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saje_1321 209..227

FISCAL SUSTAINABILITY AND THE FISCAL REACTION

FUNCTION FOR SOUTH AFRICA: ASSESSMENT OF THE

PAST AND FUTURE POLICY APPLICATIONS

, *,

AbstractHow does the South African government react to changes in its debt position? In investigating thisquestion, this paper estimates fiscal reaction functions using various methods (ordinary leastsquares, threshold autoregressive, state-space modelling and vector error-correction model). Thispaper finds that since 1946, the South African government has run sustainable fiscal policy by

reducing the primary deficit or increasing the surplus in response to rising debt. Looking ahead,this paper considers the use of fiscal reaction functions to forecast the debt/gross domestic product(GDP) ratio and gauging the likelihood of achieving policy goals with the aid of probabilisticsimulations and fan charts.JEL Classification: H62, H63Keywords: Fiscal reaction function, public debt, deficits

1. INTRODUCTION

This paper considers the reaction in the past of the South African government to its debt

position, and, if that behaviour is set to continue in future, what its implications willbe for the public debt/gross domestic product (GDP) ratio up to 2014/2015. Thus,understanding how the South African government in the past reacted to the variation inpublic debt/GDP ratio provides a framework to assess how government is likely to reactfollowing the upwards pressure on the public debt/GDP ratio that it currently experiencesas a result of the 2008/2009 global financial crisis.

More specifically, this paper first considers South Africas past debt trajectory and thetheoretical underpinnings of fiscal reaction functions, followed by estimates of the fiscalreaction function. The fiscal reaction functions are estimated using ordinary least squares(OLS) and a vector error-correction model (VECM). To deal with non-linearities, fiscal

reaction functions are also estimated using state-space and threshold autoregressive (TAR)modelling. It is quite reassuring that the application of these four methods yield results thatare largely in agreement with each other. Looking ahead, the paper considers the use of fiscalreaction functions to forecast the debt/GDP ratio up to the 2014/2015 fiscal year. Thispaper concludes that fiscal policy will remain sustainable in the next few years, with limitedrisk of significant upwards pressure on public debt. The projected budget deficit reductionoutlined in recent budget documentation is quite feasible by historical standards.

Corresponding author: Department of Economics, University of the Free State, Bloemfontein,South Africa. E-mail: [email protected]

* Corresponding author: National Treasury of South Africa, 40 Church Square, 0001 Pretoria,Gauteng, South Africa. E-mail: [email protected] National Treasury of South Africa. International Monetary Fund.

bs_bs_banner South African Journal

of Economics

South African Journal of Economics Vol. 80:2 June 2012

2012 The Authors.Journal compilation 2012 Economic Society of South Africa. Published by Blackwell Publishing Ltd, 9600 GarsingtonRoad, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.

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2. SOUTH AFRICAS PAST DEBT TRAJECTORY

Unlike that of many OECD countries, the South African public debt/GDP ratio has notexceeded the 50% mark since 1960 (see Fig. 1).1 However, the public debt/GDP ratio didincrease significantly in the early 1990s, immediately prior to the first democratic

election. Weak economic growth resulting from low investment and a lack of investorconfidence contributed to lower revenue collection. Political tension, combined withdomestic and international recession meant that the government at the time could notintroduce expenditure cuts. The large conventional deficits of the early 1990s, averagingabout 4.5% per year, caused the debt/GDP ratio to increase from 35% in 1990 to 50%in 1995. Underlying these large conventional deficits was a significant weakening of theprimary balance. In 1992, it peaked at 3% (see Fig. 2).

With the debt/GDP ratio at its post-apartheid peak in 1996/1997, debt service costsamounted to 15% of revenue, making it one of the largest expenditure items on the

government budget. Through its growth, employment and redistribution strategy, thenew democratic government aimed to reduce the conventional budget deficit/GDP ratioto below 3% per year. Specifically, the government reversed some of the increases inexpenditure as a percentage of GDP, while improved growth and better tax administrationresulted in revenue growth. The government continued pursuing a prudent fiscal policywell through the following decade. Indeed, in 2006 and 2007, government registered asmall budget surplus taking advantage of the boom of the middle of the last decade andthe public debt/GDP ratio decreased to 23.8% by 2008. Public debt started rising againas government ran larger fiscal deficits to provide countercyclical fiscal stimulus to combat

1

In the late 1990s, it was widely believed that the debt/GDP ratio had reached 60% in themid-1990s. However, there was also an increasing awareness that the GDP figures (i.e. thedenominator of the debt/GDP ratio) did not capture the informal sector of the economy. Thus,when in 1999 the GDP figures were revised to include the informal sector more fully, themid-1990s debt/GDP ratio fell from approximately 60-50%.

0

10

20

30

40

50

60

70

80

1946

1949

1952

1955

1958

1961

1964

1967

1970

1973

1976

1979

1982

1985

1988

1991

1994

1997

2000

2003

2006

Debt/GDP

Figure 1. Public debt/GDP in South Africa (%)Source: Statistics South Africa, National Treasury and authors calculations.


2012 The Authors.Journal compilation Economic Society of South Africa 2012.

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the 2008/2009 recession. Debt will continue to grow for a few more years, as the exitfrom stimulus is set to take place gradually. The 2010 Budget projected that it would risesomewhat above 40% of GDP by 2013.

3. FISCAL REACTION FUNCTIONS AND DEBT SUSTAINABILITY THE BASICS

Establishing how a government reacts to its debt burden can be done through theestimation of a fiscal reaction function. Fiscal reaction functions usually specify, forannual data, the reaction of the primary balance/GDP ratio to changes in the one-periodlagged public debt/GDP ratio, controlling for other influences. According to Bohn(1995, 2007), this represents an error-correction mechanism: if the public debt/GDPratio increases, government should respond by improving the primary balance, to arrestand even reverse the rise in the public debt/GDP ratio. The rationale behind this is rootedin the budget constraint of government (cf. Bohn, 1998, 2007; Gali and Perotti, 2003;De Mello, 2005). In simplified terms, this constraint can be written as:

D D iD B t t t t = + 1 1 , (1)

whereDis public debt,iis nominal interest rate on government bonds and Bis primarybalance (+surplus;-deficit)

Using equation (1), substituting forward and taking expectations yields the expression:

D E B E D t j t t j j j t t j j

= ( ) + ( )+ +=

lim ,1

(2)

where j ss

j

= =1 and s si= +

1

1 .

