eq. (5).6 Households' first-order conditions are given by
1γCt
−1þ τVATt
� �1þ 1−τð ÞItð Þ
1−τð ÞW t
¼ 0 ð6Þ
Qt
1þ τVATt
� �Ct
−Etβ 1−δð ÞQtþ1 þ 1−τð ÞRtþ1
1þ 1−τð ÞItþ1
� �1þ τVATtþ1
� �Ctþ1
24
35 ¼ 0 ð7Þ
and
EtQtþ1
Qt
1þ 1−τð ÞI�tþ1
1þΠ�tþ1
−1þ 1−τð ÞItþ1
1þΠtþ1
� ¼ 0 ð8Þ
At an optimum the marginal rate of substitution between con-sumption and leisure is equal to the relative price of consumption;that is, the ratio of the after-tax effective price of consumption andthe after-tax real wage rate. The effective price of consumption is thesum of its market price (equal to unity) and the opportunity cost ofhaving to hold money to purchase consumption goods, (1−τ) It. Fur-ther, the marginal rate of substitution between after-tax consumptiontoday and next period is equal to the effective return from accumulat-ing an additional unit of capital. The effective return is given by a unitvalue of the capital stock net of depreciation plus the after-tax rate ofreturn on capital adjusted for the opportunity cost of having to holdmoney to purchase capital. Moreover, in equilibrium after-tax realrates of return from holding domestic and foreign bonds are equal.
The first-order conditions show how VAT and the interest rateaffect the real economy. VAT alters the effective price of consumption(Eq. (6)). In addition, when VAT is the stabilization tool, i.e. the rateof VAT is variable, it influences households' savings and investmentdecisions over time (Eq. (7)). Eq. (7) thus illustrates how a variableVAT rate would increase the economic costs of taxation by distortingbetween current and future consumption.
A change in the interest rate also alters incentives to consume andinvest (Eqs. (6) and (7)). But changes in the interest rate have lessadverse supply effects, in terms of savings and hence investmentdecisions, than a variable VAT rate. This is because a change in theinterest rate only affects this period's marginal rate of substitutionbetween current and future consumption, whereas a variable VAT rateinfluences this period's and next period's marginal rates of substitution
6 Dividends are paid at the end of each period and do not affect households' optimi-zation problem.
(Eq. (7)). That is, a change in It+1 affects savings decisions, Ct+1/Ct, inperiod t, while a change in τt+1
VAT alters savings decisions in period tand t+1.
Movements in the interest rate also impact on the exchange rate(Eq. (8)). All else equal, an increase (decrease) in the domestic inter-est rate leads to an inflow (outflow) of funds and appreciation(depreciation) of the real exchange rate. This lowers (raises) the priceand rate of return of imported capital (Eq. (7)) and hence reduces thesupply side effects of interest rate changes. A variable VAT rate doesnot directly influence the real exchange rate and hence has no suchoffsetting effects.
3.2. Firms
Firms are monopolistic competitors and specialize in production.A typical firm produces output of consumption good j, Yt (j), undera constant elasticity of substitution (CES) technology by hiringlabor, Lt (j), and capital, Kt−1(j), from households. Firm j's productionfunction is thus given by
Yt jð Þ ¼ ηl ZtLt jð Þð Þν þ 1−ηl� �
Kt−1 jð Þð Þν� i1
νh
ð9Þ
where ηl∈(0, 1] is a parameter and νb1; that is, the marginal returnto each input is diminishing. The elasticity of substitution in produc-tion is given by 1/(1−ν) and Zt denotes aggregate productivity.
