Understanding and assessing fiscal sustainability is essential in ensuring financial and macro-economic stability. Fiscal sustainability has emerged as an important subject for Swaziland given the increasingly volatile government revenues especially those coming through the South African Customs Union (SACU), which threw the country into a severe fiscal crisis between 2010 and 2012, as well as the pressures on increased government spending in the post-fiscal crisis era.

This article primarily focuses on studying whether Swaziland’s fiscal policy remains on a sustainable path or whether corrective measures would be required.

Study focuses on Swaziland, a small open economy that is vulnerable to external shocks. The country also relies heavily on South African Customs Union (SACU) revenues.

The study employs a broad approach to assessing fiscal sustainability in Swaziland covering both deterministic and stochastic analysis. On the deterministic analysis, the article studies the evolution of debt given macro-economic variables and further estimates fiscal sustainability indicators such as the primary gap and tax-gap. From a stochastic analysis, the article uses the Trehan and Walsh Methodology as well as Hakkio and Rush Methodology.

Fiscal sustainability indicators reflected that the country is on an unsustainable path with a primary gap and tax-gap of about 7% of gross domestic product (GDP) that has to be corrected. The econometric results also portray an evidence of ‘weak-form’ sustainability in the long-run. This is because public expenditures are rising at a faster pace than revenues thereby rendering government deficits unsustainable in the medium term. The econometric results also suggest a tax-spend hypothesis in the long-run, while short-run developments point to a spend-tax hypothesis. In both instances the correction measure is cutting expenditure, mainly recurrent expenditure.

The study recommends corrective measures (mainly cuts in government expenditure) for fiscal policy to be brought back into a sustainable path without which a fiscal crisis is imminent. The recommendations are mainly based on the fiscal sustainability indicators as they are more forward looking for the short to medium term. The article suggests fiscal rules based on these indicators.

The prominence of fiscal policy as a tool has waxed and waned. Before 1930 an approach of limited government or laissez-faire prevailed (Horton & El-Ganainy

Following 2 years of severe fiscal crisis a recovery in SACU revenues led to improvement in both fiscal and external balances, exerting pressure on the Swaziland Government to the restore growth and social spending which had been sacrificed during the crisis period. Socio-economic challenges faced by the country include ^{1}^{2}

The smallness and openness of the economy has resulted in the Swaziland Government becoming the largest player therein, with a number of State-owned and small-medium enterprises being heavily dependent on business from the government (Basdevant, Forrest & Borislava

In light of heavy reliance on the government to drive economic growth there is a demand for it to continuously embark on expansionary policies, with expenditure exceeding revenue, which cumulates in increasing public debt. Revenue sources have become increasingly volatile, especially from SACU. Persistent increases in expenditure against shrinking, volatile revenues signal concern regarding sustainability of the fiscus. As noted by Bernanke (

Fiscal adjustments tend to be more painful in an environment of a looming or actual crisis – hence it is very important to assess fiscal sustainability beforehand in order to implement corrective measures if current fiscal policy is deemed unsustainable. This is also important since credibility and sustainability are key in the continuous financing of public debt.

The rest of this article is organised as follows. The next section provides a brief overview of Swaziland’s fiscal characteristics, followed by a view of the conceptual framework for analysing fiscal sustainability. This is followed by an empirical strategy with deterministic and stochastic methods for assessing fiscal sustainability, empirical results and conclusions and policy recommendations.

This section provides a brief review of Swaziland’s fiscal characteristics in terms of historical trends and composition of fiscal variables. This provides some stylised facts on public sector developments in Swaziland and sets the background for assessing fiscal sustainability in the country.

Historical data for the past 35 years show that the highest government revenues were recorded in 2008 at 34.2% of gross domestic product (GDP), while government expenditures peaked at 32.8% of GDP in 2008 and 2009. In the past 10 years (2006–2015), government revenues retained high volatility, mainly associated with volatile SACU revenues. In general, government expenditures tend to lie above government revenues: even when revenue falls, expenditure does not fall to the same degree. The historical trend of government revenue and expenditure is shown in

Government revenue and expenditure trends.

Over the years SACU transfers have been a major contributor to government revenues, albeit on a declining trend, as illustrated in

Composition of (a) government revenue and (b) government expenditure.

