Spatiotemporal Difference-in-Differences: A Dynamic Mechanism of Socio-Economic Evaluation

*Lijia Mo*

### **Abstract**

Advances in econometric modeling and analysis of spatial cross-sectional and spatial panel data assist in revealing the spatiotemporal characteristics behind socioeconomic phenomena and improving prediction accuracy. Difference-in-differences (DID) is frequently used in causality inference and estimation of the treatment effect of the policy intervention in different time and space dimensions. Relying on flexible distributional hypotheses of treatment versus experiment groups on spillover, spatiotemporal DID provides space for innovation and alternatives, given the spatial heterogeneity, dependence, and proximity into consideration. This chapter gives a practical econometric evaluation of the dynamic mechanism in this spatiotemporal context as well as a toolkit for this fulfillment.

**Keywords:** spatial difference-in-differences (SDID), causality inference, spillover, random effects, fixed effects, direct effects

#### **1. Introduction**

Spatial panel data are used to investigate the spatial reliance in different regions, and some of the spillover effects are between regions, and ordinary least squares cannot reveal.

Spatial difference-in-differences (SDID) is used to investigate policy effect on the socio-economic variable, given the temporal-lagged variable into consideration. Usually, OLS fails to estimate the model with unbiased that Moran's I reveals. The function of segregation of direct, indirect, and total effects in terms of the specification of the fixed and random effect model makes the SDID's advantage over the traditional DID model.

#### **2. Assumptions of SDID**

#### **2.1 DID model assumptions**

To study the fixed effect of individual and time respectively, difference-in-differences (DID) specify the time and location designs in an experiment setting by an

estimator of the fixed effect of panel data in average treatment effect on the treated [1, 2]. However, the spatial spillover effect complicates the estimation process. In the experiment group and treatment group, the impact of the treatment is measured before and after the treatment is applied.

Spatial Policy Effect:

$$Y\_{it} = \mu\_t + C\_i + \tau D\_{it} + \varepsilon\_{it} \tag{1}$$

Individual fixed effect *Ci* captures the difference between the treatment and control groups on the time-invariant characteristic. *μt*, the temporal fixed effect of timevariant characteristics between control and treatment groups, is assumed to be of the same variance between the control and treatment groups on time-variant characteristics with respect to a specific time.

Time-variant control *Dit* satisfies conditional independence assumption (CIA) to work as a core in the causality inference, while assuming time is exogenous, that is, *E εit* ½ j*treatment*, *time*� ¼ 0*:*

The ordinary least square (OLS) is a consistent estimator for the effect of the causality inference.

$$\pi = E[Y\_{i1}(\mathbf{1}) - Y\_{i1}(\mathbf{0}) | D\_i = \mathbf{1}] \tag{2}$$

After the bias is removed, *E*½ �¼ ^*τ τ* þ *Treatment group Spillover* þ *Control group Spillover* þ *Spillover between different group type*

So far, only the spillover between treatment and control groups is not treated.

$$D\_{it} = \left(D\_{it}^{(1)} - \overline{D}^{(1)}\right) \times \left(D\_{it}^{(2)} - \overline{D}^{(2)}\right) \tag{3}$$

*Dit* is DID, the interaction term of temporal and spatial difference; that is, *β*^*DID* in **Figure 1**, the observable time-dependent variable as control. *D*ð Þ<sup>1</sup> *it* is a dummy variable to denote the group being treated, valued at 1; or group not being treated, values at 0. *D*ð Þ<sup>2</sup> *it* is a dummy variable indicating a local policy or temporal element, values at 1 in

**Figure 1.** *DID estimation illustration.*

*Spatiotemporal Difference-in-Differences: A Dynamic Mechanism of Socio-Economic Evaluation DOI: http://dx.doi.org/10.5772/intechopen.107357*

the year of policy implementation and thereafter, or 0 for the years before. *D*ð Þ<sup>1</sup> *D*ð Þ<sup>2</sup> are the means of two dummy variables.

The strict set of assumptions of the DID is there is no spillover in treatment, control, or between treatment and control groups. When an assumption of same spillover effect within the control and treatment groups is added to the strict set, the assumption becomes relaxed restriction set 1. When there is no spillover between treatment and control groups, the assumption of relaxed restriction set 1 is changed to the spillover effect on control and treatment groups are same and the assumption becomes relaxed restriction set 2.

$$
\hat{\pi} = \hat{E}[Y\_{i1} - Y\_{i0}|D\_i = \mathbf{1}] - \hat{E}[Y\_{i1} - Y\_{i0}|D\_i = \mathbf{0}] \tag{4}
$$

*E Y* ^½ � *<sup>i</sup>*<sup>1</sup> � *Yi*0j*Di* <sup>¼</sup> <sup>1</sup> : Counterfactual trend + *<sup>τ</sup>* +treatment group spatial spillover *E Y* ^½ � *<sup>i</sup>*<sup>1</sup> � *Yi*0j*Di* <sup>¼</sup> <sup>0</sup> : Counterfactual trend + control group spatial spillover The traditional DID

$$\pi = E[Y\_{i1}(\mathbf{1}) - Y\_{i1}(\mathbf{0}) | D\_i = \mathbf{1}] \tag{5}$$

#### **2.2 Spatial model assumptions**

The spatial spillover has the properties of spatial heterogeneity, spatial dependence (the butterfly effect and spatial association), and spatial proximity. Spatial heterogeneity denotes the different structures of spatial units in different locations [3–5]. Without the assumption on spatial homogeneity parameters, it is hard to estimate the model with the increase of observations. In the spatial model, most of the estimation assumes locations are regional homogeneous. The definition of spatial heterogeneity is the non-smoothness of a spatial random process, which comprises change of function form or parameters and heteroscedasticity of two categories.

Spatial dependence means the adjacent spatial locations have the propensity to be associated with each other and work in coordination synchronously.

Spatial proximity denotes that in spatial areas everything is related to everything else, but near things are more related than distant things (Waldo Tobler).