Upon imposing the standard transversality condition, the second term in equation (2)falls away, which then means that in a sustainable equilibrium debt equals the sum of thediscounted value of all future primary surpluses.

-6.0

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

Primary balance/GDP

Figure 2. Primary balance/GDP in South Africa (%)Source: National Treasury and authors calculations.

211South African Journal of Economics Vol. 80:2 June 2012


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One can also use equation (1) to derive equation (3) for the change in the level ofindebtedness measured against the yardstick of GDP (where we have omitted the timeindex from the parametersrand gto prevent clutter):

( ) = ( ) +( )( )( ) ( )D Y r g g D Y B Y t t t1 1 , (3)

whereris real interest rate, gis real economic growth rate and Yis nominal GDP.Equation (3) leads immediately to the well-known expression for the primary balance

that will ensure the debt/GDP ratio remains unchanged:

B Y r g g D Y D Y t t t

( ) = ( ) +( )( )( ) = ( )

11 1

. (4)

If we start from a position in which debt levels are considered acceptable, equation (4)can be interpreted as a fiscal rule, with the rule defining the primary balance/GDP

ratio required to keep to such a debt/GDP target. To study the actual behaviour ofgovernment, one can estimate a fiscal reaction function of the analogous form:

B Y D Y t

Act

t

Act

t( ) = ( ) + * , (5)

where superscript Act indicates the actual time series, as opposed to the requiredprimary balance/GDP ratio or the target debt/GDP ratio, and where one mightconjecture that the coefficienta*should be on average equivalent to (r-g)/(1+g) if thegovernment wishes to maintain a stable public debt/GDP ratio.

To allow for inertia in government behaviour, a lag of the primary balance B Y tAct

( ) 1can be added to the right-hand side of equation (5) (De Mello 2005:10). The output gapycan also be added to the right-hand side as a control variable to allow for the possibilitythat government pursues short-run demand stabilisation (Bohn, 1998:951; De Mello,2005:10; cf. Taylor, 2000 for a rule based on the output gap). The basic fiscal reactionfunction is then specified as:

B Y B Y D Y y t

Act

t

Act

t

Act

t t( ) = + ( ) + ( ) + ( ) +

1 2 1 3 1 4 . (6)

Before estimating it, a question can be raised regarding the stationarity of the variables in

equation (6). Note that if the change that government brings about in the primarybalance in reaction to changes in the level of debt, i.e. a3/(1-a2) from equation (6),

2

is close to ain equation (4), it would mean that government is attempting to stabiliseits debt ratio at the realised level in the previous period. Indeed, if a3/(1-a2)=a=(r-g)/(1+g), the debt/GDP ratio and the primary balance will befirst-difference stationary; while, ifa3/(1-a2)>a=(r-g)/(1+g), the debt/GDP ratioand the primary balance will be stationary. That said, equation (3) can be rewritten thus:

D Y r g D Y B Y t t t

( ) = +( ) +( )( )( ) ( )

1 11

. (7)

Equation (7) indicates that the debt/GDP ratio depends on its own lag, the interest rate,the economic growth rate and the primary balance. Even though the debt/GDP series

2 Wherea3/(1- a2) is the long-term reaction taking into consideration the short-run reaction,a3, and the level of inertia,a2.



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may be stationary, standard stationarity tests could have difficulty rejecting the nullhypothesis of a unit root (Bohn, 1998:955). For instance, ifr=2% and g=4%, then(1+r)/(1+g)=0.98, which is very close to a unit root. So, we have both a potential issuewith the data and a difficult case for testing.

The paper addresses the problem of possible non-stationarity in the data from threeangles. It first estimates equation (6) with OLS as if the data were stationary. Secondly, itestimates equation (6) as state-space and TAR models assuming non-linearities inbehaviour. Thirdly, it treats the debt/GDP ratio and the primary balance/GDP data as ifthe data are non-stationary and estimates a VECM. In the case of a VECM, one does notestimate equation (6) directly, but rather a model containing equations (8) and (9)(assume for reasons of exposition that there is one lag in the short-run dynamics of themodel), with equation (6) then derived from equation (8).

( )

= + ( )

( )

( )+

( ) B Y c B Y D Y B Y tAct

t

Act

t

Act

t11 11 1 12 1 13 11

11

12 1 11

Act

t

Act

t tD Y y

+

( ) + ( ) +

,11(8)

( ) = + ( ) ( ) ( ) + ( ) D Y c B Y D Y B Y tAct

t

Act

t

Act

t21 21 1 12 1 13 21

11

22 1 21 21

Act

t

Act

t tD Y y

+

( ) + ( ) +

.(9)

where B Y D Y t

Act

t

Act( ) ( )

1 12 1 13 in both equations (8) and (9) represents the

deviation from the long-run relationship given by:

B Y D Y t

Act

t

Act( ) = ( ) +

1 12 1 13 . (10)

Equations (8) and (9) include the output gap in the short-run dynamics of the model,catering for the possibility that fiscal policy might react to the business cycle. The fiscalreaction to the debt/GDP position is captured bya11in equation (8), which representsthe error-correction term, i.e. the response of B/Y to deviations from the long-runrelationship captured in equation (10). Equation (8) can be rewritten as a VAR in levels,which in turn can be used to obtain a VECM equivalent of equation (6):

B Y c B Y B Y t

Act

t

Act

t

Act( ) = + + + +( )( ) ( ) +

11 11 13 11 11 1 11 21

111 12 12 1 12 2 11 11 +( )( ) ( ) + ( ) +

D Y D Y y

t

Act

t

Act

t t .

