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Fiscal Austerity in Emerging Market Economies�
Chetan Davey Chetan Ghatez Pawan Gopalakrishnanx
Suchismita Tarafdar{
April 30, 2018
Abstract
We build a small open economy RBC model with �nancial frictions to analyzeexpansionary �scal consolidations in emerging market economies (EMEs). We cali-brate the model to India, which we view as a proto-typical EME. When factor incometax rates are low, a contractionary �scal shock has an expansionary e¤ect on output.The economy�s debt/GDP ratio falls, and tax revenues rise. When factor income taxrates are high, a contractionary �scal shocks has an expansionary e¤ect on outputif government spending is valued su¢ ciently highly relative to private consumptionby households in utility. We identify the mechanisms behind these results, and theirimplications for actual economies undertaking �scal reforms.
Keywords : Expansionary Fiscal Consolidations, Fiscal Policy in Small Open Economies,Emerging Market Business Cycles, Financial Frictions.
JEL Codes : E32, E62
�We thank seminar participants at Virginia Tech and the 13th Annual Conference on Growth and De-velopment (2017) at ISI Delhi for helpful comments. We are grateful to PPRU (Policy Planning ResearchUnit) for �nancial assistance related to this project. The views and opinions expressed in this article arethose of the authors and no con�dential information accessed by Chetan Ghate during the monetary policydeliberations in the Monetary Policy Committee (MPC) meetings has been used in this article.
yDepartment of Economics, New York University - Abu Dhabi. Tel: (971)50-831-9256. E-mail: [email protected].
zCorresponding Author: Economics and Planning Unit, Indian Statistical Institute, New Delhi �110016,India. Tel: (91)-11-4149-3938. Fax: 91-11-4149-3981. E-mail: [email protected].
xStrategic Research Unit, Reserve Bank of India, Mumbai � 400001, India. Tel: (91)-22-2260-2206.E-mail: [email protected].
{Department of Economics, Shiv Nadar University, Gautam Buddha Nagar, Uttar Pradesh - 201314,India. Tel: (91)-120-266-3801. E-mail: [email protected].
1. Introduction
While many countries undertake �scal consolidations to reduce their �scal de�cits, there
is little consensus on the short and long term e¤ects of �scal austerity on public debt and
potential economic growth. The 2010 World Economic Outlook (WEO) published by the
IMF �nds that domestic demand falls by about 1 percent in response to consolidation. It also
�nds that �scal contractions that rely on spending cuts tend to have smaller contractionary
e¤ects than tax based adjustments (IMF WEO, page 95). Building on the seminal work
of Giavazzi and Pagano (1990), another branch of the literature however shows that �scal
retrenchments can stimulate growth in the short run, a phenomenon referred to as the
"expansionary �scal contraction" hypothesis.1 Such expansions happen if the consolidation
is structured in a way that increases con�dence.
Most of the quantitative macroeconomic literature on �scal contractions however is in
the context of advanced economies.2 What is missing is an understanding of the mechanisms
behind �scal consolidations in emerging market economies. Our paper attempts to �ll this
gap. We build a small open economy real business cycle (SOE RBC) model with �nancial
frictions and �scal policy that is more suited to analyzing �scal contractions in EMEs.
Our model builds on the work of Neumeyer and Perri (2005), Ghate, Gopalakrishnan, and
Tarafdar (2016), and Hansen and Imrohoroglu (2016). We calibrate the model to India,
which we view as a proto-typical small open economy, to understand the e¤ects of �scal
contractions in small open emerging market economies.3 Our main result is that when factor
income tax rates are low, a contractionary �scal shock can have an expansionary e¤ect on
GDP. The rise in GDP makes the economy�s debt/GDP ratio fall. In contrast, when factor
income tax rates are high, a contractionary �scal shock has an expansionary e¤ect on output
1See Alesina and Ardagna (2010).2A large literature on �scal consolidation on economic activity in advanced economies (Aiyagari et al.,
1992; Baxter and King, 1993; Christiano and Eichenbaum, 1992; Gali, Lopez-Salido, and Valles, 2007)�nds that with in�nitely lived Ricardian households, an increase in (non-productive) government spendingpurchases (�nanced by current or future lump sum taxes) lowers the present value of after tax income andgenerates a negative wealth e¤ect on consumption. The empirical literature on the e¤ects of �scal policy(Blanchard and Perotti (2002), Romer and Romer (2010)) also �nds similar results.
3Neumeyer and Perri (2005), Aguiar and Gopinath (2007), and Chang and Fernandez (2013) provideimportant frameworks for understanding the impact of interest rate shocks in small open economy RBCmodels.
1
if government spending is valued "su¢ ciently highly" relative to private consumption by
households in utility. If the relative weight on government spending by households in utility
is low, contractionary �scal policy reduces output. Public debt/GDP rises in the transition
to the steady state, and tax revenues falls, thereby worsening macroeconomic outcomes.
Our analysis is policy relevant since in recent years many emerging market economies
have undergone �scal consolidations to reduce their �scal de�cits and public debt/GDP
ratios. Figure 1, which plots the �scal de�cit/GDP ratio of Malaysia since 2009, depicts a
fairly large reduction in the �scal de�cit/GDP ratio approximating 3.7%.
Figure 1. Fiscal De�cit as % of GDP in Malaysia.
65
.55
4.5
43
.5Fi
scal
Def
icit
as %
of
GD
P
2010 2012 2014 2016 2018Year
Fiscal Deficit as % of GDP for India
Figure 2. Fiscal De�cit as % of GDP in India.
Figure 2, which depicts the Indian case, also shows a central �scal de�cit/GDP reduction
of a similar order of magnitude. The 2018 IMF Fiscal Monitor notes that many emerging
market countries have already (Brazil, Saudi Arabia) or are in the process of implementing
(Russia, China) �scal consolidation plans. The novel aspect of our framework is that we build
2
a uni�ed dynamic stochastic general equilibrium framework that identi�es conditions under
which, (i) �scal contractions are contractionary, and (ii) �scal contractions are expansionary.
1.1. Description of Model
Our theoretical framework builds on Neumeyer and Perri (2005), Ghate, Gopalakrishnan,
and Tarafdar (2016), and Hansen and Imrohoroglu (2016). In particular, we add public debt
to the framework of Ghate, Gopalakrishnan, and Tarafdar (2016) along the lines of Hansen
and Imrohoroglu (2016).