#### **3. Model specifications-generalized spatial model**

The panel data regression is a linear regression with the combination of three types of spatially lagged variables across time, which traces the same observation unit over different times. The observation unit's characteristic over time and spatial location are the research interest. The classical panel data regression takes the following form based on Arbia [6], Cerulli [2], LeSage and Pace [3], and Wooldridge [5]:

$$\mathcal{Y}\_{\rm it} = X\_{\rm it} \beta + c\_i + \nu\_{\rm it} \tag{6}$$

*<sup>i</sup>* <sup>¼</sup> 1,2, … *<sup>N</sup>* index corresponding to ith different observation units in the cross-sectional data.

*t* ¼ 1,2, … *T* denotes time. *ci* is fixed effect w.r.t. observation unit, or spatial specific effect invariant to time. Alternatively, or simultaneously, *ct* a time-specific fixed effect w.r.t. different time, and invariant to observation unit can be embedded to the model. *υit* is an independent identical distributed error term, iid. (0, *σ*2).

The generalized spatial model includes the following variations. Spatial Autoregression Model (SAR-SDID)

$$\mathcal{Y}\_{\rm it} = \rho \sum\_{j=1}^{N} \alpha\_{\rm ij} \mathcal{Y}\_{\rm jt} + X\_{\rm it} \beta + \tau D(\ ) + c\_{\rm i} + \nu\_{\rm it} \tag{7}$$

Before the spatial regression, Moran's I test is used to measure and test spatial autoregression in general. It is also called a global spatial autoregression test; that is, it measures the degree of similarity to each other between the spatial observations in the sample.

$$I = \frac{n}{\sum\_{i} \sum\_{j} \alpha\_{\overline{i}\overline{j}} \left(\frac{\infty - \overline{\varpi}}{\sum\_{i} (\infty\_{i} - \overline{\varpi})^{2}}\right)} \frac{\sum\_{i} \sum\_{j} \left(\infty\_{j} - \overline{\varpi}\right)}{\sum\_{i} \left(\infty\_{i} - \overline{\varpi}\right)^{2}} \tag{8}$$

where n is the number of observations, and *ωij* is the element in ith row and jth column from the spatial weight matrix W. *xi*, *xj* are ith and jth observation in the spatial unit, and *x* is the average of the observations.

The positive Moran's I denotes a positive correlation, while a negative value means a negative correlation. The standardization of the spatial weight matrix simplifies the notation as follows.

$$I = \frac{X^\prime WX}{X^\prime X} \tag{9}$$

It is obvious that Moran's I is the Pearson correlation coefficient between X and WX. It follows an asymptotic distribution, which simplifies the process of using Moran's I to test spatial autocorrelation in the residual of the test. It is a statistical inference through the z-test.

A partial Moran's test is

$$I\_i = \frac{n(\mathbf{x}\_i - \overline{\mathbf{x}}) \sum\_{i \neq j} a\_{ij} \left(\mathbf{x}\_j - \overline{\mathbf{x}}\right)}{\sum\_i \left(\mathbf{x}\_i - \overline{\mathbf{x}}\right)^2} \tag{10}$$

Partial Moran's test *Ii* averages over *i* is the overall Moran's I. Partial Moran's test *Ii* is often used. Overall Moran's I is the slope of the scatter plot as in **Figure 2**, where the X-axis denotes X and Y-axis denotes lagged variable WX of X. The slope of the line reflects the relation between the observed variable and the spatial lagged observed variable. The line across the 1st and 3rd coordinates denotes a positive spatial correlation.

'Columbus' data are generated by geographical information systems (GIS) [7] based on US census data<sup>1</sup> on Columbus boundary systems, with the data type ".shp." The file stores feature geometry such as coordinates of polygon centroids and their boundary. The W matrix is derived from the contiguity-based neighbors' list [6].

The summary statistics of the "crime" variable in the "Columbus" data, totally 49 observations, are as follows (**Table 1**):

<sup>1</sup> http://www.census.gov/geo/maps-data/data/tiger-line.html

*Spatiotemporal Difference-in-Differences: A Dynamic Mechanism of Socio-Economic Evaluation DOI: http://dx.doi.org/10.5772/intechopen.107357*

**Figure 2.** *Moran's I scatter plot of Columbus crime data.*


#### **Table 1.**

*Summary statistics of crime variable.*

The test of Moran's I depends on the distribution of its input variable and is done *via* Monte Carlo simulation. Through the random multiple interchanging location of the spatial units, the model recalculates the weight matrix W and Moran's I statistic to obtain Moran's I after multiple replacements. In a frequency rectangle picture, Moran's I empirical distribution is developed and compared with the statistic from the direct calculation.

The assumption of the method is when the spatial units are randomly distributed, the variable is not autocorrelated, and Moran's I is close to 0. When Moran's I is with a low probability of occurrence, the null hypothesis of no autocorrelation is rejected. When the input variable is the residual of classical linear regression, assumed to follow a normal distribution, Moran's I follows a normal distribution as well, where the z-test is applicable to avoid the heavy calculation of Monte Carlo simulation.

#### **3.1 Spatial error model (SEM-SDID)**

$$\mathbf{y}\_{\rm it} = \mathbf{X}\_{\rm it}\boldsymbol{\beta} + \tau \mathbf{D}(\cdot) + \mathbf{c}\_{\rm i} + \mathbf{u}\_{\rm it} \tag{11}$$

$$u\_{\rm it} = \rho \sum\_{j=1}^{N} m\_{\rm ij} u\_{\rm jt} + v\_{\rm it} \tag{12}$$

#### **3.2 Spatial Durbin model (SDM-SDID)**

$$\mathbf{y}\_{\text{it}} = \rho \sum\_{j=1}^{N} \alpha\_{\text{i}j} \mathbf{y}\_{j\text{t}} + \mathbf{X}\_{\text{it}} \boldsymbol{\theta} + \sum\_{j=1}^{N} \alpha\_{\text{i}j} \mathbf{X}\_{j\text{t}} \boldsymbol{\theta} + \tau \mathbf{D}(\cdot) + \sum\_{j=1}^{N} \alpha\_{\text{i}j} \mathbf{D}(.) + \boldsymbol{\pi} + c\_{\text{i}} + v\_{\text{it}} \tag{13}$$

