# Time-Varying Elasticity of Cyclically Adjusted Primary Balance and Effect of Fiscal Consolidation on Domestic Government Debt in South Africa

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Review of Fiscal Consolidation Measures

#### 2.1. Primary Approach

#### 2.2. Blanchard Approach

#### 2.3. Asset Price Approach

#### 2.4. OECD Approach

#### 2.5. International Monetary Fund Approach

#### 2.6. Narrative Approach

#### 2.7. Definition Approach

## 3. Literature Review of Fiscal Consolidation Measures

## 4. Methodology

#### Model Specification

## 5. Empirical Results

#### 5.1. Comparison of the CAPB of This Paper and the IMF

#### 5.2. Impact of Fiscal Consolidation of Domestic Government Debt Using Time-Varying CAPB

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Variables | Dickey-Fuller Test for Unit Root | Phillips–Perron Test for Unit Root | |||||||
---|---|---|---|---|---|---|---|---|---|

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

$d.gd$ | Z(t) | −3.902 | −3.634 | −2.952 | −2.61 | −3.924 | −3.634 | −2.952 | −2.61 |

$d.g$ | Z(t) | −7.018 | −3.634 | −2.952 | −2.61 | −7.124 | −3.634 | −2.952 | −2.61 |

$d.tgr$ | Z(t) | −9.221 | −3.634 | −2.952 | −2.61 | −3.506 | −3.628 | −2.95 | −2.608 |

$d.m3$ | Z(t) | −6.166 | −3.634 | −2.952 | −2.61 | −2.677 | −3.628 | −2.95 | −2.608 |

$gdp$ | Z(t) | −4.71 | −3.634 | −2.952 | −2.61 | −4.649 | −3.634 | −2.952 | −2.61 |

$d.rd$ | Z(t) | −9.403 | −3.736 | −2.994 | −2.628 | −10.045 | −3.736 | −2.994 | −2.628 |

Selection-Order Criteria for Variables | ||||||||
---|---|---|---|---|---|---|---|---|

Lag | LL | LR | df | p | FPE | AIC | HQIC | SBIC |

0 | −340.914 | 95795 | 17.1457 | 17.1762 | 17.2301 * | |||

1 | −336.294 | 9.2392 | 4 | 0.055 | 92,923.1 | 17.1147 | 17.2063 | 17.368 |

2 | −330.807 | 10.974 | 4 | 0.027 | 86,443.4 | 17.0404 | 17.193 | 17.4626 |

3 | −324.851 | 11.913 * | 4 | 0.018 | 78,752.5 * | 16.9425 | 17.1563 * | 17.5336 |

4 | −320.78 | 8.1412 | 4 | 0.087 | 79,135.9 | 16.939 * | 17.2138 | 17.699 |

Maximum Rank | Parms | LL | Eigenvalue | Trace Statistic | 5% Critical Value |
---|---|---|---|---|---|

0 | 6 | −368.913 | 36.9264 | 15.41 | |

1 | 9 | −353.482 | 0.52042 | 6.0628 | 3.76 |

2 | 10 | −350.45 | 0.13442 |

Eigenvalue Stability Condition | ||
---|---|---|

Eigenvalue | Eigenvalue | Modulus |

0.8781253 | 0.87813 | |

−0.391861 | +0.6125297i | 0.72715 |

−0.391861 | −0.6125297i | 0.72715 |

0.0827303 | +0.5868185i | 0.59262 |

0.0827303 | −0.5868185i | 0.59262 |

0.0545967 | 0.0546 |

Parameter | Mean | Stdev | 95% U | 95% L | Geweke | Inef. |
---|---|---|---|---|---|---|

sb1 | 0.0029 | 0.0006 | 0.002 | 0.0043 | 0.157 | 9.97 |

sb2 | 0.0028 | 0.0006 | 0.002 | 0.0042 | 0.346 | 6.59 |

sa1 | 0.0056 | 0.0016 | 0.0034 | 0.0097 | 0.912 | 12.51 |

sa2 | 0.0058 | 0.0022 | 0.0034 | 0.0109 | 0.319 | 26.66 |

sh1 | 0.0056 | 0.0017 | 0.0034 | 0.01 | 0.995 | 14.81 |

sh2 | 1.5984 | 0.4177 | 0.9125 | 2.5323 | 0.42 | 11.63 |

Parameter | Mean | Stdev | 95% U | 95% L | Geweke | Inef. |
---|---|---|---|---|---|---|