Each firm treats the price in domestic currency, Pt (j), of the con-sumption good j it produces as a choice variable, while taking thedomestic aggregate price level, Pt, the nominal exchange rate, St,and the foreign price level, Pt∗, as given. Having chosen Pt (j), thefirm then produces the quantity of output demanded at that price.Firms may not price discriminate and the price of good j sold toforeign consumers (denominated in foreign currency) is given byPt (j)/St. Firms sell their output to domestic households and the gov-ernment and export to the rest of the world. Let Ct (j), EXt (j) and Gt
(j) be the quantity of consumption good j demanded by a typicalhousehold and foreign consumer and the government, i.e. Yt(j)=Ct(j)+EXt(j)+Gt(j). It can be shown (e.g. Obstfeld and Rogoff,1996) that the household's and government's demand functionsfor good j are given by
Ct jð Þ ¼ Pt jð ÞPt
�−θCt ð10Þ
and
Gt jð Þ ¼ Pt jð ÞPt
�−θGt ð11Þ
where Ct and Gt denote total consumption by the typical house-hold and the government. Similarly, foreign demand for consump-tion good j is given by
EXt jð Þ ¼ Pt jð ÞPt
�−θEXt ð12Þ
where EXt denotes aggregate exports.7 Aggregate export demand is afunction of the real exchange rate, Qt, and foreign demand for the do-mestic country's output, Yt∗.8 Thus, the economy's aggregate exportsare assumed to be given by
EXt ¼ Qtð Þκ Y�t
� �ς ð13Þ
8 The domestic economy's exports are assumed to form an insignificant proportionof foreigners’ demand and have a negligible weight in the rest of the world's priceindex.
where κ, ς>0 are the price and foreign demand elasticities ofexports. Exports are zero-rated, i.e. they are not subject to VATconsistent with the destination principle. When the central bankuses an interest rate as the stabilization tool, exports are an addi-tional channel through which monetary policy affects the realeconomy and hence inflation. A change in the interest rate that istransmitted to the real exchange rate affects the price of exports andforeign demand for firms' output. These effects do not arise with avariable VAT rate.
Each firm chooses {Pt(j), Lt(j), Kt−1(j)} to maximize profitssubject to its production function (9) and demand function, Yt(j)=(Pt(j)/Pt)−θYt,
Ωt jð Þ ¼ Pt jð ÞYt jð Þ−WtLt jð Þ−RtKt−1 jð Þ½ �
¼ Pt jð Þ−PtMCt½ � Pt jð ÞPt
�−θYt
ð14Þ
where MCt denotes the real marginal cost. Firm j's first-order condi-tions are given by
Pt jð Þ ¼ θθ−1
PtMCt ð15Þ
Wt
Pt jð Þ ¼ηl Ztð Þν Yt jð Þ
Lt jð Þ
�1−ν
θθ−1
ð16Þ
and
Rt
Pt jð Þ ¼1−ηl� � Yt jð Þ
Kt−1 jð Þ
�1−ν
θθ−1
ð17Þ
In a symmetric equilibrium, all firms charge the same relativeprice and hire the same labor and capital. The first-order conditionscan then be re-written as
MCt ¼1θ
θ−1
ð18Þ
W t ¼ηl Ztð Þν Yt
Lt
�1−ν
θθ−1
ð19Þ
and
Rt ¼1−ηl� � Yt
Kt−1
�1−ν
θθ−1
ð20Þ
Eqs. (19) and (20) show that firms sell their output of consump-tion goods at a mark-up over production costs and factor prices arebelow their marginal products. Under price flexibility the mark-upis constant and equal to θ/(θ−1). Under price stickiness it isgiven by ξt/(ξt−1), where ξt is the price elasticity of demandwith sticky prices. The mark-up gives rise to economic profits of(ξt−1)Yt/ξt, which are paid to households as dividends at the endof each period.
3.3. Government
The government collects taxes on households' income and con-sumption. Moreover, it issues government bonds, which are held byhouseholds, B
gt , and international investors, B
g�t . Foreign investors'
interest payments are taxed at the domestic tax rate, τ. The government
uses this revenue to purchase an index of consumption goods, Gt,from firms and to make interest payments on government bonds,1−τð ÞIt Bg
t = 1þΠtð Þ and 1−τð ÞItQtB�t = 1þΠ�
t
� �. The government's
primary fiscal deficit, F t , in real terms is thus given by
F t þ τ W tLt þ RtKt−1 þ Ωt þI�t Q tB
�t
1þΠ�t
!þ τVATt Ct
−Gt−1−τð ÞIt Bg
t
1þΠt− 1−τð ÞItQtB
g�t
1þΠ�t
¼ 0
ð21Þ
Note that the VAT collected and paid on government consumptionis recycled as tax revenue and nets out.