(8a)

Parameters a1,a2anda3in equation (6) can then be arrived at by summing parametervalues over the lags in equation (13), so that a1=c11-a11b13, a2=(1 +a11) anda3= -a11b12.

4. DATA AND METHODS

The fiscal reaction function as specified in equation (6) is used for modelling purposes inthe following. Public debt/GDP data for South Africa can be found in the South AfricanReserve Bank (SARB, 2010) database and represents national government debt(provinces and local authorities have no or negligible power to issue securities). The



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annual data series exists from 1946. The South African government published primarybalance data for a while in the late 1990s in its Budget Review but ceased its publicationsubsequently. Thus, primary balance data for national government based on GovernmentFinance Statistics (GFS) was obtained from the South African Reserve Bank for theperiod of 1974-2008. To obtain a time series that is even longer, the paper uses Systemof National Accounts (SNA) data, available since 1946, to reconstruct the generalgovernment primary balance.3 Furthermore, equation (6) also includes the output gap,which is constructed in two ways, first with a Hodrick-Prescott filter4 and secondly witha Kalman filter.5 Equation (6) was estimated for both fiscal and calendar years. The GFSdata pertain to fiscal years, while SNA data pertain to calendar years. When using SNAdata for the primary balance, the debt/GDP ratio is in calendar years, while in the case ofGFS data, the ratio is in fiscal years.

The paper uses a variety of modelling techniques to ensure robustness and explore

various aspects of the data. Initially, we estimate simple OLS models. Because there mightbe concern about non-linearity and more complex interactions between variables, thepaper also presents fiscal reaction functions estimated with TAR models. A TAR modelconsiders differentiated reactions of the primary balance/GDP ratio to positive andnegative output gaps.

The paper also estimates equation (6) using state-space modelling over the longestsample to investigate parameter changes. More specifically, equation (6) becomes thesignal equation in which the debt/GDP parameter,a3, is specified as a state variable thatis allowed to vary over time. The other parameters are specified as fixed parameters, whilea3 is specified as a random walk (see Rapach and Weber, 2004). If the governments

choice of primary balance value depends on the primary balance needed to stabilise thedebt/GDP ratio (i.e. if the size ofa3 is influenced by (r-g)/(1+g), then the datagenerating process underlyingrandgwill also influencea3. The log of GDP usually is anI(1) variable, sogis I(0). Rapach and Weber (2004), however, showed that real interestrates in many countries are non-stationary variables. A non-stationaryrwill also cause(r-g)/(1+g) to be non-stationary. Thus, ifa3 depends on (r-g)/(1+g), then a3 canbe expected to be non-stationary hence, the decision to specifya3as a random walk.The fixed parameter models can only be estimated for 1974-2008, because structural

3 Until recently, this was straightforward given that the SARB tables reported current income andcurrent expenditure of general government. Using interest payments, depreciation and investmentby general government, one could reconstruct the primary balance. However, the production,distribution and accumulation accounts of the national accounts introduced in 2006 cover thedetail of sectors differently. Therefore, with no current expenditure and revenue reported explicitly,the balances had to be reconstructed from the production, distribution and accumulation accountfor general government. This reconstruction in addition to earlier data yielded an annual seriesavailable since 1946.4 To tackle the end-point problem in calculating the HP trend (see Mise et al., 2005), an AR(n)model (with n set at 12 to eliminate serial correlation) was used. The AR model was used toforecast two additional years that were then added to each of the series before applying the HP

filter.5 Signal extraction using a Kalman filter allows for separating out an unobservable componentfrom an observable component that contains noise. The model is xt=Etxt+ et and Etxt=Et-1xt-1+vt, where xt and Etxt, respectively, are the observable variable and unobservablecomponent (cf. Valente, 2003:526).



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changes imply that those specifications would not be adequate for longer sample periods.The state-space model, with its variable parameter, is estimated for the period 1946-2008.

The paper also estimates the VECM contained in equations (8) and (9). The model isestimated further using the Johansen procedure, where equations (8) and (9) aremodelled as:

X X X Z ct t i t i t i

k

j t jt j

n

t kt= + + + + =

=

1 , (11)

where Xt=(B/Y, D/Y, Constant) is a 31 vector that includes the endogenous I(1)variables,Zt=(y) is a 11 vector that includes the exogenous I(0) variables, Giare 22short-run coefficient matrices, jjis a 21 vector containing coefficients of the exogenousvariable, ctis a vector containing the constants and ektare normally and independentlydistributed error terms. The trace test is used to determine the number of cointegratingvectors. The symbol P in equation (11) can be decomposed as the typical a and bmatrices whereais a matrix that contains the error-correction (adjustment) parametersandbcontains the long-run parameters.

5. ESTIMATION RESULTS

How has the South African government reacted to its debt position and the cycle? Did itsreaction ensure the sustainability of fiscal policy? Has the reaction function evolved overtime? This section seeks to answer these and other related questions. We first explore sometime series properties of the data with a view to inform our work on estimating the fiscalreaction function, which we then proceed to do. As Bohn (1998) has warned, however,the time series properties of the data should not themselves be taken as indicators of fiscalsustainability.

5.1 The Stationarity of the DataA first statistical question to consider is whether or not the debt/GDP ratio is stationary.The top two panels of Table 1 therefore report Augmented DickeyFuller (ADF) test andKwiatkowskiPhillipsSchmidtShin (KPSS) test results for the debt/GDP ratio. Theresults from various tests do not reveal a consistent pattern. As Table 1 shows, accordingto the ADF test, the debt/GDP ratio is an I(0) variable for the period 1946-2008 but an

I(1) variable for the period 1974-2008. The KPSS results, though, are virtually theopposite: for the period 1946-2008, the KPSS test rejects the null hypothesis ofstationarity at a 5% level but not at a 1% level, while for the period 1974-2008, thedebt/GDP ratio is an I(0) variable.

