# Threshold of the CAPB That Can Be Attributed to Fiscal Consolidation Episodes in South Africa

^{*}

## Abstract

**:**

## 1. Introduction

- Null:
- There is a threshold of the cyclical adjusted primary balance that can be attributed to the fiscal consolidation episode.
- Alt:
- There is no threshold of the cyclical adjusted primary balance that can be attributed to the fiscal consolidation episode.
- Null:
- There is fiscal consolidation though government expenditure cuts and tax increases that impact government debt.
- Alt:
- There is no fiscal consolidation though government expenditure cuts and tax increases that impact government debt.
- Null:
- There is fiscal consolidation that reflects success in reducing government debt.
- Alt:
- There is no fiscal consolidation that reflects success in reducing government debt.

## 2. Literature Review

#### 2.1. Measures of Fiscal Consolidation

#### 2.2. Threshold of Fiscal Consolidation

## 3. Methodology

#### 3.1. The Theoretical Framework of Fiscal Deficit

#### 3.2. Model Specification

## 4. Results

## 5. Discussion and Recommendation

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Notes

1 | (Blanchard 1990). Defined fiscal consolidation as large observed improvements in the cyclically adjusted primary balance (CAPB). CAPB is intended to capture discretionary fiscal policy by excluding the estimated effects of business cycle fluctuations on the government budget. Therefore, taxes and transfers are cyclically adjusted with net interest payments also to be subtracted. CAPB is a discretionary measure of fiscal policy as it excludes interest payments from past government liabilities on the accumulated debt. |

2 | The paper uses the HM filter to find the growth of nominal potential GDP. |

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**Figure 1.**Fiscal consolidation of tax increase. Author’s processing of the figure above. Note: the blue line $thre\_g\_tvpelstcy\_CAPB\_tgr$ is the threshold estimate, the vertical green box is successful full fiscal consolidation episodes, the black vertical box is unsuccessful full fiscal consolidation, $tvp\_elstcy\_CAPB\_tgr$ is the time-varying CAPB for total government revenue, and $g\_dg$ is the growth rate of domestic government debt.

**Figure 2.**Fiscal consolidation of government expenditure cut. Author’s processing of the figure above. Note: the blue line $thre\_g\_tvpelstcy\_CAPB\_g$ is the threshold estimate, the vertical green box is successful full fiscal consolidation episodes, the black vertical box is unsuccessful full fiscal consolidation, $tvp\_elstcy\_CAPB\_g$ is the time-varying CAPB for government expenditure, and $g\_dg$ is the growth rate of domestic government debt.

**Figure 3.**Fiscal consolidation of government expenditure cuts and tax increases. Author’s processing of the figure above. Note: the blue line $thre\_g\_tvpelstcy\_CAPB$ is the threshold estimate, the vertical green box is successful full fiscal consolidation episodes, the black vertical box is unsuccessful full fiscal consolidation, $tvp\_elstcy\_CAPB$ is the time-varying CAPB, and $g\_dg$ is the growth rate of domestic government debt.

Economic Variables | Description of the Definition of Fiscal Consolidation Using Economic Variables |
---|---|

Government debts share to gross domestic product | A 4.5% decrease in government debt share to the gross domestic product in $(t+1),(t+2),$ and $(t+3)$ (Alesina and Ardagna 2010). Mean less than 5% from the initial government debt share to GDP for 3 successive years (Alesina and Perotti 1995; Alesina and Ardagna 2010). |

Government deficit | A fall of 2% below the initial rate for government deficit in $(t+1),(t+2),$ and $(t+3)$ (Alesina and Perotti 1995; Alesina and Ardagna 2010). |

Economic Growth | Economic growth is higher for 2 successful years for the growth rate means of cases where there was a fiscal consolidation (Alesina et al. 1998). The average economic growth rate at, $\left(t\right)$ is higher than, $(t-1)$ and $(t-2)$ (Giudice and Turrini 2007). |

The cyclically adjusted primary balance | If there is a 1% change in the cyclically adjusted primary balance in 3 years (Tavares 2004). The cyclically adjusted primary balance improve by 1.5% in $\left(t\right)$ (Alesina and Perotti 1997; Alesina et al. 1998; Alesina and Ardagna 2010; Gupta et al. 2005; Hernández De Cos and Moral-Benito 2013; Schaltegger and Weder 2014). The cyclically adjusted primary balance improve by 1.5% in $(t+1)$ and $(t+2)$ (Alesina et al. 1998). The cyclically adjusted primary balance increased by 2% in $(t+1)$ (Alesina et al. 1998). The cyclically adjusted primary balance improves by mean $(\mu )$ plus standard deviation $\left(\sigma \right)$ in $\left(t\right)$ (Yang et al. 2015). The cyclically adjusted primary balance increase by the mean, $(\mu )$, plus standard deviation, $\left(\sigma \right)$, in $\left(t\right)$ (Yang et al. 2015). |