The government's budget constraint is given by
Bgtþ1 þ QtB
g�tþ1−
Bgt
1þΠt− QtB
g�t
1þΠ�t−F t ¼ 0 ð22Þ
3.4. Monetary authority
The central bank sets the consumer price inflation target rateΠT>0. To maintain this target following a shock to the economy,the central bank adjusts its monetary policy tool. Two stabilizationinstruments are considered – the nominal rate of interest paid ondomestic bonds, It, and the VAT rate, τtVAT. The central bank's reactionfunction is given by a Taylor rule (Taylor, 1993), i.e. it depends ondeviations of inflation from target and deviations of output from fullcapacity, flexible price output. It is constrained to be linear in thelogs of the relevant arguments and given by
ln1þ It1þ �I
�¼ μ1ln
1þΠt
1þΠT
�þ μ2ln
Yt�Y
�ð23Þ
or
lnτVATt
�τVAT
!¼ μ1ln
1þΠt
1þΠT
�þ μ2ln
Yt�Y
�ð24Þ
depending on whether the interest rate or the VAT rate is used as astabilization tool. Ī, �τVAT and �Y denote the steady state interest rate,VAT rate and full capacity, flexible price output and μ1, μ2>0 areparameters.
Moreover, the central bank adjusts the money supply to imple-ment a particular interest rate or VAT rate target. Changes in themoney supply are assumed to not have any additional real effects.This allows ignoring the central bank's budget constraint.
3.5. Welfare effects
To assess the impact of the two stabilization instruments (VATand interest rate) a measure of welfare is introduced. It is basedon the change in consumption that households would require tobe as well off as under the absence of a shock and monetary policyresponse. The welfare measure is obtained by solving Eq. (25) for�Ct
�U �C �;N� � ¼ ln Ct−Δ�Ct
� �þ γ 1−Ntð Þ ð25Þ
where �U �C �;N� �
is households' utility attained in steady state, and Ctand Nt are consumption and labor following a shock to the econo-my. Welfare changes are calculated for the VAT and interest ratemodels and expressed as a percent of steady state output, �Y .
370 I. Claus / Economic Modelling 30 (2013) 366–374
3.6. Equilibrium conditions
The labor market clearing condition and the resource constraintare given by9
Lt−Nt ¼ 0 ð26Þ
and
Ct þ Gt þ EXt−Yt ¼ 0 ð27Þ
The capital stock obeys the following law of motion
Kt− 1−δð ÞKt−1−INt ¼ 0 ð28Þ
where INt denotes investment. All physical capital is imported and theforeign sector clearing condition is given by
QtB�tþ1 þ QtINt−QtB
g�tþ1
þ 1þ 1−τð ÞItð ÞQtBg�t
1þΠ�t
−1þ I�t� �
QtB�t
1þΠ�t
−EXt ¼ 0
ð29Þ
Moreover, uncovered interest rate parity holds
Et1þ 1−τð ÞI�tþ1� �
Stþ1
St− 1þ 1−τð ÞItþ1� ��
¼ 0 ð30Þ
It implies that households are indifferent between holding domesticand foreign bonds.
The real exchange rate evolves according to
EtQtþ1
Qt
� ¼ Et
Stþ1St
P�tþ1P�t
Ptþ1Pt
" #ð31Þ
and the sequences of the foreign interest rate, prices, inflation andforeign demand {It∗,Pt∗,Πt
∗,Yt∗} are given to the small open economy.
3.7. Parameterization of the model
A period in the model corresponds to one quarter. Parametervalues are chosen so that the steady state of the model is broadlyconsistent with New Zealand data and / or assumptions made in theliterature. Moreover, for simplicity, the government's budget constraintis assumed to balance in each period, i.e. there is no debt financing. Nodebt financing implies that B
gt ¼ B
g�t ¼ 0 for all t. Appendix A contains
details of the parameterization and the steady state equations.