Government expenditure constitutes a capital budget, recurrent budget and statutory expenditure. Recurrent expenditure is broadly broken down into wages and salaries, goods and services and transfers. The capital programme largely consists of road projects, dams/irrigation, construction of buildings, agriculture, housing and amenities and manufacturing. Goods and services under recurrent expenditure largely consist of travel, communication, rentals, drugs, supplies and durables, while transfers include subscriptions to international organisations and subsidies to State-owned enterprises.

Wages and salaries have historically dominated government expenditure, accounting for about 40% thereof (about 10% of GDP), followed by goods and services, which on average accounted for 30% (8% of GDP) and then capital expenditure at 20% of total expenditure (6% of GDP). What can be observed is that during difficult times government responds by reducing the capital budget, as shown in

While estimates for 2016/2017 indicate that capital expenditure is rising, wages and salaries are also on the rise. Overall recurrent expenditure accounted for approximately 25% of GDP, while capital expenditure accounted for approximately 7% of GDP over the past 10 years (2005–2015). It is clear that the bulk of government expenditure is recurrent in nature, which loosely means that government has been running recurrent deficits.

Historically the Swazi Government’s debt has been characterised by a low domestic debt to external debt ratio, at around 19% to 81% respectively. This trend persisted from the early 1990s to the mid-2000s. In 2005 government started issuing Treasury bills in a bid to develop the domestic market. As expenditure continued to increase and SACU revenue began falling, the Treasury bills programme became a financing item for government.

Composition of public debt.

It was established during this period that the domestic market uses SACU revenue as a risk indicator for government securities. When SACU receipts fall, the market perceives lending to government to be a risk, hence the fall in domestic debt during the crisis period. Consequently, an increase in external debt is observed in 2008–2010, not because of new financing but rather because the share of domestic debt to total public debt fell during this period. Perceived risk led foreign creditors to reduce the credit they advanced to government. Confidence was later regained by the market when SACU receipts picked up in the post-crisis era, with domestic debt sitting at 45.8% and external debt at 54.2% of total public debt (as at December 2015).

The conceptual framework covers fiscal sustainability definitions and assessment methods which could be applied in the case of Swaziland.

The concept of fiscal sustainability refers to the ability of a government to sustain its current spending, tax and other policies in the long run without threatening government solvency or defaulting on liabilities or promised expenditures. While the concept seems easy to understand in theory, there is no consensus among economists on the operational definition. According to Krejdl (

In broader terms, Schick (

The study on Swaziland’s fiscal policy sustainability uses a number of methodologies, mainly geared towards assessing the fiscal sustainability via different indicators, and also runs policy scenarios that yield recommendations needed for correcting the fiscal policy path if results show current policies not to be sustainable in the medium to long term.

As noted by Chalk and Hemming (

where _{t} is the stock of public debt at time t and

Noting that the private agents cannot forever remain indebted to the government, implying that the government cannot use Ponzi schemes forever^{3}

Thus from a PVBC standpoint the sustainability test, as suggested by Chalk and Hemming (

This test checks whether the data-generating process for fiscal data is likely to result in the violation of PVBC. The increase in public debt in real terms should not increase indefinitely at a growth rate beyond the real interest rate.

In assessing Swaziland’s fiscal sustainability the main focus will rest on studying the evolution of the Swaziland Government’s debt over time, covering both deterministic debt sustainability analysis (DDSA) and stochastic debt sustainability analysis (SDSA).

For an open economy the government’s budget constraint with no seigniorage^{4}

Where _{t} represents the rate of depreciation for the Lilangeni/rand against the US dollar. D_{t} represents the sum of both domestic and foreign debt adjusted by the nominal exchange rate, and pd_{t} represents the primary balance (government revenues – government expenditure excluding interest payments).

Dividing everything in

where d_{t} = debt to GDP ratio and pb_{t} is the primary balance as a percentage of GDP, r is the implicit real interest rate while g represents real GDP growth.