#### **3.3 Spatial lag of X model (SXL-SDID)**

$$\mathcal{Y}\_{\text{it}} = \mathbf{X}\_{\text{it}}\boldsymbol{\theta} + \sum\_{j=1}^{N} a\_{\text{i}\dagger} \mathbf{X}\_{j\dagger} \boldsymbol{\theta} + \tau \boldsymbol{D}(\cdot) + \boldsymbol{c}\_{\text{i}} + \sum\_{j=1}^{N} a\_{\text{i}\dagger} \mathbf{D}(.) \boldsymbol{u}\_{j\dagger} + \boldsymbol{v}\_{\text{it}} \tag{14}$$

The spatial weight matrix *ωij* and *mij* are invariant to time changes. Spatial and temporal-specific effects can be treated as fixed or random effects. If treated as a fixed effect, the specific effect is taken as a parameter to estimate. Whereas a random effect, it is treated as a random variable following iid. (0, *σ*2). The deterministic factor is to tell whether *ci* is correlated with *Xit*. The fixed effect is used to treat the correlation, while the random effect is for the uncorrelation. The random effect has the advantage of improving effectiveness with the observation number and distinguishes the factor invariant to time. Because *ci* is invariant to time, it is hard to separate observed information from individual effect. *ρ* the spatial lag term is used to test the spatial spillover effects between neighboring regions [3]. The positively significant coefficient of *ρ* indicates a positive spatial spillover effect.

To account for the direct impact and indirect impact, the transformation of Eq. 13 is taken as follows.

In matrix format, let the constant vector *<sup>n</sup>* and relevant parameters *α* to be embedded in Eq. 13.

$$\mathbf{y} = \left(I\_n - \rho \mathbf{W}\right)^{-1} \mathbf{l}\_n a + \left(I\_n - \rho \mathbf{W}\right)^{-1} \mathbf{X}\beta + \left(I\_n - \rho \mathbf{W}\right)^{-1} \varepsilon \tag{15}$$

$$\mathbf{y} = \sum\_{r=1}^{k} \mathbf{S}\_r(\mathbf{W}) \mathbf{X}\_r + \left(\mathbf{I}\_n - \rho \mathbf{W}\right)^{-1} \mathbf{I}\_n a + \left(\mathbf{I}\_n - \rho \mathbf{W}\right)^{-1} \mathbf{e} \tag{16}$$

The sum of the rows of *Sr*ð Þ *W* denotes the total impact of a region to an observation (ATITO); the sum of columns of *Sr*ð Þ *W* is the total impact of a region from an observation (ATIFO). The average of the sum of rows or columns is the average total impact (ATI). The average of elements on the main diagonal is the average direct impact (ADI), and average indirect impact (AII) is defined as the difference between average total impact (ATI) and average direct impact (ADI).

$$\mathcal{S}\_r(\mathcal{W}) = (I\_n - \rho \mathcal{W})^{-1} \beta\_r = \frac{\partial E(\mathbf{y})}{\partial \mathbf{x}\_r} = \begin{bmatrix} \frac{\partial E(\mathbf{y}\_1)}{\partial \mathbf{x}\_{1r}} \dots \quad \frac{\partial E(\mathbf{y}\_1)}{\partial \mathbf{x}\_{nr}}\\\cdots \quad \frac{\partial E(\mathbf{y}\_n)}{\partial \mathbf{x}\_{1r}} \dots \quad \frac{\partial E(\mathbf{y}\_n)}{\partial \mathbf{x}\_{nr}} \end{bmatrix} \tag{17}$$

where ADI denotes the average impact of change of local explanatory variable *xr* on the specific local dependent variable y.

$$ADI = n^{-1} \sum\_{i=1}^{n} \frac{\partial E(\mathbf{y}\_i)}{\partial \mathbf{x}\_{ir}} = n^{-1} tr[\mathbf{S}\_r(W)] \tag{18}$$

*Spatiotemporal Difference-in-Differences: A Dynamic Mechanism of Socio-Economic Evaluation DOI: http://dx.doi.org/10.5772/intechopen.107357*

ATITO is the average impact on the specific local dependent variable y from the change in the explanatory variable *xr* of all regions.

$$\text{ATITO} = n^{-1} \sum\_{i=1}^{n} \sum\_{j=1}^{n} \text{S}\_{r}(\mathcal{W})\_{ij} = n^{-1} \sum\_{i=1}^{n} \sum\_{j=1}^{n} \frac{\partial E(\mathbf{y}\_{i})}{\partial \mathbf{x}\_{jr}} \tag{19}$$

ATIFO is the average impact on all regional dependent variable y from the change in the explanatory variable *xr* of a specific region.

$$\text{ATIFO} = n^{-1} \sum\_{j=1}^{n} \sum\_{i=1}^{n} \text{S}\_{r}(\mathcal{W})\_{ij} = n^{-1} \sum\_{j=1}^{n} \sum\_{i=1}^{n} \frac{\partial E\left(y\_{i}\right)}{\partial \mathbf{x}\_{jr}} \tag{20}$$

ATITO and ATIFO are equal values and are called by a joint name ATI.

$$\text{AII} = \text{ATI} - \text{ADI} \tag{21}$$

#### **4. Tests on model assumptions**

A robust test is performed to study whether the estimation is sensitive to the change in the width of the event window. Wald test follows an asymptotic chisquared distribution with N degree of freedom.

The test on correlation coefficient *ρ* is positive significance.

The estimation is done with spatial inverse-distance contiguity weight matrix. A parallel test is used to test that the change of temporally dependent variable as control will or will not impact the direction of policy influence. A good control ensures the conditional independent assumption (CIA) holds. The different outcomes between the treatment group subject to intervention and the control group in the absence of intervention produce reliable results if both groups are similar in their characteristics and have parallel trends before the intervention, that is, the parallel trends assumption. If the assumption holds, the different outcomes between groups attributed to the intervention ([1, 8–11]). It differs from the Granger test in that a parallel test is performed in the periods before policy intervention to reveal the significant parameters *H*0 : *τ*<sup>0</sup> ¼ *τ*�<sup>1</sup> ¼ … ¼ *τ*�*<sup>k</sup>* ¼ 0 that spans over more than two time periods, while the Granger test requires only a minimum of two periods and is much simpler [12]. If the assumption *μ<sup>t</sup>* of the same fixed time effect of both groups is the same holds, incorporating new control variable *Xit* will not change the estimation of parameters except their variance.

$$Y\_{it} = \mu\_t + C\_i + \tau D\_{it} + \varepsilon\_{it} \tag{22}$$

$$Y\_{it} = \mu\_t + C\_i + \tau D\_{it} + \sum\_{k=0}^{m} \tau\_{-k} D\_{i, t-k} + \sum\_{k=1}^{q} \tau\_{+k} D\_{i, t+k} + X\_{it} \beta + \varepsilon\_{it} \tag{23}$$

Granger test is focused on the after-event periods, to investigate whether the parameters of DID after the policy intervention, *τ*<sup>1</sup> … *τk*, are significant. Using lags and leads provides a test to determine whether past treatments affect the current outcome or for the presence of anticipatory effects, that is, to estimate *τ*�*<sup>k</sup>* and *τk*, thus challenging the conventional idea that causality works only "from the past to the present" [13].