The economy consists of �rms, a government, and households. Firm wage payments
are subject to working capital constraints, as in Neumeyer and Perri (2005) and Ghate,
Gopalakrishnan, and Tarafdar (2016). Working capital constraints are the key �nancial
friction in the model. To meet the working capital constraint, �rms borrows from house-
holds domestically and abroad by issuing corporate debt which is priced at the international
interest rate, R�:
In�nitely lived households derive utility over private consumption (Ct) and government
consumption (Gt) which are assumed to be perfect substitutes but with di¤erent weights;
leisure (1�Ht); government bonds (Dt), as in Hansen and Imrohoroglu (2015); and private
bonds (Bt). We assume that households value holding government bonds relatively more
than private bonds since private bonds are assumed to be relatively more riskier compared
to the risk free asset. Consumers form habits in their expenditure formation with utility
depending on current consumption, Ct; relative to a habit reference level, Ct�1: E¤ective
consumption is given by C�t = Ct + �Gt; where � > 0 is the relative weight of government
consumption in utility.4
The government collects tax revenue by imposing time invariant distortionary taxes on
wage and capital incomes, does not balance its budget, and borrows by issuing debt at
a rate RGt > 1. The government allocates Gt of it�s total revenue towards government
consumption. The residual is transferred to households in the form of a lump-sum transfer
(Tt). The sovereign risk premium on public debt depends on the deviation of the period t
4The presence of habits ensures that �scal shocks lead to sluggish adjustments in e¤ective consumptionwhich ensures that steady state consumption, C > 0:
3
debt-GDP (dt) ratio relative to its steady state value ( �d). If the debt-GDP ratio is higher
than its steady state, than the rate at which the government borrows is higher Thus,
the sovereign risk premia required to borrow in international capital markets depends on
domestic fundamentals in the economy. Finally, the interest rate on corporate debt, Rpt > 1;
is priced o¤ the RGt , as in many emerging market economies, which implies that RPt > R
Gt
(see Caballero, Fernandez, and Park (2016)). Hence, RPt > RGt > R
�
We calibrate the model using a broad set of parameters representative of the Indian
economy. Using Sims (2002), the solution to the log-linearized system is the state equation
of the model in the form of a VAR (1). We discuss the intuition behind the impulse response
functions generated by three main shocks in the model: government spending shocks, foreign
interest rate shocks, and total factor productivity shocks.
1.2. Main Results
The main insight obtained is to identify the mechanism and conditions under which �s-
cal contractions can be contractionary or expansionary in the short run. We �rst consider
the case when factor income tax rates are low. A reduction in government consumption
leads to a rise in private consumption, but a decline in e¤ective consumption, since govern-
ment consumption and private consumption are substitutes in utility. A decline in e¤ective
consumption increases the marginal utility from e¤ective consumption, which induces the
household to work more. Despite the fall in government spending, low tax collections from
factor incomes leads to a rise in public debt, plus a lump sum tax that is required for the
government budget constraint to hold. The negative wealth e¤ect from higher lump sum
taxes induces households to work more. As a result, employment rises and wages fall. Since
the capital stock is given in time period t; higher hours worked leads to higher GDP. Hence,
on impact, a contractionary �scal shock is expansionary. Higher output also induces house-
holds to buy more government and private bonds, since these enhance utility. Because the
increase in government bonds increases by less than the increase in output, the debt-GDP
ratio falls on impact. The reduction in the debt-GDP ratio relative to its steady state value
reduces the sovereign risk premium, and depresses RGt : Since private sector debt is priced o¤
of RGt ; working capital loan rates fall. Higher output increases the gross marginal product
4
of capital, Rt: While ordinarily this would depress capital accumulation, higher labor sup-
ply increases the marginal productivity of private capital increasing investment and capital
accumulation overall. This provides a further boost to output in the next period. We �nd
that a �scal contraction increases hours worked, GDP, investment and capital accumulation.
It also reduces the public debt-GDP ratio and which reduces the sovereign risk premium.
Now consider the case when factor income tax rates are high.5 We show that the inci-
dence of a contractionary �scal consolidation being expansionary now depends on the value
of �; the parameter denoting the relative superiority of government consumption vis-a-vis
private consumption in utility.6 When � is low, a negative government spending shock in-
creases private consumption and e¤ective consumption. The marginal utility from e¤ective
consumption falls. Hours worked falls, and wages rise. A reduction in hours worked drives
GDP down which reduces R on impact. A lower R increases investment and capital accu-
mulation in the next period. However, the reduction in the marginal utility from e¤ective
consumption requires a reduction in the marginal utility of holding public and private debt
by households to maintain their marginal rate of substitution conditions. Hence, the de-
mand for private and public debt rises. This raises the public debt-GDP ratio, pushing up
the sovereign risk premium, the government borrowing rate, RGt ; and therefore RPt : When
� is high, the key di¤erence is that a negative government spending shock increases pri-
vate consumption, but reduces e¤ective consumption. Hours work rises, which raises GDP,
investment (because the marginal product of capital rises with higher employment), and
capital, increasing output in the next period as well. Higher GDP implies that households
demand more private and public debt, but because output has risen, the public-debt to GDP
ratio falls. This reduces the sovereign risk premium, implying that both RGt and RPt fall.
To balance its budget, the government lump sum taxes households. These lump sum taxes
impose a negative wealth e¤ect on households which induces the household to work more.
We compare these results with the propagation mechanism from foreign interest rate
shocks, and TFP shocks. For these cases, the dynamics of the economy respond similarly
5In the experiments we conduct later on, we arbitrarily set factor income taxes to be 10 times higherthan the baseline case.
6 . Consistent with the empirical literature, we restrict 0 < � < 1 ( see Ambler and Paquet (1996), andBarro (1981)).
5
to the low and high tax cases. A foreign interest rate shock raises RP and RG on impact.
This reduces private consumption and e¤ective consumption, and increases the demand for
public and private debt since these now give higher returns. The reduction in e¤ective
consumption raises hours worked, but in the net hours worked falls, since higher lump sum
taxes are required to balance the government budget constraint. This pushes hours worked
down, and GDP falls.
Our analysis uncovers an interesting point of departure with respect to Neumeyer and
Perri. A reduction in GDP because of a rise in foreign interest rates also obtains in Neumeyer
and Perri (2005). In that paper however, there is no �scal policy. Unlike Neumeyer and Perri
(2005), we also don�t have to assume GHH preferences to obtain this result.