The behaviour of the debt/GDP ratio may be close to a random walk, and standardstationary tests such as the ADF test might have difficulty rejecting the null hypothesis ofa unit root, even though the series might be stationary (Bohn, 1998:955). The KPSS test(with its null hypothesis of stationarity) might also have difficulty distinguishing betweenstationary and non-stationary series when the behaviour of the series, even when

stationary, is very close to being non-stationary. To take a different approach to thisproblem, we follow Bohn (1998) and present in the third panel of Table 1 what in essenceis a DickeyFuller test, but one that also includes a control variable. In addition, this testis estimated with General Method of Moments (GMM) with critical values that weregenerated in a Monte Carlo simulation (the Monte Carlo results are reported in



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Table1.Stationaritytestforthedebt/GDPratioandtheprimarybalan

ce/GDPratio

The

debt/GDPrat

io

1946-2

008

1974-2008

ADFtest

(OLS)

H0:

D/YisI(1)

H0:

D/YisI(2)

H0:D

/YisI(1)

H0:

D/YisI(2)

(D/Y)t

-1

d(D/Y)t

-1

(D/Y)

t-

1

d(D/Y)t

-1

-0.0

19**[-2.5

1]

-0.13

[-1.0

62]

-0.4

47**[-2.1

78]

KPSStest

H0:

D/YisI(0)(teststat

istic)

H0:

D/YisI(1)(teststat

istic)

H0:D

/YisI(0)(teststat

istic)

H0:

D/YisI(1)(teststat

istic)

0.5

8

0.1

8

0.1

6

ADF-typeregress

ion(GMM)

(H0:

D/YisI(1

))

Withoutcontrolvariab

le

(D/Y)t

-1

(D/Y)

t-

1

-0.0

24[-3.4

6]

-0.021

[-1.3

51]

Withcontrolvariab

le

(D/Y)t

-1

(y)

(D/Y)

t-

1

(y)

-0.0

15[-1.7

67]

-0.4

46(0.0

42)

-0.035

[-3.3

4]

-1.0

4(0.0

00)

Theprimary

balanc

e/GDPratio

(SNAdata)

Theprimary

balance

/GDPratio

(GFSd

ata)

1946-2

008

1974-20

08

1974-2

008

Level

1stdiff

Level

1st

diff

Level

1stdiff

ADFtestt-an

dp-values

-2.6

42***0.0

09)

-2.2

03**

(0.0

29)

-3.5

5***(0.0

03)

KPSStestva

lue

0.8

7

0.2

2

0.5

8

0.2

8

0.5

0

0.2

6

Notes:Values

in[]aret-values;valuesin()arep-values.

ADFtestcriticalt-values(1%,

5%and10$):-

2.60,-

1.9

5and-

1.6

1(indicatedb

y***,

**and

*)for1946-2

008and-

2.6

3,-

1.9

5and-

1.6

1(indicatedby***,**and*)fo

r1974-2008.

KPSScriticalvalu

es(1%,

5%and10%):0.7

3,0.4

6and0.3

5

(indicatedby

,

and).ADF-typeregression(GMM)criticalt-values(1

%,

5%

and10%):-

2.6

4,-

1.9

9and-

1.6

5(indicatedby

,

and).



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Appendix 1). The test first regresses the change in the debt/GDP ratio on the level of thedebt/GDP ratio. Because GMM already corrects for autocorrelation, there is no need toinclude lags of the dependent variable. Like Bohn, it then re-estimates this relationshipbut also includes a control variable; in the case of this paper, the output gap is taken ascontrol. Running the Bohn, ADF-type regressions shows that debt is mean reverting and,thus, stationary, irrespective of the sample period (1946-2000 or 1974-2008). However,because of the weakness of all these tests, the analysis will consider the possibility that thedebt/GDP series is non-stationary.

We also examined the stationarity of the primary balance series, also with dissonantresults (bottom panel of Table 1). The primary balance/GDP ratio over 1946-2008 is anI(0) variable according to the ADF test, but an I(1) variable according to the KPSS test.For the 1974-2008 period, the tests are performed on both the SNA and the GFS datafor the primary balance. The ADF test still indicates that the primary balance/GDP ratio

is an I(0) variable, but the KPSS test indicates that the null hypothesis of stationarity cannot be rejected at a 1% level of significance, although it can be rejected at a 5% level ofsignificance. As will be argued in the following, the longer 1946-2008 period wascharacterised by a change in the primary balance needed to keep debt/GDP stationary which is an issue that will be explored in the following non-linear analysis. The non-stationarity that exists according to the KPSS test might result from the non-linearity inbehaviour during this longer sample period. With respect to the period 1974-2008, itseems that it would be safe to treat the debt/GDP ratio and the primary balance/GDPratio as stationary. Again, because of the weakness of these tests and the nature of theprimary balance/GDP series, the analysis will consider the possibility that the primary

balance/GDP series, together with the debt/GDP series, is non-stationary.

5.2 Estimation Results: OLS and TAR ModelsThis section presents the results for the OLS and TAR models. To deal with possiblecritique that the primary balance/GDP and debt/GDP ratios are non-stationary andtherefore invalidate the results of this section, the following section presents the results ofthe VECM and state-space modelling. As will be seen from all these models, the resultsare largely consistent whichever method is used. The results for the OLS and TAR modelsare presented in Table 2 and refer to data for the period 1974-2008. Both regressionsinclude a lag of the output gap, which in the case of the TAR model is split into positive

and negative gap variables. In both regressions, a3 is statistically significant, indicatingthat government does react to the level of its debt/GDP ratio. The output gap parametersare positive and statistically significant in the OLS estimation, pointing to countercyclicalbehaviour by the government. The estimates for the parameter of the lag of the primary

Table 2. Fiscal reaction functions for South Africa

OLS TAR

(B/Y)t-1 0.75 [2.87] 0.68 [6.89](D/Y)t-1 0.04 [2.76] 0.04 [2.80](y)t-1 0.25 [2.24](y)t-1positive 0.21 [1.10]

(y)t-1negative 0.38 [1.72]C 0.04 [7.67] 0.02 [3.11]

Adj R-sq 0.71 0.74

Notes: Values in [ ] represent t-values. Estimated with HP-generated output gap.