To be specific, Buerger et al. [12] use Granger equations to test the parallel trends assumption, the most important DID framework assumption to improve evidence on causal claims.

When relaxing the parallel assumption, the placebo test answers the question that does the policy matter if one period before or behind implementation? It is tested on the significance of *τ*1,*τ*�1. As a "fake" treatment effect in the pre-period, which is another way to observe parallel trends [14] while requiring three or more time periods prior to the treatment implementation [15].

Hausman test is the test on the choice of fixed effect model or random effect model.

If Corr(*ci*, *Xit*) = 0, parameters of FE or RE models are consistent estimators. Although the estimators are almost the same, the RE model estimation is more effective.

If Corr(*ci*, *Xit*)6¼ 0, the estimators follow different asymptotic distributions, and the estimators are significantly different. Only the FE estimator is consistent.

Under the normality assumption, the maximum-likelihood estimator *θ* ^ *<sup>r</sup>* of the random effect, model is consistent and asymptotic effective, while *θ* ^ *<sup>f</sup>* is consistent and asymptotic effective only in the existence of a correlation between individual effect and exogenous variable.

Hausman test compares the difference of two estimators to infer the existence of correlation *via* the statistic:

$$m\left(\hat{\theta}\_r - \hat{\theta}\_f\right)' \mathbf{\hat{Q}}\_n^+ \left(\hat{\theta}\_r - \hat{\theta}\_f\right) \tag{24}$$

Ω*n:* is the covariance matrix of ffiffiffi *n* p *θ* ^ *<sup>r</sup>* � *θ* ^ *f* � � under the null hypothesis. Ω<sup>þ</sup> *<sup>n</sup>* is a generalized inverse matrix of <sup>Ω</sup>*n*. This statistic follows a *<sup>χ</sup>*<sup>2</sup>ð Þ *rank*ð Þ <sup>Ω</sup>*<sup>n</sup>*

The Lagrangian multiplier is used to test the possible spatial autocorrelation in the residual of the model, which is like Moran's I test on the potentially existing spatial autocorrelation. The difference lies in the individual effect as the spillover effect in the dependent variable lagged spatial model.

Under the setting of the individual and temporal dual fixed effect model in Eq.13, the two restrictive constraint tests on the coefficients are as follows.

$$\mathbf{H}\_0^\mathbf{a} : \boldsymbol{\theta} = \mathbf{0}$$

$$\mathbf{H}\_0^\mathbf{b} : \boldsymbol{\theta} + \boldsymbol{\rho}\boldsymbol{\beta} = \mathbf{0}$$

If *H<sup>a</sup>* <sup>0</sup> holds, Eq. 13 becomes Eq. 7. Under *H<sup>b</sup>* 0, it becomes Eq. 11.

If both hypotheses are rejected, Eq. 13 is selected.

If *H<sup>a</sup>* <sup>0</sup> is accepted robustly and the RLM test indicates a spatial autoregression model, Eq. 7 is selected.

If *H<sup>b</sup>* <sup>0</sup> is accepted robustly and the RLM test indicates a spatial error model, Eqs. 11 and 12 are selected.

If the two restrictive constraint tests yield a different result from that of RLM, Eq. 13 is selected.

#### **5. Application: an example**

In Gu [16] policy evaluation research, DID estimator is renewed as development in academic patent activities following a spatial autoregressive process with respect to the dependent variable. The DID is proposed as a spatial DID estimator to account for *Spatiotemporal Difference-in-Differences: A Dynamic Mechanism of Socio-Economic Evaluation DOI: http://dx.doi.org/10.5772/intechopen.107357*

spatial spillover effects. The empirical analysis of 31 Chinese provinces indicates that an incentive patent policy plays a positive role in the output and commercialization of academic patents during the period from 2010 to 2019. Incentive patent policies are found to play as a placebo in academic patent activities.

The traditional DID method ignores the geographical proximity and spatial spillover effects of academic patent activities. Gu [16] shows the spatial DID model is used to find out three treatment effects, that is, treatment effects based on patent incentive policies and spillover effects within the treatment and control groups. Spatial DID models, including the spatial dependence between adjacent provinces, effectively investigate the spatial spillover effects of policies.

The number of academic patents granted (NGP) in each province is a common indicator of the output of academic patents, and the commercialization rate of academic patents (CAP) and the number of academic patents sold divided by the number of patents granted to the university are used as two explanatory variables in the research.

GDP per capita (PGDP), the number of universities (NCU) in a province, the teacher-to-student ratio (TSR), and the number of enterprises above the designated size (NIE) as indicators of the scale of large industrial enterprises in a region are four explanatory variables in the model.

$$\text{NGP}\_{it} = \text{C} + \rho \text{WNGP}\_{it} + \beta\_1 \text{PGDP}\_{it} + \beta\_2 \text{NCM}\_{it} + \beta\_3 \text{TSR}\_{it} + \beta\_4 \text{NIE}\_{it} + \beta\_5 \text{DID}\_{it} + e\_{it} \tag{25}$$

$$\text{CAP}\_{it} = \text{C} + \rho \text{WCAP}\_{it} + \beta\_1 \text{PGDP}\_{it} + \beta\_2 \text{NCM}\_{it} + \beta\_3 \text{TSR}\_{it} + \beta\_4 \text{NIE}\_{it} + \beta\_5 \text{DID}\_{it} + e\_{it} \tag{26}$$

$$e\_{\rm it} \sim \mathbf{N}(\mathbf{0}, \sigma^2 \mathbf{I}\_{\rm n}), \mathbf{i} = \mathbf{1}, \dots \mathbf{31}$$

Except for the policy variable *DIDit*, *ρWNGPit*, and *ρWCAPit*, the rest variables are controls. If the second right-hand side variables in Eqs. 25 and 26, *ρWNGPit* and *ρWCAPit*, are omitted, two equations are the traditional DID. *DIDit* is the multiplication of two dummy variables, denoting whether and when the policy is implemented.