With a TFP shock, both factor prices, wages, and the marginal product of capital, rise.
Households work more, which increases GDP. More employment raises the marginal product
of capital which increases investment and the capital stock in the next period. Higher GDP
raises consumption and e¤ective consumption. The demand for public and private debt falls,
which reduces RP and RG:
2. The Model
2.1. Firms
The economy consists of �rms, a government, and households. At any given time t a
representative �rm produces �nal output using labor employed at time t and capital carried
forward from time period t� 1. However, prior to actual production, the �rm needs to pay
a portion � 2 [0; 1] of its total wage bill. To meet this working capital constraint, the �rm
borrows from households by issuing debt. The �rm issues corporate bonds (Bt) to households
to whom they promise a return of RPt�1 which is considered to be a markup over the domestic
government bond interest rate, RGt�1.
The �rm hires labor (Ht) and uses capital (Kt�1) accumulated in time period t � 1 to
6
produce the �nal output Yt such that
maxfKt;Htg
Yt �RtKt�1 � (1� �)WtHt � �WtHtRPt�1, (1)
where,
Yt = AtK�t�1H
1��t (2)
and At denotes exogenous total factor productivity (TFP). This yields the following �rst
order conditions for �rms.
(1� �)YtHt
= Wt
�1� � + �RPt�1
�(3)
�YtKt�1
= Rt (4)
The timing of events and decisions is identical to Neumeyer and Perri (2005) and Ghate
et al. (2016). In the beginning of period t, which we denote as t�, �rms borrow �WtHt to
make advance payments to labor prior to actual production (which occurs at t). Firms then
produce output and repay the loan borrowed at the end of time period (t+), with workers
receiving the rest of their wage bill (1 � �)WtHt at time t+. Since the time gap between
t� and t, and between t and t+ is very small, we drop these superscripts and consider the
entire period as time period t.
2.2. Households
The economy is populated by in�nitely lived households with a mass normalized to 1.
The representative household consumes and invests a homogenous good and supplies labor
and capital to �rms. As in the vast literature on habit formation, we assume that consumers
form habits in their expenditure formation with utility, U; depending on current consumption,
Ct; relative to a habit reference level, Ct�1: The representative household has the following
expected discounted lifetime utility
E0
1Xt=0
�tU(C�t ; Ht; Bt; Dt); (5)
7
where � 2 (0; 1) denotes the households subjective discount factor. We assume that
Ct + �Gt; (6)
where household consumption (Ct) is augmented by government consumption (Gt). The
parameter � captures the weight of public consumption in household utility, where � > 0.
Given our speci�cation in equation (6), Ct and Gt are assumed to be perfect substitutes.7
We assume that agents treat Gt as a given covariance stationary stochastic process (CSSP).
Finally, households also derive utility from holding private and government debt (Bt and
Dt respectively). Our speci�cation of the household deriving utility over public debt follows
Hansen and Imrohoroglu (2016). In the calibration exercise later, we assume that the pref-
erence for holding public debt is higher than private debt since public debt is the risk free
asset.
We adopt a unitary elasticity of substitution speci�cation for instantaneous utility
U(C�t ; Ht; Bt; Dt) = � ln (Ct � �Ct�1 + �Gt) + (1� �� '1 � '2) ln (1�Ht) (7)
+ '1 ln (Dt) + '2 ln (Bt) :
The household faces the following constraint
Ct +Xt +Bt + �1(Bt) +Dt + �2(Dt) (8)
= (1� �w)WtHt + (1� �k)RtKt�1 +RPt�1Bt�1 +R
Gt�1Dt�1 + Tt
where Bt denotes private bond holdings, Xt denotes investment, �w 2 [0; 1] is the tax on
labor income, and �k 2 [0; 1] is the tax on capital income. Agents take the competitive wage
rate (Wt) and return to capital (Rt) as given in deciding optimal choices. For private bond
7In an emerging markets context, an example of Gt can be public health or public transportation serviceswhose quality is typically seen as being superior to private alternatives. See Barro (1981), Christiano andEichenbaum (1992), and Ghate et al. (2016).
8
holdings the term �(Bt) in (8) is the bond holding cost,
�1(Bt) =�12Yt
�BtYt��B�Y
�2: (9)
Households also invest in government bonds (Dt) and holding these involve an analogous
cost,
�2(Dt) =�22Yt
�Dt
Yt� D�Y
�2: (10)
The term Xt in (8) is the level of private investment
Xt = Kt � (1� �)Kt�1 + �(Kt; Kt�1); (11)
where �(Kt; Kt�1) is the capital adjustment costs such that8
�(Kt; Kt�1) =�
2Kt�1
��Kt
Kt�1
�� 1�2: (12)
Therefore,
Xt = Kt � (1� �)Kt�1 +�
2Kt�1
�Kt
Kt�1� 1�2
(13)
is the law of motion of capital accumulation.
2.3. Government Budget Constraint
The government in our model follows a non-discretionary �scal policy. It collects tax
revenue by imposing time invariant distortionary taxes on wage and capital incomes, does
not balance its budget, and borrows by issuing debt at a rate RGt . The government allocates
Gt of it�s total revenue towards government consumption. The residual is transferred to
households in the form of a lump-sum transfer (Tt). The following is the government budget
constraint, in every time period t.
Gt + Tt = �wWtHt + �kRtKt +Dt �RGt�1Dt�1, (14)
8An investment adjustment cost is required to make the volatility of private investments relative to outputmatch empirically observed values. This is also a standard practice in RBC models.
9
where
RGt = �R�t exp
�Dt
Yt��D�Y
�: (15)
RGt is assumed to be a mark-up over the international interest rate R�t .9 The mark-up is the
spread over the international interest rate, to capture sovereign risk, modelled as deviations
from the steady state debt to GDP levels, i.e.,
�t = � exp
�Dt
Yt��D�Y
�; where � > 0: (16)
We further assume that the interest rate on private bonds is equal to the interest rate on
government bonds with an additional mark-up, i.e.,
RPt = �RGt : (17)
This re�ects the fact that there is a risk premium in corporate bonds over government bonds.