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balance/GDP are 0.75 and 0.68, respectively, indicating a high degree of inertia presentin government behaviour when it sets its primary balance.

The TAR model presents the results for governments reaction during different phasesof the business cycle thus, the output gap serves as transition variable. The threshold wasset at zero. The coefficient on the output gap given an expansion/contraction is 0.21/0.38,

with only that of the contraction statistically significant at a 10% level. This points tocountercyclical policy, particularly during slowdowns and recessions.

But what do the main parameter estimates shown in Table 2 tell us about fiscalsustainability? The discussion from earlier sections indicated that fiscal policy will besustainable ifa3/(1-a2)>a=(r-g)/(1+g). Fig. 3 presents an empirical estimate of(r-g)/(1+g), calculated with the 10-year government bond rate, the real GDP growthrate and the GDP deflator for the period 1947-2008.6As can be seen using the values fora3that can be derived from the estimates in Table 2, for most of the period 1974-2008,a3/(1-a2)>a=(r-g)/(1+g), except possibly for a period in the 1990s (peaking in

1998 when interest rates peaked following the SARBs reaction to the Asian crisis). Thismay also help explain why except for the 1990s, the public debt/GDP ratio in SouthAfrica in general remained stable or decreased. Fig. 3 also indicates that for most of our60-year sample period, the cost of funding for government was moderate enough to allowit to control the dynamics of its debt with relative ease.

5.3 The VECM EstimatesIn view of concerns regarding the stationarity of the debt/GDP ratio and the primarybalance/GDP ratio, we estimated a VECM for the period 1974-2008. However, as this

6 This is a rough indicator. An alternative indicator could use the effective interest rate on debt,

which is total interest payments divided by total debt, and can be understood as a weighted averageof the rates on the various instruments outstanding. (This, however, is not the same as thehistorical cost of financing, particularly on bonds carrying a coupon but also issued at a discount).The effective rate, being a weighted interest rate, would be expected to be somewhat smootherthan the actual 10-year government bond rate.

-15

-10

-5

0

5

10

1947

1950

1953

1956

1959

1962

1965

1968

1971

1974

1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

2007

Figure 3. The(r-g)/(1+g)ratio (%)Source: South African Reserve Bank and authors calculations.



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section will show, the results are consistent with the OLS findings presented previously,indicating that the government reacted to its debt/GDP position. The analysis was donewith the SNA primary balance data (the SNA data provide a slightly better fit than the GFSdata). The primary balance/GDP ratio and the debt/GDP ratio are included in thelong-run component of the model, while the output gap, given its stationarity, is includedin the short-run dynamics of the model. The information criteria indicate that no lagsshould be included in the short-run component of the model. The analysis nevertheless

includes one lag to discern possible short-run effects in a VECM-Granger (the model wasalso run with no lags, and the results do not differ in any substantial way even theparameters are approximately the same). The trace tests (done for one and zero lags)indicate the presence of one cointegrating equation (see Table 3 for the model withone lag).

The VECM estimates are presented in Table 4. The estimations do not suffer fromserial correlation, while the impulse-response functions (Appendix 2) are all stable. Notethat in the cointegration equation panel of Table 4, containing the long-run component,aminusin front of a parameter means apositive relationshipbetween the variable to which

the parameter applies and the variable on which the vector is normalised. The long-runcomponent indicates that for every 1% increase in the debt/GDP ratio, the primarybalance/GDP will increase by 0.131%. With a constant of-4.6%, a debt/GDP ratio of40% translates into a primary surplus in the long run of 0.6%, while a 50% ratiotranslates into a long-run primary surplus of 1.95%.

Table 3. Unrestricted cointegration rank (trace) test

National accounts primary balance and national debt

Hypothesised no. of CE(s) Eigenvalue Trace statistic Critical value (0.05) Prob.

None* 0.402 17.47 15.5 0.025

At most 1 0.015 0.51 3.84 0.475

Note: * Rejection of null hypothesis: trace test indicates one cointegrating equation at the 5%level.

Table 4. VECM results

Cointegrating equation(B/Y)t-1 1(D/Y)t-1 -0.131 [-2.144]C 0.046Error correction equation D(B/Y) D(D/Y)

Cointegrating equation -0.445 [-3.285] -0.552 [-2.232]D(B/Y)t-1 0.253 [1.639] -0.177 [-0.627]D(D/Y)t-1 -0.074 [-0.69] -0.063 [-0.323]C 0.002 [0.768] -0.009 [-2.055](y) 0.096 [0.920] -0.512 [-2.687]

Adj R-sq 0.28 0.39Weak exogeneity test c2 (prob) 0.001 0.023D(D/Y)t-1does not Granger cause D(B/Y)t-1(prob)* 0.49D(B/Y)t-1does not Granger cause D(D/Y)t-1(prob)* 0.53

Serial corr LM (1) (lag 1) (prob) 0.19Serial corr LM (1) (lag 2) (prob) 0.39Serial corr LM (1) (lag 3) (prob) 0.20

Note: Values in [ ] represent t-values. Estimated with a Kalmanfilter-generated output gap. * Probability of the VECM Grange

causality test.



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The parameter estimates from Table 4 confirm the findings from the previous section.As can be seen in Fig. 3, the (r-g)/(1+g) ratio was mostly negative during the 1970s,most of the 1980s and 2000s, with only the 1990s positive. Given a continuously positivedebt/GDP ratio during the sample period, the estimates of the primary balance/GDPratio calculated with equation (10) imply that the long-run primary balance/GDP ratiothat the government ran was positive. Therefore, with the possible exception of part of the

1990s, the long-run primary balance/GDP ratio that the government ran exceeded theprimary balance/GDP ratio required to ensure sustainability.