The data obtained from the China Statistical Yearbook span from 2011 to 2020, 10 years in 31 provinces, which makes 310 observations in total. The data on the commercialization of academic patents are obtained from the Compilation of Science and Technology Statistics in Universities, compiled by the Science and Technology Department of the Ministry of Education of China.

The population is divided into an experimental group comprised of 17 provinces, and a control group including 14 provinces. Two sets of models are consisted of fixed effect or random effect factorization and applied to Eqs. 25 and 26, totally four models (**Table 2**).

Positively significant *ρ* and Wald test of spatial terms indicate the spatial spillover effects are not ignorable. Significant coefficients of DID indicate the incentive patent policy promotes the output and commercialization of patents. Hausman test is ignored due to the insignificant difference between FE and RE models. The SDID is applicable (**Tables 2** and **4**).

SDID spillover effect develops indirect effects in adjacent areas, outperforming the DID model; that is, the indirect effect in models 3 and 4 of dependent variable CAP are insignificant. In this way, the policy effect in the neighborhood provinces is further segregated (**Table 3**).


#### **Table 2.**

*Results of estimation [16].*


#### **Table 3.**

*Results of policy effect tests [16].*

The placebo tests in **Table 4** show that there is no change of significance in the DID if the policy is implemented in the year before or after the actual year of implementation. The result is problematic to convince that the incentive patent policy promotes the outcome or commercialization of a patent. The DID is rather a placebo without an effect on the patent on its own, whereas a proxy of province systemic difference makes the diversity.

*Spatiotemporal Difference-in-Differences: A Dynamic Mechanism of Socio-Economic Evaluation DOI: http://dx.doi.org/10.5772/intechopen.107357*


**Table 4.** *Results of placebo tests [16].*

#### **6. Conclusion**

This chapter outlines the methodology and application of DID in spatial analysis. The impact of incentive policy on economic activities is controversial. The empirical evidence results from a correlation test rather than causality analysis. SDID as a tool to segregate the direct effect, indirect effect, and total effect in the fixed-effect and random-effect models finds a causal relationship between the policy and relevant economic activities under the influence while dealing with the spillover effects in quasi-natural experiments. The placebo effect of policy can expand the horizon of policy evaluation, which helps consolidate the scientific foundation of policy evaluation. Regional policies are proxies for other variables that characterize the systemic differences in policies between regions.

In the policy evaluation, the SDID reveals the spatial spillover effect on the neighborhood regions, causing them to imitate the policies and promote economic activities. It is not appropriate to study the policy effect independently, but a comprehensive evaluation from a local perspective is preferred.

#### **Acknowledgements**

I thank Jiafeng Gu, Tongying Liang, and Feifei Liang for their generous comments.

### **Conflict of interest**

The author declare no conflict of interest.

### **A. Appendix**

```
Stata Code
   /*Create time fixed effect and individual fixed effects.*/
   sort time id
   by time: gen ind = _n
   sort id time
   by id: gen T = _n
   /*Generate treat and post two dummy variables, with 2010 set as time spot of
policy intervention and observations from 17 to 31 are treatment group, and rest is
```
control group.\*/ gen treat = 0

```
replace treat = 1 if id >17
gen after = 0
replace after = 1 if time > = 2010
/* Create Weight matrix:*/
spmatrix create idistance M /*spatial inversed distance matrix*/
spmatrix dir
spmatrix create contiguity W/*spatial distance matrix*/
spmatrix dir
```

```
estat moran, errorlag (W)
estat moran, errorlag (M)
```

```
gen treatafter = treat*after
spmatrix create contiguity W if year == 2010
spxtregress NGP treatafter PGDP NCU TSR NIE i.time,re dvarlag (W)
```

```
gen treatafter = treat*after
spmatrix create contiguity W if year == 2010
spxtregress CAP treatafter PGDP NCU TSR NIE i.time,re dvarlag (W)
/*General application*/
1)SAR-SDID
> spmatrix create contiguity W if year == 2010
>spxtregress NGP treatafter PGDP NCU TSR NIE i.time, re dvarlag (W)
```
2)SEM-SDID > spmatrix create contiguity W if year == 2010 >spxtregress NGP treatafter PGDP NCU TSR NIE i.time,re errorlag (W)

3)SDM-SDID

> spmatrix create contiguity W if year == 2010

>spxtregress NGP treatafter PGDP NCU TSR NIE i.time, re dvarlag (W) ivarlag (W: X)

*Spatiotemporal Difference-in-Differences: A Dynamic Mechanism of Socio-Economic Evaluation DOI: http://dx.doi.org/10.5772/intechopen.107357*

#### 4)SXL-SDID

> spmatrix create contiguity W if year == 2010 >spxtregress NGP treatafter PGDP NCU TSR NIE i.time,re ivarlag (W: DX)

### **Author details**

Lijia Mo Suzhou University, Suzhou, Anhui, China

\*Address all correspondence to: molijia@hotmail.com

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### **References**

[1] Angrist JD, Pischke J. Mostly Harmless Econometrics: An Empiricist's Companion. Princeton, NJ: Princeton University Press; 2008

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[10] Pomeranz D. Impact evaluation methods in public economics: A brief introduction to randomized evaluations and comparison with other methods. Public Finance Review. 2017;**45**(1):10-43 [11] St Clair T, Cook TD. Difference-indifferences methods in public finance. National Tax Journal. 2015;**68**(2): 319-338

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## **Chapter 5** The Impact of Inflation Expectations and Public Debt on Taxation in South Africa

*Thobeka Ncanywa and Noko Setati*

#### **Abstract**

The study investigates the impact of inflation expectations and public debt on taxation in South Africa, employing the autoregressive distributive lag model and Granger Causality techniques. The results indicate a long-run positive significant relationship between inflation expectations and taxation and a negative significant relationship between public debt and taxation. This reveals that when consumers and businesses expect the inflation rate to rise, taxable income will also increase. The public debt-taxation nexus can imply that the South African government finances its debts through borrowing than through taxation. Therefore, economic participants must have full knowledge of what can influence taxation.