sb1 | 0.1937 | 0.1175 | 0.0298 | 0.4728 | 0.409 | 206.57 |

sb2 | 0.5593 | 0.2142 | 0.202 | 1.0391 | 0.841 | 148.62 |

sa1 | 0.0055 | 0.0017 | 0.0034 | 0.0096 | 0.119 | 9.93 |

sa2 | 0.0024 | 0.0003 | 0.0019 | 0.0031 | 0.12 | 0.54 |

sh1 | 0.0024 | 0.0003 | 0.0019 | 0.0031 | 0.762 | 1.11 |

sh2 | 0.1937 | 0.1175 | 0.0298 | 0.4728 | 0.409 | 206.57 |

**Figure A1.**Estimates of the moments and posterior distributions of the model for $G$. Note: The estimates of ${\mathsf{\Sigma}}_{a}$ and ${\mathsf{\Sigma}}_{\beta}$ are multiplied by 100. Composed by the authors.

**Figure A2.**Estimates of the moments and posterior distributions of the model for $TGR$. Note: The estimates of ${\mathsf{\Sigma}}_{a}$ and ${\mathsf{\Sigma}}_{\beta}$ are multiplied by 100. Composed by the authors.

**Figure A3.**Posterior mean estimates for stochastic volatility of the structural shock for $TGR$. Where $g{d}_{t}\text{}\mathrm{is}\text{}\mathrm{domestic}\text{}\mathrm{government}\text{}\mathrm{debt},\text{}{g}_{t}$ is government expenditure, $r{d}_{t}$ is the government debt service payment, $tg{r}_{t}$ is government revenue, $m{3}_{t}$ is the money supply, and $CAPB\_tg{r}_{t}$ is the cyclically adjusted primary balance for government revenue. Composed by the authors.

**Figure A4.**Posterior mean estimates for stochastic volatility of the structural shock for $G$. Where $g{d}_{t}\text{}\mathrm{is}\text{}\mathrm{domestic}\text{}\mathrm{government}\text{}\mathrm{debt},\text{}{g}_{t}$ is government expenditure, $r{d}_{t}$ is the government debt service payment, $tg{r}_{t}$ is government revenue, $m{3}_{t}$ is the money supply, and $CAPB\_{g}_{t}$ is the cyclically adjusted primary balance for government expenditure. Composed by the authors.

**Figure A5.**Graph (

**a**–

**i**) is the time-varying elasticity of government revenue. Where $tgr$ is the total government revenue $tgr=g\left(y/Y\right)$ is the g total government revenue times the proportion of potation gross domestic product and $gdp$ is the gross domestic product per person. Composed by the authors.

**Figure A6.**Graph (

**a**–

**i**) is the time-varying elasticity of government expenditure. Where $g$ is the government expenditure $dg=g\left(y/Y\right)$ is the government expenditure times the proportion of potation gross domestic product and $gdp$ is the gross domestic product per person. Composed by the authors.

**Figure A7.**Graph (

**a**–

**c**) is the posterior draws for each data series for government revenue. Estimation results of ${\overline{a}}_{1,t}$ on the TVP regression model for the simulated data. True value (solid line), posterior mean (bold) and 95% credible intervals (dashed). The True models are Markov-switching coefficient and stochastic volatility. The TVP regression model with time-varying coefficient and stochastic volatility is fitted. Where $tgr$ is the total government revenue $tgr=g\left(y/Y\right)$ is the g total government revenue times the proportion of potation gross domestic product and $gdp$ is the gross domestic product per person. Composed by the authors.