In light of the above environment, given fAt; R�t ; Gtg1t=0, a vector of �scal policy para-
meters f�k; �w; �g, and initial conditions K�1; B�1; D�1; RP�1; R
G�1; a competitive equilib-
rium for our model is a vector of allocations of fCt; Kt; Dt; Bt; and Htg1t=0 and factor prices
fWt and Rtg1t=0 such that, for the given sequence of factor prices, (i) fKt and Htg1t=0 solves
the �rm�s pro�t maximization problem (1), and FOCs (3-4), (ii) fCt; Kt; Bt; Dt; Htg1t=0 max-
imizes the utility of the representative agent (5) subject to (2), (8), (6), (9), (10), (12), and
(13) together with Ct; Kt > 0, (iii) Tt satis�es (14), (iv) a no-Ponzi associated with the
initial conditions K�1; B�1; and D�1 holds for the representative agent, and �nally, (v) all
markets clear for all time periods. .
Collecting the decision rules and constraints across all economic actors, this de�nition of a
competitive equilibrium results in the following system of nonlinear expectational di¤erence
9We assume R�t to be an exogenous process. Typically in the literature, the international interest rateR�t is assumed to be the US 91 day T-Bill rates (see Neumeyer and Perri (2005), Ghate et al. (2016)).
10
equations that describe this �cycles only�model10:
�t =�
Ct � �Ct�1 + �Gt� ��
Ct+1 � �Ct + �Gt+1(N1)
(1� �w)�tWt =1� �� '1 � '2
1�Ht(N2)
Et
8><>:��t+1
�1� � � �
2
hKt+1
Kt� 1i2+ �Kt+1
Kt
hKt+1
Kt� 1i+ (1� �k)Rt+1
�= �t
h1 + �
hKt
Kt�1� 1ii
9>=>; (N3)
Et
���t+1R
Pt = �t
�1 + �1
�BtYt��B�Y
��� '2Bt
�(N4)
Et
���t+1R
Gt = �t
�1 + �2
�Dt
Yt��D�Y
��� '1Dt
�(N5)
Ct +Kt � (1� �)Kt�1 +�
2Kt�1
�Kt
Kt�1� 1�2+Bt +
�12Yt
�BtYt��B�Y
�2+Dt (N6)
+�22Yt
�Dt
Yt��D�Y
�2= (1� �w)WtHt + (1� �k)RtKt�1 +R
Pt�1Bt�1 +R
Gt�1Dt�1 + Tt
(1� �)YtHt
= Wt
�(1� �) + �RPt�1
�(N7)
�YtKt�1
= Rt (N8)
Yt = AtK�t�1H
1��t (N9)
Gt + Tt = �wWtHt + �kRtKt +Dt �RGt�1Dt�1 (N10)
RGt = �R�t exp
�Dt
Yt��D�Y
�(N11)
RPt = �RGt (N12)
Gt � CSSP ( �G; �G; �G) (N13)
At � CSSP ( �A; �A; �A) (N14)
R�t � CSSP ( �R�; �R� ; �R�) (N15)
where CSSP denotes (an exogenous) covariance stationary stochastic process. The assump-
tion that government debt has utility value following Hansen and Imrohoroglu (2016) asserts
itself in the system above. The Euler equations governing private and public debt (equations
10We note that there is no source of deterministic growth in this model and so the log-linearized versionwe analyze next is to be interpreted in terms of Hodrick-Prescott �ltered data analogs.
11
(N4) and (N5) respectively) are distinct from each other and distinct from that governing
the determination of physical capital (equation (N3)). The working capital friction clearly
introduces a wedge into the equation governing the determination of wages from the �rms�
side (equation (N2)). The remaining equations are standard relative to a baseline RBC
model with real frictions.
3. Calibration
We analyze the log-linearized version of the model, which, for instance following Sims
(2001), can be written as a system of 15 equations in 15 variables:
�0Xt+1 = �1Xt +"t +��t
where; Xt = fCt; Ht; Dt; Kt; Bt; Yt;Wt; Rt; RPt ; R
Gt ; Tt;�t; Gt; At; R
�tg
and the matrices �0, �1, and � are functions of 25 model parameters:
�; �; �; �; '1; '2; �; �; �1; �2; �w; �k; �; �;�; �; �G; �A; �R�; �G; �A; �R� ; �G; �A; �R� ;
with �G = �A = 1, and three new variables re�ecting idiosyncratic rational expectations errors
(�t) have been subsumed in the notation (see DeJong and Dave (2011)). Given the above
representation, any linear solution method including that of Sims (2001) solves a system of
linear expectational di¤erence equations under rational expectations as
Xt+1 = FXt +G"t; E("t"0t) =
26664�2G 0 0
0 �2A 0
0 0 �2R�
37775 ;
which is the state equation of the model in the form of a VAR (1).11
Next, we calibrate the model to India, a proto-typical small open emerging market econ-
omy. Our baseline calibration proceeds as follows. We chose the value of R�to equal 1:0035
11We analyze the model using DYNARE v. 4.5.0.
12
so that it is close to the long run real interest rate on 91-Day US T-Bill bonds (with f�R� ; �R�g
being (0.7400, 0.0030)). Given that India has a very narrow income tax base and depends
more on generating revenue from indirect taxation, we allow for low income taxes. In par-
ticular, we �x the factor income tax rates at �k = �w = 0:01 following the estimated average
e¤ective tax rates in Poirson (2006). Given data on RPt (Indian commercial paper) and RGt
(91-day Indian T-bill rate) we obtain � and � as 1.01259 and 1.00131 respectively. Since
we have included bond holding costs in our household constraint not just for realism in the
EME context but also to ensure that the corresponding �rst order conditions do not follow
a random walk, we assume them to be small (�1 = �2 = 0:0062). For similar realism in the
Indian context, we set � to be 0.5 and � to be 8.8591. The impulse responses we discuss
below are invariant to these parameter choices.
Our choices for preference parameter values re�ect the following intuition. We set � to be
0.4 to give the highest weight to consumption and '1 and '2 to be 0.2 and 0.15 respectively
to re�ect that due to risk aversion considerations households would give less weight to private
bonds than government bonds. These parameter values then imply a weight of approximately
a third on leisure which corresponds to the notion that households spend approximately
that amount of time on non-employment activity. Table 1 below summarizes our choice of
parameters in our model.