**Keywords:** taxation, inflation expectations, public debt, ARDL approach, granger causality

#### **1. Introduction**

In South African economic history, the maintenance of price stability and debt stability has always been the major macroeconomic objective that South African policymakers must strive to achieve. In the world of globalization, the cross-border transmission of inflationary forces is undeniable and one of the dynamic macroeconomic issues confronting most economies around the world [1]. Therefore, the risks of inflation must be managed prudently and with caution. South Africa's public debt has always remained a challenge for policymakers. For example, [2] states that policymakers still do not grasp what drives inflation expectations almost 10 years after the Great Recession of 2008–2009. In February 2000, the South African Reserve Bank (SARB) adopted the inflation target as a guideline, which describes an acceptable inflation rate in South Africa. However, inflation risks should be quantified into inflation expectations, and policymakers must consider them. Tax authorities when formulating tax systems, because if tax rates are not adjusted for inflation, this may lead to distortions in the economy [3]. Therefore, the primary aim of this research study is to give attention to how public debt and inflation expectations influence taxation.

Economic participants such as investors, financial analysts, workers, trade unions, and businesses all have opinions on the future rate of inflation, which are referred to as inflation expectations or expected inflation. As a result, people evaluate this rate when making judgments about various economic activities that they want to engage in shortly. In the world of central banking, inflation expectations serve at least two purposes. They provide a summary of statistics where inflation is expected to be because they are essential inputs into the price level. Secondly, they can be used to judge the central bank's inflation target's legitimacy. According to [4], the expected inflation for 2021 was estimated to be 4.6% in 2020 and 5.1% in 2021. Inflation expectations reversed course in the second quarter of the 2021–2022 financial year after declining by 0.3 percentage points relative to the fourth quarter in the previous survey, and on average inflation is expected to edge up from 4.2% in 2021 to 4.4% in 2022 and 4.5% in 2023 [5]. The trend analysis for the two conductors of the inflation expectations surveys depicts a stable price level in South Africa. Hence, on average inflation is expected to be within the official inflation target (3–6%). The rate of inflation expectation affects the behavior of various economic participants on how they should spend and invest, thus affecting taxable income [6].

The study on the effect of inflation expectations and public debt on taxation is important in South Africa. Researchers in South Africa have attempted to establish the link between public debt and taxation. For example, a study by [7] attempted to study the relationship between public debt, economic growth, and inflation based on data among BRICS countries. Based on the literature reviewed in this study, most studies around the world only focused on the relationship between inflation and public debt, which are the explanatory variables in this study [8–10]. From the literature review, it appears that there is a lack of studies about the effects of inflation expectations and public debt on taxation in South Africa. The studies reviewed do not link inflation expectation to public debt and taxation. Therefore, this study will make a significant contribution to the existing body of knowledge in South Africa, because of the unique selection of variables in the specified model. The study adopts the Autoregressive Distributive Lag (ARDL) estimation method for empirical analysis covering the period from 2000 to 2020, which includes the global financial crisis and two health crises.

As alluded to above, non-inflation-adjusted tax rates create distortions in the economy. However, taxation is also a distortion because there is no economic activity involved. Such small negligence in policy decision-making can be problematic, for example, by overestimating or underestimating the true value of the economic activity. Tax thresholds often do not increase in line with inflation [11]. If employees gain a salary increase to match inflation, then they are not better off in real terms. In addition, with a nominal salary increase, individuals may enter a higher tax bracket and therefore be worse off. This phenomenon is called bracket creep. In South Africa, a progressive personal income tax system is used to reduce inequality [12].

#### **2. Literature review**

This section is divided into two subsections, which are theoretical literature and empirical literature. The first subsection outlines theories associated with economic time series variables understudy. The second subsection presents empirical evidence related to the topic under review.

#### **2.1 Theoretical literature**

The study investigates the influence of inflation expectations and public debt on taxation, which may create distortions in the economy. The fiscal theory of the price level is proposed as a suitable theory that attempts to form and explain the nature of the relationship between inflation expectations and taxation in this study. This theory originates from the work of Woodford in 1994 [13]. This theory emphasizes the role of fiscal policy, including taxes (present and future taxes) and the debt level in determining inflation [14]. Traditionally, this role is tasked to the monetary policy as advocated in the Quantity Theory of money by Friedman in 1980. This theory opposes the monetarist view that states that the money supply is the primary determinant of the price level and inflation [13]. However, both theories share a common view on how an increase in government spending (through public debt) represents an injection in the economy and this increases the flow of money In the end, price levels are expected to increase because of the notion that too much money ceases few goods (ceteris paribus).

The fiscal theory of the price level suggests that in real terms, the government can inflate its debt away [14]. This means that high inflationary pressures caused by the fiscal policy will devalue government debt and the amount that must be repaid will be smaller in real terms. In terms of this theory, high price levels do not warrant the need for present and future tax increases. However, understanding that tax cuts and increases in government spending do not necessarily have to be paid by higher taxes later, may create room for too much government and unstable government debt. This theory will be tested against the Ricardian equivalence hypothesis, which will be reviewed in this subsection.

Ricardian equivalence hypothesis is proposed in this study, because of how it differs from the fiscal theory of the price level on taxation perspective when government increases spending. Ricardo in 1951 developed this theory, which was later elaborated upon by Barro in 1979 [15]. This theory assumes that economic participants are rational, and this allows them to anticipate an increase in taxes when government increases spending. According to this theory, all government purchases must be paid by taxes. Unlike the fiscal theory of the price level, this theory does not consider inflation expectations caused by an increase in government spending through borrowing [16]. Government debt must be repaid by increasing taxes. This theory for the interest of this study anticipates an increase in taxes when public debt increases. This theory suggests that a tax cut today is balanced by tax increases in the future.