**Figure A8.**Graph (

**a**–

**c**) is the posterior draws for each data series for government expenditure. Estimation results of ${\overline{a}}_{1,t}$ on the TVP regression model for the simulated data. True value (solid line), posterior mean (bold) and 95% credible intervals (dashed). The True models are Markov-switching coefficient and stochastic volatility. The TVP regression model with time-varying coefficient and stochastic volatility is fitted. Where $g$ is the government expenditure $dg=g\left(y/Y\right)$ is the government expenditure times the proportion of potation gross domestic product and $gdp$ is the gross domestic product per person. Composed by the authors.

**Figure A9.**Graph is the evolution sequence of structural information for government revenue. Where $tgr$ is the total government revenue $tgr=g\left(y/Y\right)$ is the g total government revenue times the proportion of potation gross domestic product and $gdp$ is the gross domestic product per person. Composed by the authors.

**Figure A10.**Graph is the evolution sequence of structural information for government expenditure. Where $g$ is the government expenditure $dg=g\left(y/Y\right)$ is the government expenditure times the proportion of potation gross domestic product and $gdp$ is the gross domestic product per person. Composed by the authors.

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**Figure 1.**Graph (

**a**–

**g**) is the Hodrick–Prescott filter for GDP. Note Graph (

**a**) and $gdpperperson$ is the gross domestic product, Graph (

**b**) and $gdp\_chpfilter$ is the gross domestic product cyclical component from the Hodrick-Prescott (HP) Filter, Graph (

**c**) and $gdp\_chpfilter$ is the gross domestic product cyclical component from the Hodrick-Prescott (HP) Filter, Graph (

**d**) and $tgr$ is the total government revenue, Graph (

**e**) and $tgr=tgr\left(y/Y\right)$ is the total government revenue times the proportion of the output gap, Graph (

**f**) and $g$ is government expenditure, Graph (

**g**) and $g=g\left(y/Y\right)$ is government expenditure times the proportion of the output gap. Composed by the authors.

**Figure 2.**Graph (

**a**–

**g**) is the CAPB with constant elasticity. Note the economic variable that $gdp$ is the gross domestic product, $gdp\_chpfilter$ is the gross domestic product cyclical component from the Hodrick-Prescott (HP) Filter,$gdp\_chpfilter$ is the gross domestic product cyclical component from the Hodrick-Prescott (HP) Filter, $tgr$ is the total government revenue, $tgr=tgr\left(y/Y\right)$ is the total government revenue times the proportion of the output gap, $g$ is government expenditure, and $g=g\left(y/Y\right)$ is government expenditure times the proportion of the output gap. Composed by the authors.

**Figure 3.**Graph (

**a**–

**g**) is the CAPB with time-varying constant elasticity. Where Graph (

**a**,

**d**) and $dg=g\left(y/Y\right)$ shows the government expenditure times the proportion of potation gross domestic product, Graph (

**b**,

**e**) and $tgr=g\left(y/Y\right)$ shows the g total government revenue times the proportion if potation gross domestic product, Graph (

**c**) and $tvp\_elstcy\_CAPB\_tg{r}_{t}$ is the time-varying cyclically adjusted primary balance for government revenue, Graph (

**f**) and $tvp\_elstcy\_CAPB\_{g}_{t}$ is the time-varying elasticity cyclically adjusted primary balance for government expenditure and Graph (

**g**) and $tvp\_elstcy\_CAP{B}_{t}$ is the cyclically adjusted primary balance for government expenditure. Composed by the authors.

**Figure 4.**Graph (

**a**–

**d**) show the time-varying CAPB of this paper and time-invariant CAPB of the IMF. Where Graph (

**a**,

**b**) $tvp\_elstcy\_CAPB$ show the cyclically adjusted primary balance with time-varying elasticity. While Graph (

**c**,

**d**), as well as $CAPB\_IMF$ shows the cyclically adjusted primary balance from the International Monetary Fund. Composed by the authors.

**Figure 5.**Time-varying impulse response functions. Where $g{d}_{t}$ is the doedomesticvernment debt, ${g}_{t}$is government expenditure, $r{d}_{t}$ is the government debt service payment, $tg{r}_{t}$ is government revenue, $m{3}_{t}$ is the money supply, and $CAPB\_{g}_{t}$ is the cyclically adjusted primary balance for government expenditure. Composed by the authors.