Author | Definition | EB | TB | TE | TS | % S |
---|---|---|---|---|---|---|

Alesina and Perotti (1995) | Threshold of 1.5% CAPB | 59 | 60 | 119 | 66 | 55.46% |

Alesina and Perotti (1997) | Changes in the CAPB that are at least 5% | 125 | 98 | 223 | 43 | 19.28% |

McDermott and Wescott (1996) | Threshold of 1.5% CAPB | 34 | 74 | 108 | 43 | 39.81% |

Alesina et al. (1998) | Threshold of 2% CAPB | 23 | 28 | 51 | 19 | 37.25% |

Zaghini (2001) | Threshold of 1.6% or 1.4% of CAPB | 52 | 48 | 100 | 52 | 52.00% |

Afonso et al. (2006) | Threshold of 2% CAPB | 72 | 20 | 27.78% | ||

Alesina and Ardagna (2010) | Threshold of 1.5% CAPB | 107 | 91 | 85.05% | ||

Barrios et al. (2010) | Threshold of 1.5% CAPB | 235 | 71 | 30.21% | ||

Amo-Yartey et al. (2012) | 1% improvement in CAPB | 107 | 51 | 47.66% | ||

Alesina and Ardagna (2013) | Debt to GDP ratio falls 2 years | 17 | 35 | 107 | 25 | 23.36% |

Yang et al. (2015) | Narrative approach | 66 | 19 | 28.79% | ||

de Rugy and Salmon (2020) | Debt-to GDP ratio declines by at least 5 percentage points | 45 | 67 | 112 | 66 | 58.93% |

Ardanaz et al. (2020) | Narrative approach and threshold of 1.5% CAPB | 41% | 42% | 56.6% | ||

Nunes (2019) | Threshold of 1.5% CAPB | 113 | 63 | 55% | ||

Afonso and Silva Leal (2019) | Threshold of 1.5% CAPB | 51 | 18.61% | |||

Quaresma (2021) | Threshold of 1.5% CAPB and the narrative approach | 76 | 60 | 136 | 36 | 26.47% |

Wiese et al. (2018) | Threshold of 1.5% CAPB and the narrative approach | 42 | 58 | 110 | 50 | 45.45% |

Nunes (2019) | Threshold of 1.5% | 61 | 52 | 113 | 25 | 22.12% |

Agnello et al. (2019) | Threshold of 1.5% CAPB and the narrative approach | 51 | 15 | 29.41% | ||

Afonso and Silva Leal (2022) | Threshold of 1.5% CAPB and the narrative approach | 81 | 98 | 179 | 45 | 25.13% |

Variable | Obs | Mean | Std. Dev. | Min | Max | Skewness | Kurtosis | Shapiro–Wilk |
---|---|---|---|---|---|---|---|---|

$GD$ | 44 | 37.2268 | 11.2063 | 21.99 | 73.18 | 0.000 | 0.69 | 0.548 |

$G\_GD$ | 43 | 0.01971 | 0.09279 | −0.176 | 0.28484 | 0.032 | 0.40 | 0.895 |

$G$ | 44 | 27.9489 | 3.00313 | 23.3 | 37.5 | 0.000 | 0.08 | 0.901 |

$TGR$ | 44 | 14.32779 | 8.754365 | −5.2537 | 36.8419 | 0.024 | 0.20 | 0.533 |

$GDFCY$ | 44 | −3.3545 | 1.92178 | −7.2 | 0.7 | 0.001 | 0.07 | 0.951 |

$tvp\_elstcy\_CAPB\_tgr$ | 44 | −1.35659 | 12.22918 | −47.3 | 49.72 | 0.317 | 0.67 | 0.928 |

$tvp\_elstcy\_CAPB\_g$ | 44 | 5.259546 | 45.5113 | −247.4 | 67.85 | 0.001 | 0.32 | 0.901 |

$tvp\_elstcy\_CAPB$ | 44 | 6.616136 | 56.26286 | −297.13 | 115.15 | 0.000 | 0.05 | 0.908 |