Another measure for fiscal sustainability used by Cruz-Rodriguez (

From _{j} ^{*<} 1; that is, whether the implicit real interest rate is less than the real GDP growth (i.e. r* < g). If this is achieved then the debt converges; if not, then the debt will explode and fiscal policy will be deemed unsustainable. From

Given the real interest rate, real GDP growth and fiscal variables, the study focuses on two fiscal sustainability indicators: the ‘primary gap’ and ‘tax-gap’. According to Blanchard (

where _{t} is the debt stock as a percentage of GDP at time t, (_{t}^{*} is the primary deficit at time t. From a forward-looking perspective a constant sustainable primary deficit (^{*}) that will stabilise debt at its initial level is given by the following:

However, if the intention is to achieve a debt level different from initial debt at time T, then the sustainable primary deficit is given by the following:

where b_{T} is the targeted debt to GDP ratio at period T and b_{0} is the initial debt stock, and r and g represent implicit real interest rate and real GDP growth. The primary gap for both _{t}) from the sustainable deficit (p*), in other words pd*–pd_{t}. If the current/projected primary deficit is higher than the calculated sustainable primary deficit (i.e. pd*–pd < 0) then debt will increase without limit; thus current fiscal policy will be deemed unsustainable. The sustainable primary deficit can be used as a yardstick to guide government towards a sustainable deficit path. The primary gap is then computed by subtracting pd_{t} from pd*, and measures the magnitude of adjustment needed to return fiscal balance to a sustainable level.

Given that the primary deficit is calculated from government primary expenditure and tax revenue, by decomposing the primary deficit to its components more fiscal indicators can be retrieved, one of which is the ‘tax-gap’. Like the primary gap, one has to calculate the sustainable tax ratio then compare it with projected tax ratios as a percentage of GDP. The sustainable tax ratio that stabilises debt at its initial level is given by the following:

where τ^{*} is the sustainable tax ratio, and ε_{j} is the planned primary government expenditure. If the targeted future debt level at time t (b_{T}) is different from the initial debt level (b_{0}), then the sustainable tax ratio is given by:

The tax-gap is then calculated by subtracting the current/projected tax ratio (τ) from the calculated sustainable one (τ^{*}). If the tax-gap is positive (τ* > τ), that means the current level of tax revenue is not sufficient to cover future government expenditure and debt repayment. Thus adjustments will be needed in fiscal policy if the target of stabilising the debt to GDP ratio at a desired level is to be achieved.

According to Krejdl (

Given the tax-gap, any delays in the adjustment process entail increased future costs, because the level of debt to GDP ratio which will have to be stabilised in future would be higher. According to Monogios (

To improve results from the simplistic deterministic debt analysis carried out earlier, this article adopts two econometric methods suggested by Afonso (

where L is the lag operator and _{t} is the public debt stock. The point of interest is to test whether (1 – _{t} is a stationary process. Using the following hypothesis _{0}:β_{0}= 0, _{1}:β_{0} < 0, if the null hypothesis is rejected then debt is sustainable, but if we fail to reject the null hypothesis then that might signal sustainability problems.

The Hakkio and Rush (^{5}

If government revenues (_{t}) and government expenses, including interest payments (_{t}), are I(1), then the point of interest is to test whether the residual series _{t} is stationary using unit root tests.

The empirical results can be interpreted as follows:

If there is no co-integration between R and GG, the fiscal deficit is not sustainable.

If there is co-integration with

If there is co-integration, with

In estimating the long-run equilibrium shown by

Given results from co-integration tests, the causality relationship between government revenues and government expenditures is tested using the Granger causality test. From the JJ procedure, a vector error correction model (VECM) is used to confirm the direction of causality and estimate the speed of adjustment to the deviation from the long-run equilibrium between government revenue and government expenditure. The error correction model is based on the following two equations:

where (_{t-1}) and (_{t-1}) represent the error-correction term lagged residual from the co-integration relations. The error-correction terms will capture the speed of short-run adjustments towards long-run equilibrium. Models 14 and 15 also allow for long-run causality between government expenditure and revenue. Negative and statistically significant values of the coefficients of the error-correction terms indicate the existence of long-run causality.

The relationship between government revenue and expenditure would then be interpreted within four hypotheses: (1) the tax-and-spend hypothesis by Friedman (

The study uses government sector accounts with data on the primary balance, government expenditures, revenues and interest payments – all of which are sourced from the Medium-Term Framework (MoF) as at December 2015 as well as the Budget Estimate Book of 2016/2017. Data on national accounts (GDP) was sourced from the combined sewer overflow (CSO) computed after the 2011 rebasing exercise and published in 2015. Complementary data were sourced from Central Bank quarterly and annual report bulletins. For the variables of interest, such as government revenue, expenditure and debt, annual data for the period 1980–2015 were used. E-views version 9 was used for analysis of data for the different methods highlighted in the conceptual framework.