Table 1: Baseline Parameters
13
Parameters Values Source Parameters Values Source
� 0.4 Arbitrary �1 = �2 0.006 Arbitrary
� < 1 Barro (1981) �G 0.59 Anand and Prasad. (2010)
� 0.4 Arbitrary �A 0.82 Basu et al. (2018)
#1 0.2 Arbitrary �R� 0.74 Authors�Calculation
#2 0.15 Arbitrary �G 0.026 Anand et al. (2010)
� 0.36 Ghate et al. (2016) �A 0.016 Anand et al. (2010)
� 0.98 Gabriel et al. (2012) �R� 0.003 Calculated
� 0.025 Banerjee and Basu (2017) R�
1.0035 Calculated
�w = �k 0.01 Poisron (2006) � 1.01259 Calculated
� 8.8591 Arbitrary � 1.001312 Calculated
� 0.5 Arbitrary G = A 1 Arbitrary
4. Impulse Responses
Our model features three exogenous shock processes, for Gt, R�t and At (all in logarithmic
deviations from steady state). The impulse responses for these shocks are provided below.
The following impulse responses are for our baseline case which is for �w = �k = 0:01 and
� = 0:8:
14
4.1. G Shock
Figure 3: Impulse responses for a single period bG shock
5 10 15 20 25 30 35 400
0.02
0.04
0.06
0.08C
5 10 15 20 25 30 35 4010
8
6
4
2
0
2 104 cs
5 10 15 20 25 30 35 400
1
2
3
4 103 H
5 10 15 20 25 30 35 401
0.5
0
0.5
1
1.5
2 105 D
5 10 15 20 25 30 35 400.5
0
0.5
1
1.5
2
2.5 103 R
5 10 15 20 25 30 35 400
1
2
3
4
5
6 104 K
5 10 15 20 25 30 35 401
0.8
0.6
0.4
0.2
0 105 RP
5 10 15 20 25 30 35 401
0.8
0.6
0.4
0.2
0 105 RG
5 10 15 20 25 30 35 400
0.5
1
1.5
2
2.5
3 103 Y
5 10 15 20 25 30 35 4015
10
5
0
5 104 W
5 10 15 20 25 30 35 403
2.5
2
1.5
1
0.5
0 103 d
5 10 15 20 25 30 35 402
0
2
4
6
8 103 x
5 10 15 20 25 30 35 402
1
0
1
2
3 105 B
5 10 15 20 25 30 35 400
0.005
0.01
0.015
0.02
0.025
0.03LT
5 10 15 20 25 30 35 400.03
0.025
0.02
0.015
0.01
0.005
0G
5 10 15 20 25 30 35 400.05
0.04
0.03
0.02
0.01
0FD
5 10 15 20 25 30 35 400
1
2
3
4
5
6 103 TR
Figure 3 depicts the case of a negative government spending shock (government consump-
tion falls). A reduction in government consumption leads to a rise in private consumption,
but a decline in e¤ective consumption (cs), since government consumption and private con-
15
sumption are substitutes in utility. A decline in e¤ective consumption increases the marginal
utility from e¤ective consumption, which induces the household to work more. Since the cap-
ital stock is given in time period t; higher hours worked leads to higher GDP, which directly
increases the return on capital, Rt. Despite a drop in wt, RPt , and RGt , disposable income of
households increase. Hence, on impact, a contractionary �scal shock is expansionary, and
higher output and disposable income also induces households to buy more government and
private bonds, since these enhance utility.
Because the increase in government bonds increases by less than the increase in output,
the debt-GDP ratio falls on impact. The reduction in the debt-GDP ratio relative to its
steady state value reduces the sovereign risk premium, and depresses RGt : Since private
sector debt is priced o¤ of RGt ; working capital loan rates also fall. Finally, higher output
increases the gross marginal product of capital, Rt: While ordinarily this would depress
capital accumulation, higher labor supply increases the marginal productivity of private
capital increasing investment and capital accumulation overall. This provides a further
boost to output in the next period. In sum, a �scal contraction increases hours worked,
GDP, investment and capital accumulation. It also reduces the public debt-GDP ratio, the
�scal de�cit, and therefore the sovereign risk premium.
16
Figure 4: Impulse responses for a single period bR� shock
5 10 15 20 25 30 35 401.5
1
0.5
0 105 C
5 10 15 20 25 30 35 403
2.5
2
1.5
1
0.5
0 106 cs
5 10 15 20 25 30 35 4015
10
5
0
5 107 H
5 10 15 20 25 30 35 400
1
2
3
4
5
6 108 D
5 10 15 20 25 30 35 4010
8
6
4
2
0
2 107 R
5 10 15 20 25 30 35 405
4
3
2
1
0 107 K
5 10 15 20 25 30 35 400
1
2
3
4 103 RS
5 10 15 20 25 30 35 400
0.2
0.4
0.6
0.8
1 105 RP
5 10 15 20 25 30 35 400
0.2
0.4
0.6
0.8
1 105 RG
5 10 15 20 25 30 35 401
0.8
0.6
0.4
0.2
0 106 Y
5 10 15 20 25 30 35 405
4
3
2
1
0 106 W
5 10 15 20 25 30 35 400
0.2
0.4
0.6
0.8
1 106 d
5 10 15 20 25 30 35 404
3
2
1
0
1 106 x
5 10 15 20 25 30 35 400
2
4
6
8 108 B
5 10 15 20 25 30 35 401.2
1
0.8
0.6
0.4
0.2
0 107 LT
5 10 15 20 25 30 35 400
0.5
1
1.5
2 106 FD
5 10 15 20 25 30 35 408
6
4
2
0 106 TR
4.2. R� Shock
Figure 4 depicts the case of a positive foreign interest rate, R�; shock. A foreign interest
rate shock on R� raises RP and RG on impact. This reduces private consumption and
e¤ective consumption, and increases the demand for public and private debt since these now
give higher returns. The reduction in e¤ective consumption raises hours worked, but in the
17
net hours worked falls, since falling lump sum and proportional taxes induces households
to enjoy more leisure. This pushes hours worked down, and GDP falls. The reduction in
GDP is similar to the e¤ect of a rise in foreign interest rates in Neumeyer and Perri (2005).
In Neumeyer and Perri however, there is no �scal policy. The reduction in GDP in our
model obtains because of a �scal policy channel where higher lump sum taxes are required
to balance the government budget constraint.