Variables | Dickey-Fuller Test for Unit Root | ||||
---|---|---|---|---|---|

Test | 1% | 5% | 10% | ||

$D.GD$ | Z(t) | −9.517 | −3.535 | −2.904 | −2.587 |

$G\_GD$ | Z(t) | −3.902 | −3.634 | −2.952 | −2.610 |

$D.GDFCY$ | Z(t) | −7.018 | −3.634 | −2.952 | −2.610 |

$D.G$ | Z(t) | −9.406 | −3.736 | −2.994 | −2.628 |

$D.TGR$ | Z(t) | −9.221 | −3.634 | −2.952 | −2.610 |

$thre\_g\_tvp\_elstcy\_CAPB\_tgr$ | Z(t) | −5.857 | −3.628 | −2.950 | −2.608 |

$thre\_g\_tvp\_elstcy\_CAPB\_g$ | Z(t) | −6.414 | −3.628 | −2.950 | −2.608 |

$thre\_g\_tvp\_elstcy\_CAPB$ | Z(t) | −6.481 | −3.634 | −2.952 | −2.610 |

Estimation | 1 | 2 | 3 |
---|---|---|---|

Variables | $DG$ | $DG$ | $DG$ |

$Region1$ | |||

$\_Cons$ | 36.22 ** | 34.07 ** | 34.75 ** |

(0.000) | (0.000) | (0.000) | |

$Region2$ | |||

$\_Cons$ | 45.89 ** | 45.75 ** | 45.75 *** |

(0.000) | (0.000) | (0.000) | |

$thre\_g\_tvp\_elstcy\_CAPB\_tgr$ | 2.8962 | ||

$thre\_g\_tvp\_elstcy\_CAPB\_g$ | 0.4755 | ||

$thre\_g\_tvp\_elstcy\_CAPB$ | 0.4418 | ||

$AIC$ | 213.9803 | 213.1298 | 214.8339 |

$BIC$ | 221.2665 | 220.2665 | 221.9707 |

$HQIC$ | 216.6269 | 215.7764 | 217.4806 |

$N$ | 44 | 44 | 44 |

t statistics in parentheses, * p < 0.05, ** p < 0.01, *** p < 0.001, Akaike information criterion (AIC), Bayesian information criterion (BIC) and Hannan-Quinn information criterion (HQC) is a measure of the goodness of fit of a statistical model. | |||

Estimation 1 is related to $gd=\left\{\begin{array}{c}{tvp\_elstcy\_CAPB\_tgr}_{t}\left[{q}_{t}\le \gamma \right]\\ {tvp\_elstcy\_CAPB\_tgr}_{t}+{\u03f5}_{t}^{*}\left[{q}_{t}\gamma \right]\end{array}\right.$ | |||

Estimation 2 is related to $gd=\left\{\begin{array}{c}{tvp\_elstcy\_CAPB\_g}_{t}\left[{q}_{t}\le \gamma \right]\\ {tvp\_elstcy\_CAPB\_g}_{t}+{\u03f5}_{t}^{*}\left[{q}_{t}\gamma \right]\end{array}\right.$ | |||

Estimation 3 is related to $gd=\left\{\begin{array}{c}{tvp\_elstcy\_CAPB}_{t}\left[{q}_{t}\le \gamma \right]\\ {tvp\_elstcy\_CAPB}_{t}+{\u03f5}_{t}^{*}\left[{q}_{t}\gamma \right]\end{array}\right.$ |

Estimation | 1 | 2 | 3 |
---|---|---|---|

Variables | $DG$ | $DG$ | $DG$ |

$\mathrm{R}\mathrm{e}\mathrm{g}\mathrm{i}\mathrm{m}\mathrm{e}1$ | |||

$G$ | 2.257 *** | 1.873 *** | 1.971 *** |

(0.000) | (-0.001) | (0.000) | |

$TGR$ | −0.451 ** | −0.312 | −0.358 * |

(−0.008) | (−0.059) | (−0.026) | |

$\_Cons$ | −14.82 | −11.59 | −13.31 |

(−0.347) | (−0.443) | (−0.379) | |

$\mathrm{R}\mathrm{e}\mathrm{g}\mathrm{i}\mathrm{m}\mathrm{e}2$ | |||

$G$ | 2.024 *** | 1.475 *** | 1.018 *** |

(0.000) | (−0.000) | (0.000) | |

$TGR$ | −0.3001 ** | −0.256 | −0.253 * |

(−0.000) | (−0.012) | (−0.025) | |

$\_Cons$ | −19.69 | −1.211 | −3.503 |

(−0.221) | (−0.94) | (−0.827) | |

$thre\_g\_tvp\_elstcy\_CAPB\_tgr$ | −1.2168 | ||

$thre\_g\_tvp\_elstcy\_CAPB\_g$ | 1.9182 | ||

$thre\_g\_tvp\_elstcy\_CAPB$ | 1.927 | ||

$AIC$ | 213.9803 | 213.1298 | 214.8339 |

$BIC$ | 221.2665 | 220.2665 | 221.9707 |

$HQIC$ | 216.6269 | 215.7764 | 217.4806 |

$N$ | 44 | 44 | 44 |

t statistics in parentheses, * p < 0.05, ** p < 0.01, *** p < 0.001, Akaike information criterion (AIC), Bayesian information criterion (BIC) and Hannan-Quinn information criterion (HQC) is a measure of the goodness of fit of a statistical model. | |||