This section presents results of the analysis in line with what was covered in the conceptual framework, divided into two broad areas: deterministic analysis results and stochastic analysis results.

The DDSA results mainly focus on evolution of the debt to GDP ratio and the short- and medium-term sustainability indicators.

Law of motion for the debt dynamics.

This article analyses two fiscal sustainability indicators, namely primary gap and tax-gap, for both historical series as well as short- to medium-term projections, as discussed in the conceptual framework.

Sustainable versus actual primary balance.

As noted in

In the medium term,

Primary deficit to keep debt below 25% of GDP by 2018.

Real GDP growth (%) | Sustainable pd* (% of GDP) | Projected average pd (% of GDP) | Primary gap (% of GDP) |
---|---|---|---|

1.5 | 2.78 | 10.19 | −7.41 |

2.0 | 2.87 | 10.19 | −7.32 |

3.0 | 3.05 | 10.19 | −7.14 |

4.0 | 3.22 | 10.19 | −6.97 |

^{6}

Tax-gap indicator (historical).

^{7}

Sustainable tax ratio to keep debt below 25% of GDP by 2018.

Real GDP growth (%) | Sustainable tax ratio* (% of GDP) | Projected average tax ratio (% of GDP) | Tax-gap (% of GDP) |
---|---|---|---|

1.5 | 30.42 | 23.62 | 6.80 |

2.0 | 30.40 | 23.62 | 6.78 |

3.0 | 30.36 | 23.62 | 6.74 |

4.0 | 30.33 | 23.62 | 6.71 |

From the tax-gap calculations, the cost of postponing fiscal consolidation can be calculated for the different achievable real GDP growth rates. According to

Cost of postponing fiscal consolidation.

Real GDP growth (g) | Implicit real interest (r) | [r-g] ‘Snowball effect’ | Tax-gap | Years | dTau |
---|---|---|---|---|---|

0.015 | 0.058 | 0.043 | 0.068 | 3 | 0.8772 |

0.02 | 0.058 | 0.038 | 0.0678 | 3 | 0.77292 |

0.03 | 0.058 | 0.028 | 0.0674 | 3 | 0.56616 |

0.04 | 0.058 | 0.018 | 0.0671 | 3 | 0.36234 |

, the cost of postponing fiscal consolidation in terms of sustainable tax ratio.

The findings of the study are in line with those of Mufusire (

This subsection covers results from econometric analysis, primarily the Trehan and Walsh method and the Hakkio and Rush method, as described in the conceptual framework.

Through the Trehan and Walsh method interest is on testing for the existence or lack of Ponzi schemes in the data-generating process for debt, as shown in

Test results for ‘no Ponzi scheme’ on real total debt

Debt type (in real terms) | Number of lags (k) | ADF (k) | |
---|---|---|---|

External | 0 | −4.69 |
0.003 |

Domestic | 7 | −1.33 | 0.857 |

, denotes significance at 1% level, number of lags chosen using Schwarz information criterion, maximum lag = 8.

Under the Hakkio and Rush (

Results of unit root tests.

Series | Levels |
First difference |
||
---|---|---|---|---|

ADF | PP | ADF | PP | |

Log (real government revenue) | −0.826 |
−0.727 |
−4.309 |
−4.573 |

Log (real government expenditure) | −0.211 |
−0.134 |
−3.973 |
−3.911 |

, denotes significance at 1%, MacKinnon, Haug and Michelis (1996) one-sided p-values are reported in parentheses.

The unit root tests show that both real government revenue and government expenditure are integrated at order 1 I(1) in level and integrated at order zero in first difference I(0).

Dynamic ordinary least squares estimation.

Variable | Dependant variable: Log (real government revenues) |
||
---|---|---|---|

Estimated coefficient | |||

Constant (a) | 1.312 |
23.45 | 0.000 |

Log (real government expenditure) (b) | 0.892 |
3.09 | 0.037 |

, denote significant at 5%

, denote significant at 1%.

Engle-Granger co-integration test.

Null hypothesis: H_{0} – series is not co-integrated |
Test statistic | |
---|---|---|

Engle-Granger Tau statistic | −4.37 |
0.008 |

Engle-Granger Z statistic | −40.04 |
0.000 |

, significant at 1%.

JJ co-integration tests.