The error-correction term for the primary balance/GDP ratio equation indicates afiscal response to deviations from the long-run relationship equal to -0.445. Thus, a littleunder a half of the deviation is corrected in the first period after the deviation occurs. Theweak exogeneity tests conducted on the error-correction terms indicate that the nullhypothesis of weak exogeneity can be rejected in all cases. A VECM-Granger causality testwas also conducted on the short-run component of the model, but it showed no evidenceof Granger causality. This is borne out by the initial finding that this model could also be

estimated without lags of the dependent variables in the short-run dynamics. Althoughpositive (indicating countercyclical policy), the output gap coefficient is statisticallyinsignificant in the short-run dynamics of the primary balance/GDP ratio. However, theoutput gap coefficient is negative and statistically significant in the short-run dynamicsof the debt/GDP ratio, indicating that a positive output gap lowers the change in thedebt/GDP ratio, while a negative gap increases the change. This may be a sign ofdifferentiated countercyclical fiscal policy. Using the results from Table 4, Table 5 (left-hand panel) rewrites the VECM as a VAR in levels i.e. it presents equation (8a)discussed previously, while Table 5 (right-hand panel), presents the sum of parametersand, hence, the VECM equivalent of equation (6). The results from Table 5 are very

much in line with those in Table 2, with a3=0.056 anda2=0.555.5.4 The State-Space EstimatesGiven that different administration were in power during the sample period, a questionexists regarding the stability over time of the functions estimated previously. In a bid tostudy the evolution and stability of the reaction function itself, we estimated a state-spacemodel of the fiscal reaction function. Table 6 presents the state-space estimates ofequation (6) for the period 1946-2008. A longer sample was selected to allow for morevariation over time. As discussed in the following, the analysis shows that since themid-1990s, government behaviour, and more specifically its reaction to debt, has been

very stable and indeed, is consistent with the previous OLS and VECM estimates. Thus,all results seem to point to the same behaviour with regard to debt.Note that the intercept was excluded. Its inclusion caused the results to be weaker, and

it was statistically insignificant. The model was also estimated with the contemporaneousvalue of the output gap, as it yields the best results. As noted previously, the parameter of

Table 5. VAR in levels version of VECM results

Parameters Sum of parameters

(B/Y)t-1 0.808 (B/Y) 0.555(D/Y)t-1 -0.016 (D/Y) 0.058

(B/Y)t-1 -0.253 (y) 0.096(D/Y)t-1 0.074 C -0.020(y)t-1 0.096C -0.020



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the debt/GDP ratio, a3, is specified as a random walk, while the lag of the primarybalance/GDP ratio and the output gap have constant coefficients. At 0.28, inertia is lowerthan in most of the previous models estimated. The output gap parameter is positive andstatistically significant, again indicating countercyclical behaviour by the South Africangovernment.

The end state of the state variable for the debt/GDP ratio a3 is 0.037, which isapproximately the value it maintained since the mid-1990s. Fig. 4 presents thisparameters development over time. It shows the point estimate ofa3to be negative upto the 1970s, with its confidence interval including zero. Fig. 4 also displays the primarybalances movement over the same period. The primary balance was mostly negative upto the 1970s. Except for the late 1950s and early 1960s, a3 nevertheless exceeded(r-g)/(1+g), so a3/(1-a2)> awill also hold. This explains why the debt/GDP ratiostill decreased up to the 1970s. In a sense, it would seem that over that early period policyreaction was muted as debt dynamics did not require a strong reaction to ensure

sustainability.Since the early 1970s, estimates ofa3 show a rising trajectory, indicating a strongerreaction to the debt/GDP ratio. As can be observed in the higher level for (r-g)/(1+g)in the 1980s and 1990s (see Fig. 3), the increase in a3 also reflects the changingenvironment and, hence, the need since the 1980s for a stronger reaction to debt levels

Table 6. Fiscal reaction function (state-space end states)

Fixed coefficient

(B/Y)t-1 0.286 (0.071)(y) 0.311 (0.001)

End state(D/Y)t-1 0.037 (0.03)

Note: Values in ( ) represent p-values. Estimated with a Kalmanfilter-generated output gap.

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

1949

1952

1955

1958

1961

1964

1967

1970

1973

1976

1979

1982

1985

1988

1991

1994

1997

2000

2003

2006

Figure 4. Public debt/GDP state variable (line with confidence interval) and primarybalance (SNA data) (dot-dash line)Source: South African Reserve Bank and authors calculations.



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to ensure sustainability. The significant change observed in a3 during the 1970s and1980s also explains why none of the fixed parameter models estimated for samplesstretching further back than the 1970s was successful in estimating a statisticallysignificanta3. The estimated fiscal reaction to the debt/GDP ratio is consistently positivefrom the late seventies onward, and appears remarkably stable at high levels in the periodsince the mid-1990s, even though (r-g)/(1+g) turned negative. A relatively high a3andnegative (r-g)/(1+g) explain the halving of the debt/GDP ratio during this period,from roughly 50% to 23%. In addition, for the period since the mid-1990s the results fora3estimated with the state-space model are largely consistent with the results of the OLSand VECM models estimated previously. Thus, whichever method is used, all the modelspoint to the same results.

A main conclusion from the foregoing analysis is that fiscal policy has, during mostof South Africas modern history, shown a degree of responsiveness to public debt

commensurate with what was needed to preserve debt sustainability. The specificmagnitude of the responsiveness of the primary balance to debt has varied, but it has doneso in such a way to stay ahead of the changes in the parameters governing the evolutionof the required primary balance.