Estimation 1 is related to $gd=\left\{\begin{array}{c}{\mathsf{\beta}}_{10}+{\mathsf{\beta}}_{11}{g}_{t}+{\mathsf{\beta}}_{12}tg{r}_{t}+{\mathsf{\beta}}_{13}tvp\_elstcy\_CAPB\_tg{r}_{t}\\ {\mathsf{\beta}}_{20}+{\mathsf{\beta}}_{21}{g}_{t}+{\mathsf{\beta}}_{22}{tgr}_{t}+{\mathsf{\beta}}_{23}tvp\_elstcy\_CAPB\_tg{r}_{t}+{\mathsf{\u03f5}}_{t}^{*}\end{array}\right.$ | |||

Estimation 2 is related to $gd=\left\{\begin{array}{c}{\mathsf{\beta}}_{10}+{\mathsf{\beta}}_{11}{g}_{t}+{\mathsf{\beta}}_{12}tg{r}_{t}+{\mathsf{\beta}}_{13}tvp\_elstcy\_CAPB\_{g}_{t}\\ {\mathsf{\beta}}_{20}+{\mathsf{\beta}}_{21}{g}_{t}+{\mathsf{\beta}}_{22}{tgr}_{t}+{\mathsf{\beta}}_{23}tvp\_elstcy\_CAPB\_{g}_{t}+{\mathsf{\u03f5}}_{t}^{*}\end{array}\right.$ | |||

Estimation 3 is related to $gd=\left\{\begin{array}{c}{\mathsf{\beta}}_{10}+{\mathsf{\beta}}_{11}{g}_{t}+{\mathsf{\beta}}_{12}tg{r}_{t}+{\beta}_{13}{tvp\_elstcy\_CAPB}_{t}\\ {\mathsf{\beta}}_{20}+{\mathsf{\beta}}_{21}{g}_{t}+{\mathsf{\beta}}_{22}{tgr}_{t}+{\beta}_{23}{tvp\_elstcy\_CAPB}_{t}+{\u03f5}_{t}^{*}\end{array}\right.$ |

Author | Definition | EB | TB | TE | TS | % S |
---|---|---|---|---|---|---|

Alesina and Perotti (1995) | Threshold of 1.5% CAPB | 59 | 60 | 119 | 66 | 55.46% |

(McDermott and Wescott 1996) | Threshold of 1.5% CAPB | 34 | 74 | 108 | 43 | 39.81% |

Alesina et al. (1998) | Threshold of 2% CAPB | 23 | 28 | 51 | 19 | 37.25% |

Zaghini (2001) | Threshold of 1.6% or 1.4% of CAPB | 52 | 48 | 100 | 52 | 52.00% |

Duperrut (1998) | Threshold of 1.6% or 1.4% of CAPB | 9 | 2 | 22.22% | ||

Afonso and Silva Leal (2019) | Threshold of 1.5% CAPB | 51 | 18.61% | |||

Quaresma (2021) | Threshold of 1.5% CAPB and the narrative approach | 76 | 60 | 136 | 36 | 26.47% |

Wiese et al. (2018) | Threshold of 1.5% CAPB and the narrative approach | 42 | 58 | 110 | 50 | 45.45% |

Nunes (2019) | 61 | 52 | 113 | 25 | 22.12% | |

Agnello et al. (2019) | Threshold of 1.5% CAPB and the narrative approach | 51 | 15 | 29.41% | ||

Afonso and Silva Leal (2022) | Threshold of 1.5% CAPB and the narrative approach | 81 | 98 | 179 | 45 | 25.13% |

This paper | $thre\_g\_tvp\_elstcy\_CAPB\_tgr$ 1.2168% | 8 | 8 | 3 | 37.50% | |

$thre\_g\_tvp\_elstcy\_CAPB\_g$ 1.9182% | 4 | 4 | 1 | 25.00% | ||

$thre\_g\_tvp\_elstcy\_CAPB$ 1.9270% | 4 | 1 | 25.00% |

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## Share and Cite

**MDPI and ACS Style**

Buthelezi, E.M.; Nyatanga, P.
Threshold of the CAPB That Can Be Attributed to Fiscal Consolidation Episodes in South Africa. *Economies* **2023**, *11*, 152.
https://doi.org/10.3390/economies11060152

**AMA Style**

Buthelezi EM, Nyatanga P.
Threshold of the CAPB That Can Be Attributed to Fiscal Consolidation Episodes in South Africa. *Economies*. 2023; 11(6):152.
https://doi.org/10.3390/economies11060152

**Chicago/Turabian Style**

Buthelezi, Eugene Msizi, and Phocenah Nyatanga.
2023. "Threshold of the CAPB That Can Be Attributed to Fiscal Consolidation Episodes in South Africa" *Economies* 11, no. 6: 152.
https://doi.org/10.3390/economies11060152