Null hypothesis | Trace statistic | MacKinnon et al. ( |
Max-Eigen statistic | MacKinnon et al. ( |
---|---|---|---|---|

20.46 |
0.008 | 20.29 |
0.005 | |

0.17 | 0.681 | 0.17 | 0.681 |

, significant at 1%.

The Engle-Granger Tau statistic and the normalised correlation coefficient (represented by the Z statistic), which test for unit root in the residuals of the DOLS output, show that the null hypothesis of no co-integration between government revenue and expenditure is rejected. This is further confirmed by the JJ co-integration tests.

These tests confirm that there is only one co-integrating vector. From the DOLS estimated output it can thus be concluded that government revenues and expenditures are co-integrated and the co-integrating vector is [1 -0.89]. However, the question of whether or not

Coefficient restriction Wald test results.

Null hypothesis | Variable | Wald test statistic | |
---|---|---|---|

Government expenditure coefficient ( |
−2.85 |
0.046 | |

8.11 |
0.046 | ||

Chi-square | 8.11 |
0.004 |

, denote significant at 5%

, denote significant at 1%.

The results from

Engle-Granger causality test results.

Regression | Lag(s) | Granger causality (at 5% sign. level) | ||
---|---|---|---|---|

Log (real government revenue) on log (real government expenditure) – H0: Revenue does not cause expenditure | 2 | 13.4 |
0.000 | Yes |

Log (real government expenditure) on log (real government revenue) – H0: Expenditure does not cause revenue | 2 | 2.42 | 0.108 | No |

, significant at 1% level.

The Granger causality tests show unidirectional causality from government revenue to government expenditure. The null hypothesis of no causality from revenue to expenditure is rejected, while the null hypothesis that expenditure does not cause revenue is not rejected. This means that increases in revenue induce higher expenditures and not vice versa. This implies a tax-spend hypothesis in government’s resource allocation in the long run.

The VECM is used to generate short-run dynamics. This article adopts the specification of a VECM government where revenue and expenditure are endogenous variables and national income (real GDP) is used as a control variable. As suggested by Sobhee (

Vector error correction model results.

Independent variables | Dependent variables | |||||
---|---|---|---|---|---|---|

∆log( |
∆log( |
|||||

Constant | 0.002 | 0.07 | - | 0.061 |
3.09 | - |

∆log(_{t−1} |
1.233 |
2.13 | - | −0.226 | −0.64 | - |

_{t−1} |
−0.173 | −0.83 | - | - | - | - |

_{t−1} |
- | - | −0.497 |
−4.04 | ||

∆log(_{t−1}) |
0.420 |
1.84 | - | −0.021 | −0.15 | - |

∆log(_{t−1}) |
−0.540 |
−2.27 | - | −0.028 | −0.20 | - |

^{2} |
0.326 | - | - | 0.539 | - | - |

SE equation | 0.102 | - | - | 0.062 | - | - |

Serial correlation LM test | 4.02 | - | 0.403 | 4.02 | - | 0.403 |

Jarque-Bera normality tests | 6.49 | - | 0.166 | 3.13 | - | 0.536 |

Residual heteroskedasticity (no cross-terms) | 14.6 | - | 0.932 | 14.6 | - | 0.932 |

Residual heteroskedasticity (with cross-terms) | 43.1 | - | 0.424 | 43.1 | - | 0.424 |

, denote significant at 5%

, denote significant at 1%.

The results show that in the short run the lag of expenditure variable has a negative impact on current values of revenue. This means that a 1% increase in expenditure at time t leads to a 0.54% decrease in revenue at time t + 1, and this is statistically significant at the 5% significance level. Changes in revenue have an insignificant effect on expenditure in the short run, which means that the spend-tax hypothesis is supported in the short run. The results also show that there is a strong positive association between increases in real GDP and government revenues. A 1% increase in real GDP growth leads to a 1.23% increase in government revenue.

The error correction term for the expenditure equation is statistically significant at 1% level, while the error term for the revenue equation is statistically insignificant at all conventional acceptable levels. This supports the assertion that in the long run causality runs from revenue to expenditure and not vice versa, supporting the tax-spend hypothesis which, according to Friedman (

According to these results it can be inferred that increases in SACU revenues (which are the main contributor to total revenues) resulted in more than proportionate increases in government expenditure, especially prior to the fiscal crisis between 2010 and 2012. Conversely, during the fiscal crisis a significant drop in SACU revenues led to an average 25% decrease in revenues, which led to government expenditures being curtailed from 35% of GDP in 2009 to about 23% of GDP in 2012.