4. Business cycle effects
Themodel developed in the previous section can be used to evaluatethe effectiveness of a variable VAT rate as a policy tool compared to aninterest rate. This requires solving two versions of themodel for a steadystate and taking a log-linear approximation around the steady state.In the first model the interest rate is used as the stabilization tool andin the second model the VAT rate is the policy instrument. The twolog-linearizedmodels are then subjected to a range of exogenous shocksand the impulse responses of the variable VAT ratemodel are comparedto those of the model, where the central bank uses an interest ratetool.10 Appendix B gives the log-linearized equations. It also specifiesthe inflation process and full capacity, flexible price output, whichenter the central bank's reaction function, and the shock processes.
To illustrate the effects of a variable VAT rate relative to adjustingan interest rate, two shocks are presented: to aggregate productivity
9 There is no unemployment or inventory build-up in this model. Following a shockto the economy markets clear because the central bank reacts to the shock.10 The log-linearized models are solved with the method of undetermined coeffi-cients. Uhlig's (1999) procedures for MATLAB are used.
and to foreign demand. The shocks are chosen for two reasons. First,one is a domestic shock and the other is a foreign shock. Second,the two shocks should lead to opposite effects on inflation. Thelabor-augmenting productivity shock is expected to temporarilylower inflation, while the foreign demand shock should produceupward pressure on prices. The impulse responses to a positive pro-ductivity shock and a positive foreign demand shock are plotted inFigs. 1 and 2. They are in percent deviations from steady state unlessotherwise indicated. The solid line shows the adjustment paths inthe interest rate model. The dotted line plots the impulse responseswhen the VAT rate is used as the stabilization tool by the centralbank. All variables eventually return to steady state.
The main results can be summarized as follows. A variable VATrate is a less effective stabilization tool than an interest rate. It leads tolarger adjustments in the policy instrument and fluctuations in thereal economy and inflation. Moreover, a variable VAT rate producesgreater (smaller) welfare losses (gains). This is because a variable VATrate has additional adverse supply effects. A change in the interestrate affects this period's marginal rate of substitution between currentand future consumption,whereas a variable VAT rate influences savingsand investment decisions over time. As a result, a variable VAT rate isless effective in dampening business cycles than an interest rate.
4.1. Productivity shock
The impulse responses of the variables in the VAT and interest ratemodels to a positive labor-augmenting productivity shock are plottedin Fig. 1. In both models, the positive productivity shock raises fullcapacity, flexible price output. In the interest rate model, the increasein full capacity, flexible price output leads to a negative output gap anddownward pressure on inflation. As a result, the central bank easesmonetary policy. The interest rate declines and the real exchangerate depreciates.
In the VAT ratemodel, the positive productivity shock also raises fullcapacity, flexible price output. But the rise is insufficient to meet in-creased demand and a positive output gap opens up. The positive out-put gap raises inflation and the central bank tightens monetary policy,i.e. the VAT rate increases. The rise in inflation produces a real exchangerate depreciation. The exchange rate depreciates bymore than in the in-terest rate model (due to the sharp rise in inflation), leading to a largerincrease in the cost and rental rate of capital. Also adding to the rise inthe rental rate of capital is the increase in the VAT rate, which raisesthemarginal rate of substitution between current and future consump-tion and the rate of return households demand for the use of their funds.The higher rental rate of capital in turn produces amore subdued rise infull capacity, flexible price output following the positive productivityshock and a smaller increase in investment.
In both models, the increase in output following the positive pro-ductivity shock raises tax revenue and government consumption.Moreover, the labor-augmenting productivity shock raises house-holds' wage rate and lowers employment. But household labor fallsby less in the VAT rate model than the interest rate model. This isbecause of the smaller rise in investment. Also adding to the smallerdecline in labor is a higher effective price of consumption due to therise in the VAT rate. Compared to the interest rate model, householdconsumption increases by less and exports rise by more.
Overall, the smaller increase in consumption and the smallerdecline in employment produce a smaller welfare gain followingthe positive productivity shock in the VAT rate model compared tothe interest rate model. Furthermore, deviations from steady stateof the policy instrument, inflation and the exchange rate are larger.