This economic theory suggests that when a government tries to stimulate growth in the economy by increasing debt-financed government spending will lead to a tax increase in the future [14]. Therefore, an increase in debt-financed government spending has a positive relationship in the long run. Public debt and taxation are important instruments of fiscal policy [16]. This theory demonstrates the relationship between the two instruments in the economy. In addition, this theory advocates that those taxpayers should anticipate that they will have to pay higher taxes later.

#### **2.2 Empirical literature**

Some views in the literature indicate the effects of public debt on expected inflation. For instance, there is a study that investigated fiscal policy and expected inflation in households in the United States [17]. The study used a large-scale survey of US households to assess whether expected inflation reacts to the information provided.

The study employed a Nielsen home scan panel, which included approximately 80,000 households to run the results. The findings revealed that most households do not perceive current high deficits or current debts as inflationary or as the indicator of significant changes in the fiscal outlook [17].

Although a considerable amount of research has been conducted on the issues of public debt and expected inflation, there is a research gap on the impact of inflation expectations and public debt on taxation especially in South Africa [17–19]. For instance, there is a South African study that employed the Autoregressive Distributive Lag (ARDL) to evaluate the nexus between inflation expectations and aggregated demand using secondary time series data [18]. The study revealed that when employing the Error Correction Model (ECM), a 1% increase in inflation expectations would lead to a 0.4% decrease in the level of gross domestic product, ceteris paribus. Since a shadow economy cannot be taxed, it destroys the tax base and reduces the tax revenues, forcing governments to resort to other ways to finance their expenditure [18]. In supporting this statement, another study measured the impact of the shadow economy on inflation and taxation using panel data of 162 countries from 1999 to 2007 [19]. The study observed that there is a positive relationship between the size of the shadow economy and inflation and that the size of the shadow economy and the tax burden are negatively related. From both relations, there have been causal effects running from the shadow economy and tax burden. The relationships are robust in controlling the debt ratio, estimating the two relations as a system, and using alternative estimates of the shadow economy [19].

Some researchers found contradictions in the relationship between taxation, public debt, and the inflation rate using different methodologies. For example, one researcher used an ordinary least square (OLS) methodology to find the negative effects of taxation on macroeconomic aggregates, including inflation in Nigeria [20]. Others used autoregressive distributed lag (ARDL) and discovered that the impact of public debt on inflation is positive but statistically insignificant [9, 21, 22]. The positive association is in line with the study that investigated public debt and inflation nexus using a panel of 52 African countries [7]. Contrary to the findings, it was discovered that a negative relationship exists between the inflation rate and public debt [23].

There was an examination of public debt, budget deficit, and tax policy reforms for fiscal consolidation in Sri Lanka that employed the Vector Error Correction model (VECM) [10]. It was revealed that direct government tax revenue, indirect tax revenue, and consumer price index are negatively correlated with government debt to GDP ratio in the long run. In the short run, only direct tax revenue affects it significantly [10]. In addition, there was an examination of the effects of tax policy on inflation in Nigeria, employing Johansen cointegration test technique [24]. The results of the estimates revealed that the personal income tax rate harms inflation in the long run, while the company income tax rate has a significant positive relationship with inflation in the long run. However, some researchers found conflicting results that personal income tax and company income tax have no significant relationship with GDP [25].

Many scholars utilized Granger Causality tests to reveal the direction of causality in the relations between taxation, public debt, and expected inflation [10, 26–30]. It was revealed that a unidirectional causality relationship exists between tax revenue and public debt [10, 26]. However, few studies revealed that there is a unidirectional causality running from inflation to taxation [27, 28]. Others established a unidirectional relationship between inflation to domestic debt and external debt in Malaysia [29]. In Bangladesh, the results of a study indicated the presence of unidirectional

#### *The Impact of Inflation Expectations and Public Debt on Taxation in South Africa DOI: http://dx.doi.org/10.5772/intechopen.107389*

causality running from budget deficit to inflation [30]. This budget deficit is a representation of public borrowing requirements.

In South Africa, a study investigated the relationship between oil prices, exchange rates, and inflation expectations in South Africa [31]. The study employed monthly time series data from July 2002 to March 2013, and the data were obtained from the South African Reserve Bank. The study employed a Vector Autoregression (VAR) model to run the results. The authors found out that oil prices and exchange rates have a positive relationship with inflation expectations in the long run. The food variable is inversely related to inflation expectations [31]. The study further indicated that oil, exchange rates, interest rates, and food costs are Granger causes of inflation expectations, both in the short run and long run. The study concluded that stable and low inflation together with well-anchored inflation expectations is important to monetary authorities as they help in achieving monetary policy objectives such as economic growth and financial stability.

This section laid down both the theoretical and empirical framework of the study. The first theory is the fiscal theory of the price level, which suggests that there is a need to understand that tax cuts and a rise in government spending do not necessarily have to be paid by higher taxes, and this may create too much unstable public debt [14]. Contrary to the first theory, the second theory is the Ricardian equivalence hypothesis, which does not consider the inflation expectations resulting from an increase in public debt [16]. The theory is based on the notion that a tax cut today is balanced by a rise in future taxes. In examining the empirical literature, more attention was given to taxation and inflation in most countries than the relationship between inflation expectations and taxation. Most studies reveal that there is a negative insignificant relationship between taxation and inflation. A relationship between public debt and taxation was found to be negative and that a stable relationship exists between public debt and inflation. Hence, this study will contribute by documenting new knowledge to the literature in addressing the impact of inflation expectations and public debt on taxation in South Africa.

#### **3. Research methodology**

#### **3.1 The estimated model**

The model used in this study is an econometric model, which runs multiple regression analyses between taxation as a dependent variable and the independent variables that affect taxation such as inflation expectations and public debt. Inflation (CPI) is a control variable in the model. The general model is specified as follows:

$$\text{TAX} = f(\text{INFE, PD, CPI}) \tag{1}$$

Eq. (1) describes the relationship between the dependent variable (taxation) and the independent variables (inflation expectations, public debt, and inflation rate). Where TAX is Taxation, INFE is Inflation expectations, PD is public debt, and CPI is Inflation.

#### **3.2 Data**

The study used quarterly secondary time series data obtained from the South African Reserve Bank. Due to the availability of data, especially for inflation expectations, the study covered the period from 2000 to 2020.