The error correction coefficient for the expenditure equation shows that any deviation of government expenditure from its path of equilibrium is restored at a rate of 49.7% each year, and this is statistically significant at the 1% confidence level. For revenue any deviations from equilibrium is restored at a much slower pace of 17.3% each year; however, this figure is not significant at conventional levels of testing.

The verification of short-term and long-term causality is performed using the generalised impulse response function (IRF). Given the dynamic structure of a vector autoregressive (VAR) model, the IRF reveals the effects of simultaneous positive innovation shock in one variable on the current and future values of endogenous indicators.

Generalised impulse responses for one standard deviation (SD) shock for Vector error correction model equations: (a) shows the response of real government expenditure following a shock from itself; (b) shows the response of real government expenditure following a positive shock in real government revenues; (c) shows the response of real government revenue following a positive shock in government expenditure; and (d) shows the response of real government revenue following a shock from itself.

The main purpose of this article was to use different methodologies to assess fiscal sustainability in Swaziland. The methodologies were broadly divided into two categories: deterministic and stochastic methods, the latter allowing for backward-looking assessment while the former provided futuristic assessment. Historical assessment showed that historical public debt obeyed the government PVBCs, thereby satisfying the solvency conditions. However, Swaziland satisfies a ‘weak-form’ of fiscal sustainability, suggesting that government expenditures are rising at a faster pace than revenues, rendering the deficit unsustainable in the medium term.

VECM results showed that in the short run government was operating according to a spend-tax hypothesis, while in the long run government followed a tax-spend hypothesis. It was also noted that developments in the domestic debt market could result in violation of the transversality condition, which in turn will imply violation of the government’s budget constraints and undermine solvency. With government operating under the tax-spend hypothesis, any increases in revenue translate into more than proportionate increases in government expenditure.

Fiscal sustainability indicators showed that the current and planned revenues in the short to medium term are too low to finance planned expenditures and keep debt levels sustainable. A primary gap of 7.4% of GDP and a tax-gap of 6.8% would have to be filled to keep fiscal policy sustainable. With no corrective measures, the cost of postponing fiscal consolidation is estimated at 0.75% each year in terms of widening of the tax-gap.

On the basis of these results, in the short run government spending has to be curtailed to ensure fiscal sustainability. The study recommends that the primary deficit has to be cut to below 3% to keep debt at sustainable levels. Fiscal rules based on tax-gap analysis are also ideal for a given interest growth differential.

Further research has to be undertaken into improving quality, efficiency and effectiveness of government spending in order to ensure the government achieves more from her limited resources.

The authors would like to thank the Swaziland Economic Policy Analysis and Research Centre (SEPARC) who initiated the exercise of this research article through her call for paper and the 100% funding that they provided for this article. SEPARC also facilitated the peer reviewing of the article and provided useful comments, particularly the Executive Director Dr. Thula S. Dlamini. More comments were obtained from colleagues from the Central Bank of Swaziland Research department.

Disclaimer: Welcome N. Nxumalo and Nomvuyo F. Hlophe work as Economists in the Central Bank of Swaziland under the Economic Policy Research and Statistics Department. The views expressed in this article are those of the authors and do not necessarily reflect the views or policies of the Central Bank of Swaziland. The authors assume full responsibility of any errors and omissions.

The authors declare that they have no financial or personal relationships that may have inappropriately influenced them in writing this article.

The authors worked jointly throughout the execution of this project. W.N.N. made contributions to the conceptual framework and analysis. N.F.H. worked on fiscal data preparation and interpretation of results.

According to the Swaziland Household Income and Expenditure survey of 2010.

According to the Swaziland Labour Force Survey of 2013–14.

Literature on Ponzi schemes is well documented by O’Connell and Zeldes (

Seigniorage is the revenue governments derive from printing money: the face value of the money minus the cost of physically making and distributing it.

Most recent papers use Vector Error Correction Models (VECM) e.g. Muzenda (

Using sustainable tax ratio τ* = _{t}–(g_{t}–r_{t})b_{t}

Tax revenue in this context includes both tax and non-tax revenue but excludes grants.