Economic Variables | Fiscal Consolidation Definition |
---|---|

Government debts share to gross domestic product | A 4.5% decrease in government debt share to gross domestic product (GDP) in $\left(t+1\right),\left(t+2\right),$ and $\left(t+3\right)$ (Alesina and Ardagna 2010). The Mean is less than 5% of 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 $\left(t+1\right),\left(t+2\right),$ and $\left(t+3\right)$ (Alesina and Perotti 1995; Alesina and Ardagna 2010). |

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

The cyclically adjusted primary balance | If there is a 1% change in the cyclically adjusted primary balance over 3 years (Tavares 2004). The cyclically adjusted primary balance improves by 1.5% in $\left(t\right)$ (Alesina and Perotti 1997; Alesina et al. 1998; Gupta et al. 2005; Alesina and Ardagna 2010; Hernández De Cos and Moral-Benito 2013; Schaltegger and Weder 2014). The cyclically adjusted primary balance improves by 1.5% in $\left(t+1\right)$ and $\left(t+2\right)$ (Alesina et al. 1998). The cyclically adjusted primary balance increases by 2% in $\left(t+1\right)$ (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). |

Variable | Obs | Mean | Std. Dev. | Min | Max |
---|---|---|---|---|---|

$gd$ | 44 | 37.22682 | 11.2063 | 21.99 | 73.18 |

$g$ | 44 | 27.94886 | 3.00313 | 23.3 | 37.5 |

$tgr$ | 44 | 14.32779 | 8.75437 | −5.2537 | 36.8419 |

$m3$ | 44 | 12.795 | 6.12093 | 1.79 | 27.3 |

$gdp$ | 43 | 0.255814 | 2.60926 | −7.7 | 4.4 |

Estimated data | |||||

$tvp\_elstcy\_CAPB\_tgr$ | 44 | −0.293636 | 12.2292 | −47.3 | 49.72 |

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

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

Economic Variables | Estimation 1 | Estimation 2 |
---|---|---|

$L3.D.tgr$ | 0.330 * | 0.330 * |

(−2.45) | (−2.45) | |

$L2.D.tgr$ | 0.0646 ** | 0.0646 ** |

(−2.65) | (−2.65) | |

$L3.D.tgr$ | 0.038 | |

(−1.45) | ||

$D.g$ | −5.546 *** | |

(−5.90) | ||

$L.ce1$ | 2.283 | 0.000500 |

$cons$ | (1.02) | (0.00) |

$N$ | 41 | 43 |

Variable | Obs | Mean | Std. Dev. | Min | Max |
---|---|---|---|---|---|

IMF data of CAPB for South Africa | |||||

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

IMF data of CAPB for South Africa | |||||

$CAPB\_IMF$ | 23 | 0.3516041 | 2.361112 | −4.687403 | 3.766418 |

$CAB\_IMF$ | 23 | −3.063716 | 2.552726 | −9.054413 | 0.8080437 |

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## Share and Cite

**MDPI and ACS Style**

Buthelezi, E.M.; Nyatanga, P.
Time-Varying Elasticity of Cyclically Adjusted Primary Balance and Effect of Fiscal Consolidation on Domestic Government Debt in South Africa. *Economies* **2023**, *11*, 141.
https://doi.org/10.3390/economies11050141

**AMA Style**

Buthelezi EM, Nyatanga P.
Time-Varying Elasticity of Cyclically Adjusted Primary Balance and Effect of Fiscal Consolidation on Domestic Government Debt in South Africa. *Economies*. 2023; 11(5):141.
https://doi.org/10.3390/economies11050141

**Chicago/Turabian Style**

Buthelezi, Eugene Msizi, and Phocenah Nyatanga.
2023. "Time-Varying Elasticity of Cyclically Adjusted Primary Balance and Effect of Fiscal Consolidation on Domestic Government Debt in South Africa" *Economies* 11, no. 5: 141.
https://doi.org/10.3390/economies11050141