18
Figure 5: Impulse responses for a single period bA shock
5 10 15 20 25 30 35 400
0.005
0.01
0.015
0.02A
5 10 15 20 25 30 35 400
0.01
0.02
0.03
0.04
0.05
0.06C
5 10 15 20 25 30 35 400
0.002
0.004
0.006
0.008
0.01cs
5 10 15 20 25 30 35 405
0
5
10
15 103 H
5 10 15 20 25 30 35 404
3
2
1
0
1 105 D
5 10 15 20 25 30 35 400.005
0
0.005
0.01
0.015
0.02
0.025R
5 10 15 20 25 30 35 400
2
4
6
8 103 K
5 10 15 20 25 30 35 401
0.8
0.6
0.4
0.2
0 104 RP
5 10 15 20 25 30 35 401
0.8
0.6
0.4
0.2
0 104 RG
5 10 15 20 25 30 35 400
0.005
0.01
0.015
0.02
0.025Y
5 10 15 20 25 30 35 400
0.002
0.004
0.006
0.008
0.01
0.012W
5 10 15 20 25 30 35 400.025
0.02
0.015
0.01
0.005
0d
5 10 15 20 25 30 35 400.01
0
0.01
0.02
0.03
0.04x
5 10 15 20 25 30 35 405
4
3
2
1
0
1 105 B
5 10 15 20 25 30 35 400
1
2
3
4 104 LT
5 10 15 20 25 30 35 400.05
0.04
0.03
0.02
0.01
0FD
5 10 15 20 25 30 35 400
0.01
0.02
0.03
0.04
0.05TR
4.3. TFP Shock
Figure 5 depicts the case of a positive TFP ( bA shock). With a TFP shock, both factorprices, wages, and the marginal product of capital, rise. Households work more, which
increases GDP. More employment raises the marginal product of capital which increases
investment and the capital stock in the next period. Higher GDP raises consumption and
19
e¤ective consumption. The demand for public and private debt falls, which reduces RP and
RG:
4.4. Policy Experiments
Finally, as experiments, we consider the case where taxes are high, i.e., �w = �k = 0:112
In this case, we consider two cases �a high value of �; i.e., � = 0:8 and low value of �; i.e.,
� = 0:3. Figure 6a corresponds to the case where � = 0:8: Figure 6b on the other hand
corresponds to the case where � = 0:3:
12We arbitrarily set factor income taxes to be 10 times higher than the baseline case to denote the situationof high taxes.
20
Figure 6a: Impulse responses for a single period bG shock for � = 0:8; and �w = �k = 0:1
5 10 15 20 25 30 35 400
0.05
0.1
0.15C
5 10 15 20 25 30 35 4020
15
10
5
0
5 104 cs
5 10 15 20 25 30 35 400
1
2
3
4 103 H
5 10 15 20 25 30 35 401
0
1
2
3 105 D
5 10 15 20 25 30 35 400
5
10
15
20 104 R
5 10 15 20 25 30 35 400
1
2
3
4
5
6 104 K
5 10 15 20 25 30 35 401.2
1
0.8
0.6
0.4
0.2
0 105 RP
5 10 15 20 25 30 35 401.2
1
0.8
0.6
0.4
0.2
0 105 RG
5 10 15 20 25 30 35 400
0.5
1
1.5
2
2.5
3 103 Y
5 10 15 20 25 30 35 4015
10
5
0
5 104 W
5 10 15 20 25 30 35 403
2.5
2
1.5
1
0.5
0 103 d
5 10 15 20 25 30 35 402
0
2
4
6 103 x
5 10 15 20 25 30 35 402
1
0
1
2
3
4 105 B
5 10 15 20 25 30 35 400
0.01
0.02
0.03
0.04LT
5 10 15 20 25 30 35 400.03
0.025
0.02
0.015
0.01
0.005
0G
5 10 15 20 25 30 35 400.05
0.04
0.03
0.02
0.01
0
0.01FD
5 10 15 20 25 30 35 400
1
2
3
4
5
6 103 TR
Figure 6a depicts the case of a negative government spending shock with high income
tax. A reduction in government consumption leads to a rise in private consumption, but
a decline in e¤ective consumption. The transmission channel in this case is similar to our
baseline case, as corresponding to Figure (3).
21
Figure 6b: Impulse responses for a single period bG shock for � = 0:3; and �w = �k = 0:1
5 10 15 20 25 30 35 400.01
0
0.01
0.02
0.03C
5 10 15 20 25 30 35 400
2
4
6
8
10 103 cs
5 10 15 20 25 30 35 402
1
0
1
2
3 103 H
5 10 15 20 25 30 35 402
0
2
4
6
8
10 105 D
5 10 15 20 25 30 35 401
0.5
0
0.5
1
1.5 103 R
5 10 15 20 25 30 35 405
0
5
10
15 104 K
5 10 15 20 25 30 35 4010
5
0
5 106 RP
5 10 15 20 25 30 35 4010
5
0
5 106 RG
5 10 15 20 25 30 35 401
0
1
2
3 103 Y
5 10 15 20 25 30 35 406
4
2
0
2
4
6 104 W
5 10 15 20 25 30 35 403
2
1
0
1 103 d
5 10 15 20 25 30 35 405
0
5
10
15 103 x
5 10 15 20 25 30 35 405
0
5
10
15 105 B
5 10 15 20 25 30 35 400
0.01
0.02
0.03
0.04LT
5 10 15 20 25 30 35 400.03
0.025
0.02
0.015
0.01
0.005
0G
5 10 15 20 25 30 35 400.06
0.04
0.02
0
0.02FD
5 10 15 20 25 30 35 402
0
2
4
6 103 TR
Figure 6b depicts the case of a negative government spending shock with high factor
income tax and lower �. A reduction in government consumption leads to a rise in private
consumption, and an increase in e¤ective consumption, since government consumption has
a lower coe¢ cient in utility. An increase in e¤ective consumption decreases the marginal
utility from e¤ective consumption, which induces the household to work less leading to lower
22
GDP, and lower Interest on capital, Rt. Hence, on impact, a contractionary �scal shock is
contractionary.
These experiments show that the incidence of a contractionary �scal consolidation being
expansionary depends on the value of �; the parameter denoting the relative superiority
of government consumption vis-a-vis private consumption in utility.13 When � is low, as in
Figure 6b, a negative government spending shock increases private consumption and e¤ective
consumption. The marginal utility from e¤ective consumption falls. Hours worked falls, and
wages rise. A reduction in hours worked drives GDP down which reduces R on impact.