4.2. Foreign demand shock
The impulse responses to a positive foreign demand shock areplotted in Fig. 2. In both models, the shock raises exports and output
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Household consumption Government consumption
Exports Output
Investment Rental rate of capital
Household labor Wage rate
Interest rate (in percentage points) VAT rate (in percentage points)
Inflation (in percentage points) Real exchange rate
Flexible price output Output gap
Welfare (as a percent of steady state output)
Shock
(in percentage points)
Interest rate rule VAT rate rule
Fig. 1. Impulse responses to a productivity shock (in percent deviations from steadystate unless otherwise indicated).
-0.08
-0.06
-0.04
-0.02
0.00
0.02
-0.04
-0.02
0.00
0.02
0.04
0.06
0.0
0.2
0.4
0.6
0.8
1.0
0.00
0.03
0.06
0.09
0.12
-1.5
-1.0
-0.5
0.0
0.5
-3.6-3.0-2.4-1.8-1.2-0.60.0
0.00
0.03
0.06
0.09
0.12
0.15
-0.06
-0.04
-0.02
0.00
0.02
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10 12 14 16
0.00
0.01
0.02
0.03
0.04
0.05
0.0
0.2
0.4
0.6
0.8
1.0
-0.0050.0000.0050.0100.0150.0200.025
-0.3
-0.2
-0.1
0.0
0.00
0.02
0.04
0.06
0.08
0.00
0.02
0.04
0.06
0.08
0.10
-10
-8
-6
-4
-2
0
0.00.20.40.60.81.01.2
Household consumption Government consumption
Exports Output
Household labor Wage rate
Interest rate (in percentage points) VAT rate (in percentage points)
Inflation (in percentage points) Real exchange rate
Flexible price output Output gap
Welfare (as a percent of steady state output)
Shock
Investment Rental rate of capital(in percentage points)
Interest rate rule VAT rate rule
Fig. 2. Impulse responses to a foreign demand shock (in percent deviations from steadystate unless otherwise indicated).
and leads to a positive output gap, upward pressure on inflation and atightening in monetary policy. But the output gap and inflationarypressures are larger in the VAT rate model and the central bank
tightens monetary policy by more. The output gap is larger becausethe real exchange rate appreciates by less, leading to a smaller declinein the cost of imported capital, the rental rate of capital and hence
372 I. Claus / Economic Modelling 30 (2013) 366–374
flexible price output. At the same time the smaller real exchange rateappreciation in the VAT rate model produces a larger increase inexports and output, adding further to the positive output gap.
In both models, following the foreign demand shock and real ex-change rate appreciation, the cost and rental rate of capital fall. Inthe interest rate model, the decline in the rental rate of capital leadsfirms to substitute labor with capital. Investment increases by morethan household labor and the wage rate falls. In the VAT rate model,the rental rate of capital falls by less than in the interest rate model.This is partly because of a smaller real exchange rate appreciation.Adding to the smaller decline is the rise in the VAT rate, which raisesthe marginal rate of substitution between current and future con-sumption and the rate of return households demand for the useof their funds. At the same time, the higher VAT rate increases theeffective price of consumption, leading to a decline in consumption,the growth rate of output and the wage rate. The decline in wagesproduces a substitution of capital with labor and investment falls.
A variable VAT rate leads to larger fluctuations in tax revenue andgovernment spending. In the interest rate model, the increase in ex-ports and output raises tax revenue and government consumption.Tax revenue and government consumption are also initially higherin the VAT rate model but then decline. They fall as the effect of thehigher VAT rate is more than offset by lower household consumption.
Overall, the tightening in monetary policy following the positiveforeign demand shock leads to larger welfare losses in the VAT ratemodel (due to a larger fall in household consumption and a largerrise in household labor) than in the interest rate model. Moreover,as in the case of the productivity shock, the variable VAT rate leadsto larger adjustments in the policy instrument and fluctuations inthe real economy and inflation.
5. Concluding remarks
This paper examined the use of the value added tax as a macroeco-nomic stabilization tool. It first discussed some practical implicationsthat would arise with the implementation of a variable VAT. It thendeveloped a dynamic general equilibrium model to assess its useful-ness as a stabilization instrument.