6. USES OF THE FISCAL REACTION FOR DEBT FORECASTINGAND POLICY DESIGN

Understanding how the South African government has reacted to changes in itsdebt/GDP ratio in the past provides a basis to assess how it is likely to react to the upward

pressure on the public debt/GDP ratio that it currently experiences as a result of the2008/2009 global financial crisis. Following equation (7), forward estimates of theprimary balance combined with projections of the real interest and growth rates allow oneto estimate the probable changes to the debt/GDP ratio a key measure of fiscalsustainability. In addition, the method described here allows for the consideration of theprobability of achieving policy goals, defined as future debt levels.

6.1 The Reaction Function as Basis for Probabilistic Debt ModellingDeterministic scenario testing typically involves projecting future debt paths by choosingexogenous values for growth and interest rates. This method assumes a static interplay

of variables, and it produces relatively few outcomes (e.g. high-growth vs. low-growthscenarios), to which one can not ascribe probabilities. By producing a distribution(represented by a fan chart) of a thousand possible debt/GDP outcomes, the method usedhere captures the inherently probabilistic nature of risk analysis. To do so, this sectionextends the original method of Celasunet al., (2006) to project debt service costs (and byextension the budget balance) using a calibrated, symmetrical fiscal reaction functionwith parameter values based on the OLS and TAR models estimated previously (Table 7).The section extends Celasun et al., (2006) further by producing a fan chart with anasymmetrical reaction of the primary balance to the output gap. (The reader is referred to

that article for a more detailed description of this methodology.) This is done with theTAR model parameters.Following Celasunet al., (2006), this analysis separately simulates paths for real GDP

and real interest rates using a VAR to extract the statistical properties of the innovationsto these series, which are needed for the construction of the fan chart. This analysis,



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however, also includes a GDP deflator in the VAR to produce jointly a distribution of realinterest rates, growth and inflation outcomes. The VAR sample period is from 1995Q1to 2010Q1.

Z u A L Z ut t t= + ( ) +0 1 , (13)

whereZ=(y, r, py), referring to real GDP (y), the real interest rate (r) and the GDPdeflator (py). A(L) is the lag polynomial where the number of lags (2) was selected usingthe Akaike information criterion.7 The residual variance-covariance matrix is uniquebecause the forecast residuals are affected neither by the ordering of the VAR nor byrestrictions imposed (Enders, 2010:292). Instead of assuming normality, bootstrappeddraws on the residuals were taken.

For the forward-looking part of the exercise, the bootstrapped draws, together withthe parameters estimated in equation (13), were used to forecast a thousand possiblecombinations of economic growth rates and interest rates for the next five fiscal

years. The nominal interest rate, calculated as the sum of the real interest rate and thechange in the GDP deflator, is used to calculate a plausible distribution of debt servicecosts.8

Finally, the Hodrick-Prescott filter is run on the median outcomes of the 1,000bootstrapped outcomes for real GDP to estimate potential GDP. To overcome theend-period bias in HP filter estimates of the output gap, the sample period is extendedby 12 quarters. The thousand output gaps are fed into the fiscal reaction functionfrom Table 7, to forecast a distribution of primary balance outcomes. Combiningthe distribution of debt service costs with the primary balance estimates producesa distribution of overall budget balances that can be compared against pointprojections. The combination of the projected fiscal and real variables, along with theinitial value of public debt, yields a distribution of future ratios of the publicdebt/GDP ratio.

6.2 The Fan ChartA useful way of presenting the large number of possible outcomes is with a fan chart fordebt/GDP. The thousand projected paths of debt produced by the model can be groupedinto deciles to draw a fan-chart distribution. Greyscaled colour bands represent eachof these deciles; deciles shown in darker colours are closer to the central or median

7

A de-meaned real interest rate series was used in the statistical estimation of the VAR, allowingfor a change in that series mean identified in the data; the out-of-sample forecasts were grossedup using the mean from the last part of the estimation sample period.8 The debt service costs (dsc) are estimated as follows: dsct= dsct-1+1/3(Ddebtt-1 it-1)+2/3(Ddebttit).

Table 7. Parameters for the fan-chart model

Symmetricalmodel

Asymmetricalmodel

(B/Y)t-1 0.75 0.68

(y)t-1 0.25(y)t-1positive 0.21(y)t-1negative 0.38(D/Y)t-1 0.04 0.03C 0.04 0.04



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projection. Lighter colours indicate more extreme outcomes. The most extreme outcomes(i.e. those falling outside of the 80% confidence interval) are not shown on the chart.In a symmetric, unimodal distribution, such as a bell curve, the decile bands nearthe centre would be narrower, i.e. the density of outcomes would be higher inneighbourhoods of a given size close to the central projection.

Fig. 5 shows the median forecast for debt/GDP increasing from 28% of GDP in2009/2010 to 41% of GDP in 2014/2015. By these forecasts, following 15 years ofdeclining national debt/GDP, South Africa is likely to approach its 2000/20001 level inthe 5 years following 2009/2010. The fan chart also suggests that the probability thatgovernment debt-to-GDP ratio will stay below the 50% mark is over 90%.

The debt fan chart model can be extended by introducing a business cycle-dependentasymmetric reaction by government to the output gap, as indicated in the second columnof Table 7. Calibrating the debt model according to the asymmetric fiscal reactionfunction produces a median debt outcome of around 38% of GDP and debt ratiostabilisation in 2014/2015 (see Fig. 6). The fan chart is asymmetrically distributed

around the mean with greater dispersion below the median. This indicates that there isgreater downside risk to the projections, with the potential for a large positive surprise,understood as a result well below a 40% debt/GDP ratio, exceeding the potential for alarge adverse surprise.

7. CONCLUSION

This paper estimated fiscal reaction functions to study how the South African governmenthas historically reacted to its debt position by adjusting its primary balance. The paper

remained agnostic about the statistical properties of the debt/GDP ratio and primarybalance/GDP ratio, by catering for the possibility of stationary data, non-linear data andnon-stationary data. This was done by employing a variety of techniques, including OLS,TAR, state-space modelling and VECM. From all these models, the same messageemerges: the South African government indeed, during the sample periods explored,

10

20

30

40

50

2

006/07

2

007/08

2

008/09

2

009/10

2

010/11

2

011/12

2

012/13

2

013/14

2

014/15

Figure 5. Debt/GDP for South Africa, 2006/2007 2014/2015 (%)Source: Authors calculations.