A lower R increases investment and capital accumulation in the next period. However,
the reduction in the marginal utility from e¤ective consumption requires a reduction in the
marginal utility of holding public and private debt by households to maintain their marginal
rate of substitution conditions. Hence, the demand for private and public debt rises. This
raises the debt-GDP ratio, pushing up the sovereign risk premium, the government borrowing
rate, RG; and therefore RP . When � is high, the key di¤erence is that a negative government
spending shock increases private consumption, but reduces e¤ective consumption. Hours
work rises, which raises GDP, investment (because the marginal product of capital rises with
higher employment), and capital, increasing output in the next period as well. Higher GDP
implies that households demand more private and public debt, but because output has risen,
the public-debt to GDP ratio falls. This reduces the sovereign risk premium, implying that
both RG and RP fall. To balance its budget, the government lump sum taxes households.
These lump sum taxes impose a negative wealth e¤ect on households which also reinforce
the increase in hours worked from the marginal utility channel.
5. Conclusion
To model �scal consolidations in EMDEs, we develop a simple SOE RBC model with
�scal policy and �nancial frictions to derive conditions under which �scal contractions can
be expansionary. The main result of our paper is show that the incidence of expansionary
13 . Consistent with the empirical literature, we restrict 0 < � < 1 ( see Ambler and Paquet (1996), andBarro (1981)).
23
�scal consolidations depends crucially on whether factor income tax rates are low or high.
When tax rates are high, we show that the incidence of expansionary �scal contractions
depends on the relative weight that households place on government consumption in utility.
We also show that positive foreign interest rate channels can reduce output in the short run,
but via a channel that does not require assuming that households have GHH preferences as
in Neumeyer and Perri (2005). In the future, we plan to add monetary-�scal interactions to
the model, to derive endogenous responses by the monetary authority to �scal contractions.
It would be interesting to characterize the value of the �scal multiplier in this case.
24
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27
Technical Appendix
This appendix provides the derivation of the linear system comprising the model we
analyze, we note that this model is built for use with HP-�ltered data and as such does not
feature deterministic trends.
A.1 The Household Problem
A representative household maximizes utility:
maxfCt;Ht;Bt;Dt;Ktg
E0
1Xt=0
�t
24 � ln (Ct � �Ct�1 + �Gt) + (1� �� '1 � '2) ln (1�Ht)+'1 ln (Dt) + '2 ln (Bt)
35 ,where � 2 (0; 1), Gt � CSSP ( �G; �G; �G) and subject to,
Ct +Kt � (1� �)Kt�1 +�
2Kt�1
�Kt
Kt�1� 1�2+Bt +
�12Yt
�BtYt��B�Y
�2+Dt +
�22Yt
�Dt
Yt��D�Y
�2= (1� �w)WtHt + (1� �k)RtKt�1 +R
Pt�1Bt�1 +R
Gt�1Dt�1 + Tt
where CSSP denotes a covariance stationary stochastic process. The Lagrangian of the
problem, where �t is the multiplier on the household budget constraint, is
maxfCt;Ht;Bt;Dt;Ktg
L =
" 1Xt=0
�t [� ln (Ct � �Ct�1 + �Gt) + (1� �� ') ln (1�Ht) + ' ln (Dt)]
#
�
266641Xt=0
�t�t
26664Ct +Kt � (1� �)Kt�1 +
�2Kt�1
hKt
Kt�1� 1i2+Bt
+�12Yt
hBtYt� �B
�Y
i2+Dt +
�22Yt
hDtYt� �D
�Y
i2��(1� �w)WtHt + (1� �k)RtKt�1 +R
Pt�1Bt�1 +R
Gt�1Dt�1 + Tt
�3777537775
28
and the FONC are, for Ct, Ht, Kt, Bt and Dt respectively,
�t =�
Ct � �Ct�1 + �Gt� ��
Ct+1 � �Ct + �Gt+1(1� �w)�tWt =
1� �� '1 � '21�Ht
Et
8><>:��t+1
�(1� �)� �
2
hKt+1
Kt� 1i2+ �Kt+1
Kt
hKt+1
Kt� 1i+ (1� �k)Rt+1
�= �t
h1 + �
hKt
Kt�1� 1ii
9>=>;Et
���t+1R
Pt = �t
�1 + �1
�BtYt��B�Y
��� '2Bt
�Et
���t+1R
Gt = �t
�1 + �2
�Dt
Yt��D�Y
��� '1Dt
�:
The household problem therefore delivers the following system of 7 equations:
�t =�
Ct � �Ct�1 + �Gt� ��
Ct+1 � �Ct + �Gt+1(1� �w)�tWt =
1� �� '1 � '21�Ht
Et
(��t+1
"(1� �)� �
2
�Kt
Kt�1� 1�2+ �
Kt+1
Kt
�Kt
Kt�1� 1�+ (1� �k)Rt+1
#= �t
�1 + �
�Kt
Kt�1� 1��)
Et
���t+1R
Pt = �t
�1 + �1
�BtYt��B�Y
��� '2Bt
�Et
���t+1R
Gt = �t
�1 + �2
�Dt
Yt��D�Y
��� '1Dt
�Ct +Kt � (1� �)Kt�1 +
�
2Kt�1
�Kt
Kt�1� 1�2+Bt +
�12Yt
�BtYt��B�Y
�2+Dt +
�22Yt
�Dt
Yt��D�Y
�2= (1� �w)WtHt + (1� �k)RtKt�1 +R
Pt�1Bt�1 +R
Gt�1Dt�1 + Tt
where Gt � CSSP ( �G; �G; �G)
in 15 parameters
f�; �; �; �; '1; '2; �; �; �1; �2; �w; �k; �G; �G; �Gg
and 13 variables
fCt; Gt; Ht; Dt; Kt; Bt; Yt;Wt; Rt; RPt ; R
Gt ; Tt;�tg:
29
A2. The Firm Problem
The �rm seeks to maximize it�s pro�ts given by,
maxfKt�1;Htg
Yt �RtKt�1 � (1� �)WtHt � �WtHtRPt�1,
subject to
Yt = AtK�t�1H
1��t
At � CSSP ( �A; �A; �A)
This optimization yields 2 FONCs,
(1� �)YtHt
= Wt
�(1� �) + �RPt�1
��YtKt�1
= Rt
The �rm problem therefore delivers the following system of 4 equations:
(1� �)YtHt
= Wt
�(1� �) + �RPt�1
��YtKt�1
= Rt
Yt = AtK�t�1H
1��t
At � CSSP ( �A; �A; �A)
with the addition of 5 parameters f�; �; �A; �A; �Ag and 1 variable (At) to the household
system.