The value added tax is considered less distortionary than othertaxes. This is because a constant rate VAT does not distort betweencurrent and future consumption, i.e. savings and investment decisions.A variable rate VAT would no longer be less distortionary than othertaxes. It would affect savings and investment decisions and henceraise the economic costs of taxation.
A variable VAT rate system would be more complex and difficultto manage than a constant rate system. It would increase tax admin-istration and business compliance costs and may lead to pressures fordifferential rates and exemptions. A variable VAT rate would provideincentives for tax planning and new avenues for fraud and any short-fall in VAT collection would need to be met with higher tax rates. Thiswould add further to the economic costs of taxation.
Moreover, a variable VAT rate would be a less effective stabiliza-tion tool than the conventional instrument, which is an interestrate. It would lead to larger adjustments in the policy instrumentand fluctuations in the real economy and inflation. This is because avariable VAT rate would have additional adverse supply effects. Achange in the interest rate affects this period's savings and invest-ment decisions, whereas a variable VAT rate would influence savingsand investment decisions over time. The value added tax is thereforeunlikely to be a useful stabilization instrument.
Acknowledgements
Special thanks are due to Brandon Sloan. I am grateful for valuablecomments from two referees, Matt Benge, Viv Hall, Don Harding,Kirdan Lees, Ewen McCann and John McDermott. I also benefitted
from suggestions by seminar participants at Inland Revenue, theReserve Bank of New Zealand and Otago University and participantsat the Econometric Society Australasian Meeting and the AustralasianMacroeconomics Workshop. The views expressed in this paper aremy own and do not necessarily represent those of Inland Revenue.
Appendix A. Parameterization and steady state
This appendix contains details of the parameterization and theequations solving for the steady state of the model.
Appendix A.1. Parameterization
Households' discount rate, β, equals 0.9947 and leads to an annualnominal, steady state domestic interest rate of 6%. The coefficient onleisure, γ, in households' utility function is chosen so that their workeffort accounts for a third of their time endowment in steady state.
Labor-augmenting productivity, �Z , is normalized to 1 in steady state.The elasticity of substitution between labor and capital, 1/(1−ν), isset to 0.85 in line with estimates for New Zealand by Hall and Scobie(2005). The coefficients on household labor, ηl, and capital, (1−ηl),in firms' production function are 0.64 and 0.36. These assumptionsare broadly in line with New Zealand input–output data and yield asteady state ratio of imports to output of about 12%, the same as inMcCallum and Nelson (1999). The capital depreciation rate, δ, equals8.5% per annum, the same as in the Reserve Bank of New Zealand'smacroeconomicmodel (Black et al., 1997) and firms' mark-up in steadystate is 20% (θ/(θ−1)=1.2), i.e. θ=6, the same as in McCallum andNelson (1999).
The annual domestic steady state inflation rate, ΠT, of 2% is equalto the mid-point of the Reserve Bank of New Zealand's 1% to 3% targetband for consumer price inflation. The income tax rate, τ, is set to 30%,broadly in line with the current average tax rate in New Zealand. Thesteady state VAT rate, �τVAT, is 15%, the same as the current rate. Thegovernment's budget constraint is assumed to balance in each period,i.e. there is no debt financing. The steady state foreign inflation rate,�Π�, and nominal bond rate, Ī∗, are set to be the same as for the domes-tic economy and the steady state real exchange rate, �Q , is normalizedto 1. The price and foreign demand elasticities of exports, κ and ς, areequal to unity, as in McCallum and Nelson (2000). Foreign demand ischosen to yield a steady state ratio of exports to output of 11%, thesame as in McCallum and Nelson (1999), leading to a current accountdeficit of around −1% of steady state output.
This appendix specifies the inflation process and full capacity, flex-ible price output, which enter the central bank's reaction function,and the shock processes. It also gives the equations for solving the dy-namic model. Dynamic responses are denoted by lower case letters.
Appendix B.1. Inflation process
The inflation process is derived from firms' optimal price settingfollowing Calvo (1983). With probability φ, firms can adjust theirprices each period. φ is set to 0.33, i.e. prices remain unchanged onaverage for three quarters.