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tighten fiscal policies in the face of shocks to the debt/GDP position. Furthermore, fromthe state-space estimations it is clear that this reaction has increased over time ascircumstances have required it: the fiscal response was rather muted during the periodprior to the 1970s, when a favourable combination of real interest and economic growth

rates created very favourable debt dynamics, but it became more energetic in thefollowing decades, when the combination of economic growth and real interest ratesproduced an environment that demanded more fiscal restraint to ensure sustainability.

We also found that, with the possible exception of a few short periods, (the late 1950s,early 1960s and the mid-1990s) the South African government tended to run fiscalbalances in excess of those required simply to stabilise debt (in the absence of othershocks). These were periods, especially the last one, during which slow economic growthor elevated funding costs put upward pressure on the debt trajectory. Indeed, concernover rising interest costs is often cited as the main reason for the debt reductionprogramme of the late 1990s. The containment of interest cost will likely remain an

important consideration going forward.If the past is a guide to the future, fiscal policy is such that there is little risk that public

debt will become too high. Projected debt and budget balance distributions indicate thatthe published fiscal targets are not unduly ambitious by historical standards (NationalTreasury, 2010, 2011). Our simulations also confirm that the variability of potential debtoutcomes rises the more fiscal policy focuses on stabilising output, and falls the morepolicy focuses on debt. Thus, as it is natural to expect, there is some tension between theobjectives of stabilising debt and output. Looking forward, it could be useful tocomplement point forecasts and policy targets such as those in the governments Budget

Review with a broad probabilistic assessment of the risks around a central projection.These assessments can be weaved around a model-generated central projection (derivedfrom the estimated fiscal policy reaction function), as was done in the text, or around anofficial forecast. Either way, such an assessment would help ensure that policy objectivesand strategies are robust to shocks.

10

20

30

40

50

2006/07

2007/08

2008/09

2009/10

2010/11

2011/12

2012/13

2013/14

2014/15

Figure 6. Debt/GDP for South Africa calibrated for differentiated reactions to positive andnegative output gaps, 2006/20072014/2015 (%)Source:Authors calculations.



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REFERENCES

BOHN, H. (1995). The sustainability of budget deficits in a stochastic economy. Journal of Money, Credit and Banking,27(1): 257-271.

(1998). The behaviour of US public debt and deficits. The Quarterly Journal of Economics, 113(3): 949-963. (2007). Are stationary and cointegration restrictions really necessary for the intertemporal budget constraint?Journal of Monetary Economics, 54: 1837-1847.CELASUN, O., DEBRUN, X. and OSTRY, J. D. (2006).Primary Surplus Behavior and Risks to Fiscal Sustainability inEmerging Market Countries: A Fan-Chart Approach. IMF Working Paper 06/67, Washington.DE MELLO, L. (2005).Estimating a Fiscal Reaction Function: The Case of Debt Sustainability in Brazil. OECD EconomicsDepartment Working Paper No. 423, OECD, Paris.ENDERS, W. (2010).Applied Econometric Time Series,3rd edn. Hoboken: NJ: John Wiley & Sons.GALI, J. and PEROTTI, R. (2003). Fiscal Policy and Monetary Integration in Europe. CEPR Discussion Paper No. 3933,Centre for Economic Policy Research, London.MISE, E., KIM, T. and NEWBOLD, P. (2005). On suboptimality of the Hodrick-Prescott filter at time series endpoints.

Journal of Macroeconomics, 27:53-67.NATIONAL TREASURY OF SOUTH AFRICA. (2010).Budget Review. Pretoria: National Treasury._______ (2011).Budget Review. Pretoria: National Treasury.

RAPACH, D. E. and WEBER, C. E. (2004). Are real interest rates really nonstationary? New evidence from tests with goodsize and power.Journal of Macroeconomics, 26: 409-430.SOUTH AFRICAN RESERVE BANK (SARB). (2010). Online Download Facility. Available at: http://www.reservebank.co.za [Accessed 10 August 2010].TAYLOR, J. B. (2000). Reassessing discretionary fiscal policy. Journal of Economic Perspectives, 14(3): 21-36.VALENTE, G. (2003). Monetary policy rules and regime shifts.Applied Financial Economics, 13: 525-535.

APPENDIX 1: DICKEY-FULLER T VALUES FOR GMMOLS DF (Y)* OLS ADF (Y)** GMM DF (Y)***

No trend, no intercept (1%, 5%and 10%)

-2.58,-1.95,-1.62 -2.63,-1.95,-1.61 -2.64,-1.99,-1.65

No trend, intercept -3.43,-2.86,-2.57 -3.63,-2.95,-2.61 -3.53,-2.92,-2.61Trend and intercept -3.96,-3.41,-3.12 -4.24,-3.54,-3.20 -4.02,-3.45,-3.15

Notes: * From Brooks (2008:623). ** From Eviews7 for ADF with zero lags. *** Estimated in aMonte Carlo process with a 1,000 observations and 50,000 repetitions.



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APPENDIX 2: IMPULSE-RESPONSE FUNCTIONS

-0.02

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0.02Budget-budget

Efron Bootstrapped CI

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-0.05

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0.00

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10 11 12 13 14 15 16 17 18 19 20 2194 5 6 7 81 2 3 10 11 12 13 14 15 16 17 18 19 20 2194 5 6 7 81 2 3

10 11 12 13 14 15 16 17 18 19 20 2194 5 6 7 81 2 310 11 12 13 14 15 16 17 18 19 20 2194 5 6 7 81 2 3

Debt-debt


Figure A. Cholesky one standard deviation innovations with 90% bootstrapped confidence

bands



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