A.3 Government Budget Constraint
The government budget constraint is given by
Gt + Tt = �wWtHt + �kRtKt +Dt �RGt�1Dt�1,
30
where
RGt = �R�t exp
�Dt
Yt��D�Y
�RPt = �R
Gt
R�t � CSSP ( �R�; �R� ; �R�)
The speci�cation for government behavior therefore delivers 4 additional equations to the
system so far:
Gt + Tt = �wWtHt + �kRtKt +Dt �RGt�1Dt�1
RGt = �R�t exp
�Dt
Yt��D�Y
�RPt = �R
Gt
R�t � CSSP ( �R�; �R� ; �R�)
with the addition of 5 parameters f�;�; �R�; �R� ; �R�g and 1 variable (R�t ) to the system given
by the household and �rm problems.
31
A.4 The Nonlinear System
Collecting across economic actors, the system of expectational di¤erence equations is
�t =�
Ct � �Ct�1 + �Gt� ��
Ct+1 � �Ct + �Gt+1(N1)
(1� �w)�tWt =1� �� '1 � '2
1�Ht(N2)
Et
(��t+1
"1� � � �
2
�Kt+1
Kt
� 1�2+�Kt+1
Kt
�Kt+1
Kt
� 1�+ (1� �k)Rt+1
#= �t
�1 + �
�Kt
Kt�1� 1��)
(N3)
Et
���t+1R
Pt = �t
�1 + �1
�BtYt��B�Y
��� '2Bt
�(N4)
Et
���t+1R
Gt = �t
�1 + �2
�Dt
Yt��D�Y
��� '1Dt
�(N5)
Ct +Kt � (1� �)Kt�1 +�
2Kt�1
�Kt
Kt�1� 1�2+Bt +
�12Yt
�BtYt��B�Y
�2+Dt +
�22Yt
�Dt
Yt��D�Y
�2(N6)
= (1� �w)WtHt + (1� �k)RtKt�1 +RPt�1Bt�1 +R
Gt�1Dt�1 + Tt
(1� �)YtHt
= Wt
�(1� �) + �RPt�1
�(N7)
�YtKt�1
= Rt (N8)
Yt = AtK�t�1H
1��t (N9)
Gt + Tt = �wWtHt + �kRtKt +Dt �RGt�1Dt�1 (N10)
RGt = �R�t exp
�Dt
Yt��D�Y
�(N11)
RPt = �RGt (N12)
Gt � CSSP ( �G; �G; �G) (N13)
At � CSSP ( �A; �A; �A) (N14)
R�t � CSSP ( �R�; �R� ; �R�) (N15)
which is a nonlinear system of 15 equations in:
� 25 parameters f�; �; �; �; '1; '2; �; �; �1; �2; �w; �k; �; �;�; �; �G; �A; �R�; �G; �A; �R� ; �G; �A; �R�g
32
and,
� 15 variables fCt; Ht; Dt; Kt; Bt; Yt;Wt; Rt; RPt ; R
Gt ; Tt;�t; Gt; At; R
�tg.
A.5 The Nonstochastic Steady State
Assume that the steady state values �A, �G and �R� are in hand, then �RG is in hand from
equation 11 above:
RGt = �R�t exp
�Dt
Yt��D�Y
�! �RG = � �R�:
Equation (3) above yields the expression for �R:
Et
8><>:��t+1
�1� � � �
2
hKt+1
Kt� 1i2+ �Kt+1
Kt
hKt+1
Kt� 1i+ (1� �k)Rt+1
�= �t
h1 + �
hKt
Kt�1� 1ii
9>=>;! �R =1� �(1� �)�(1� �k)
;
and �nally equation (12) above yields the expression for �RP :
RPt = �RGt ! �RP = � �RG
The remaining (9) equation system in the steady state is
�� =�(1� �)
(1� �) �C + � �G
(1� �w)�� �W =1� �� '1 � '2
1� �H
� �� �RP = ��� '2�B� �� �RG = ��� '1�D
�C + � �K + �B + (1� �RG) �D = (1� �w) �W �H + (1� �k) �R �K + �RP �B + �T
(1� �) �Y(1� � + � �RP ) �H
= �W $�W �H�Y
=1� �
1� � + � �RP� �Y�K= �R
�Y = �A �K� �H1��
�G+ �T = �w �W �H + �k �R �K + �D � �RG �D
33
from which we need to determine the steady state values for Ct, Ht, Dt, Kt, Yt, Wt, Tt, Bt
and �t. Combining the 5th and 9th equations in the above system eliminates
�T = �w �W �H + �k �R �K + �D � �RG �D � �G
and yields
�� =�(1� �)
(1� �) �C + � �G
(1� �w)�� �W =1� �� '1 � '2
1� �H
�� ='2
�B(1� � �RP )�D =
'1(��� � �� �RG)
�G+ (1� �RP ) �B = �W �H + ( �R� �) �K � �C
�W =(1� �) �Y
(1� � + � �RP ) �H� �Y�K= �R
�Y = �A �K� �H1��
Next, we can eliminate �K = ��Y�R
�Y = �A
���Y�R
���H1�� (18)
�Y =��A���R
��� 11�� �H (19)
�Y = #1 �H; #1 =��A���R
��� 11��
(20)
34
yielding
�� =�(1� �)
(1� �) �C + � �G
(1� �w)�� �W =1� �� '1 � '2
1� �H
�� ='2
�B(1� � �RP )�D =
'1(��� � �� �RG)
�G+ (1� �RP ) �B = �W �H + ( �R� �) �K � �C
�W =(1� �)#1
(1� � + � �RP )= #2
Then letting #3 = 1� �� '1 � '2
�C =���� � �G
1� �
�H =(1� �w)#2��� #3(1� �w)#2��
�B =(1� � �RP )
'2��
�D =(1� � �RG)
'1��
#6��2 � #5�� + #4 = 0
�� =#5 �
p#25 � 4#4#62#6
#4 = �R#2(1� �)'2#3 + (1� �)'2( �R� �)�#1#3 + �R#2�(1� �w)(1� �)'2
#5 =
24 �R#2(1� �)'2#2(1� �w) + (1� �)'2( �R� �)�#1(1� �w)#2+ �R#2(1� �w)'2� �G� �R#2(1� �w)(1� �)'2 �G
35#6 = �R#2(1� �w)(1� �)(1� �RP )(1� � �RP ):
35