The representative firm j sets its price to minimize a quadratic lossfunction that depends on the difference between the firm's actualprice in period t and its target price. The firm's target price, Pt jð Þ, isthe price that the firm would set in the absence of restrictions toadjust prices. It is given by Pt jð Þ ¼ θ= θ−1ð ÞPtMCt or in logarithmic de-viations from steady state as pt jð Þ ¼ pt þmct . Firm j's quadratic lossfunction and first-order condition with respect to pt(j) are given by11
If the number of firms is large, a fraction of firms φ actually adjustsprices each period and the inflation adjustment equation can be de-rived from Eq. (B.2) as πt=βEt[πt+1]+φ(1−(1−φ)β)/(1−φ)mct,where πt=pt−pt−1. That is, inflation is a function of expected futureinflation and real marginal cost. Under price stickiness, the marginalcost, MCt, is equal to the inverse of firms' price elasticity of demand,ξt, i.e. MCt=1/ξt. Using ξt= θ= θ−1ð Þð Þ ¼ ξtPtMCt= θ= θ−1ð ÞPtMCtð Þ ¼Pt=Pt jð Þ, Y t jð Þ ¼ Pt jð Þ=Pt
� �−θYt and dropping the j's (as all firms
charge the same price and produce the same output in a symmetricequilibrium), the log real marginal cost, mct, can be derived asmct ¼ − yt−yt
� �=θ. The inflation adjustment equation then is given
by
πt ¼ βEt πtþ1� þ ϱ yt− yt
� � ðB:3Þ
11 Firms' discount factor, β, is assumed to be the same as for households.
where ϱ=φ(1−(1−φ)β)/θ(1−φ) and yt denotes full capacity, flexi-ble price output. Inflation is determined by expected future inflationand the output gap, i.e. deviations of output from flexible price, fullcapacity output.
Appendix B.2. Full capacity, flexible price output
Full capacity, flexible price output, yt , is the total domestic outputof consumption goods that would be produced under price flexibility.In that case firms' mark-up is constant and output is given by
yt ¼ ηl�Z�L�Y
�ν
zt þ ηl�Z�L�Y
�ν
lt þ 1−ηl� � �K
�Y
�ν
kt−1 ðB:4Þ
where lt and kt−1 denote flexible price household labor and capital.Flexible price household labor, lt , can be derived from households'first-order condition that the marginal utility of leisure is equal to theafter-tax real wage rate and firms' first-order condition determininglabor demand (Eq. (19)). It is given by lt ¼ yt þ ν= 1−νð Þzt . Flexibleprice capital, kt−1, is derived from firms' first-order condition (20) andgiven by kt−1 ¼ yt−1= 1−νð Þrt . Eq. (B.4) can then be re-written as
yt ¼1
1−νzt−
1−ηl� � �K
�Y
� �νηl 1−νð Þ
�Z�L�Y
�ν rt ðB:5Þ
Full capacity, flexible price output is a function of labor-augmentingproductivity and the rental rate of capital.
Appendix B.3. Exogenous shocks
The productivity shock, zt, and the foreign demand shock, yt∗, areunivariate exogenous processes that are normally distributed. Theyevolve according to
The choice of shock parameters follows McCallum and Nelson(2000), except for the autocorrelation coefficient of the foreign de-mand shock. McCallum and Nelson (2000) assume that the foreigndemand shock is a random walk. Here, the autocorrelation coefficientof the foreign demand shock is assumed to be the same as for theproductivity shock, i.e. ρy� ¼ ρz ¼ 0:95. The innovation variances aregiven by σz
2=(0.007)2 and σ2y� ¼ 0:02ð Þ2.
Appendix B.4. Dynamic model
The dynamic model is described by (B.3) and (B.5) and the follow-ing equations:
⌣τVATt denotes logarithmic deviations of the VAT rate from steady
state. The choice for μ1 and μ2 is based on the parameter values in aTaylor rule (Taylor, 1993), i.e. μ1=1.5 and μ2=0.5.
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