#### **3.3 Estimation techniques**

An ARDL-based ECM is employed in this study to analyze the short-run effects of inflation expectations and public debt on taxation. After testing for stationarity, if variables portray different orders of integration like at first level [I (0)] or at first differencing [I (1)], the ARDL can be employed [18, 32, 33]. The ARDL approach simultaneously captures the cointegration between a set of variables, the long-run and short-run estimates including the speed of adjustment. The ARDL cointegration test is also called the bounds test [33] and indicates if the long-run relationship exists in the series. It is advantageous due to its ability to incorporate small sample size data and yet generate valid results [32]. The ARDL bounds test gives the lower bound critical value and the upper bound critical value. If the computed F-statistics lie above the upper critical bounds test, we reject the null hypothesis of no cointegration, indicating that cointegration exists. In the case where the computed F-statistic lies in between the two bounds test, the cointegration becomes inconclusive [33]. When the F-statistics is below the lower bound, then there is no cointegration.

To determine the long-run estimates, the short-run dynamics, and ECM, Eq. (1) can be transformed into Eq. (2):

$$\begin{aligned} \Delta \text{TAX}\_{t} &= a + \sum\_{i=1}^{k} \beta\_{1} \Delta \text{TAX}\_{t-1} + \sum\_{i=1}^{k} \beta\_{2} \Delta \text{INFE}\_{t-1} + \sum\_{i=1}^{k} \beta\_{3} \Delta \text{PD}\_{t-1} \\ &+ \sum\_{i=1}^{k} \beta\_{4} \Delta \text{LCPI}\_{t-1} + \delta\_{1} \text{TAX}\_{t-1} + \delta\_{2} \text{INFE}\_{t-1} + \delta\_{3} \text{PD}\_{t-1} + \delta\_{4} \text{CPI}\_{t-1} \\ &+ \eta \text{ECM}\_{t-1} + \varepsilon\_{t} \end{aligned} \tag{2}$$

Where Δ denotes the first difference operator in the model, α represents the constant, and ε represents the error term also known as the white noise disturbance. The long-run relationship in the model is represented by *δ*<sup>1</sup> � *δ*<sup>4</sup> coefficients. The short-run relationship in the model is represented by *β*<sup>1</sup> � *β*<sup>4</sup> coefficients, *phi* denotes the speed of adjustments, and ECM denotes the residual obtained from estimated cointegration in the equation. As Engle and Granger in 1987 put it, error-correcting or simply ECM allows long-run components of variables to obey equilibrium constraints while short-run components have a flexible dynamic specification [9, 18, 21]. After confirming the long-run equilibrium among the variables with the bounds test, the short-run, long-run and ECM coefficients (α, β's, δ, φ) are estimated using ARDL [21].

The study employs the Granger causality test to determine the nature of the relationship among the variables in the study. This study requires an assessment of whether these variables Granger cause each other and the nature of Granger causality if it is bidirectional (that is, the variables have an impact on each other) or unidirectional (only one variable has an impact on the other) or independent (they have no impact on each other) (Gujarati and Porter, 2003). The first variable is said to Granger cause the second if the forecast of the second variable improves when lagged values of the first variable are considered [28, 30].

#### **3.4 Diagnostic and stability tests**

The study conducted diagnostic tests for heteroskedasticity, serial correlation, and normality [7]. For heteroskedasticity, the study employed the Breusch-Pagan Godfrey test, for serial correlation the Breusch-Godfrey LM test, and Kurtosis for normality. The study utilized the cumulative sum of recursive residuals (CUSUM) and CUSUMsquare to check the stability of the model [11].

#### **4. Findings and discussions**

The unit-roots results indicated that the variables are integrated at different orders, which are I (0) and I (1), hence the study is employing the ARDL bounds test. **Table 1** presents the results of the ARDL bounds test approach. The estimates were found using E-views 12, which automatically chose the optimal lag length for the model.

**Table 1** shows significant levels for the lower bound and upper bound at 1%, 5%, and 10%. The number of independent variables understudy is 3, hence k = 3. The results show an F-statistic value of 8.51, which is greater than the lower bound I (0) and upper bound at all levels of significance (1%, 5%, 10%) respectively. The lower bound and the upper bound critical values are obtained from [33]. The information about F-statistics means that there is cointegration. The existence of cointegration in the model provides evidence of a long-run relationship between all the independent variables on taxation through the ARDL bounds test approach.

The cointegration results are consistent with prior expectations and other studies' findings that examined public debt, budget deficit, and tax policy reforms for fiscal consolidation in Sri Lanka [10]. In their study [10], they found a positive and statistically significant relationship between public debt and taxation. Additionally, other studies analyzed the relationship between taxation and inflation in Nigeria [9]. The study revealed that cointegration exists between the variables. It is therefore necessary to estimate the long-run and short-run coefficients and speed of adjustment, and **Table 2** indicates the results of ARDL estimates.

The results in **Table 2** show that there is a significant positive relationship between inflation expectations and taxation in South Africa. A unit change in inflation expectations will result in a 0.84 unit change in taxation (ceteris paribus) in the South African context. This relationship is statistically significant at a 1% level of significance. This is in line with economic theory, and the fiscal theory of price level because when consumers, as well as businesses, expect the inflation rate to rise in the future, this will increase their income tax, capital gains tax, and profits [14]. However, these findings differ from some studies that found a negative relationship though that study was between inflation expectation and aggregate demand [18].

The results further indicate that there is a negative significant relationship between public debt and taxation in South Africa as indicated in **Table 2**. The results show that when public debt increases by 1 unit, taxation will decline by 7.86 units (ceteris


**Table 1.** *ARDL bounds test computed from E-views 12.*


#### **Table 2.**

*ARDL results computed from E-views 12.*

paribus). Therefore, there is an inverse relationship between public debt and taxation. This relationship is statistically significant at a 1% level of significance. This inverse relationship can mean that when public debt increases, the government does not immediately finance its debt through taxation. They might borrow money from banking institutions or International Monetary Fund (IMF). The Ricardian equivalence theory confirms that when public debt increases, we should estimate that taxation will increase, but this does not occur immediately when public debt rises [15, 16]. Hence, in South Africa, the government does not finance its debt through taxation immediately when there is an increment in public debt. The results are in line with studies that found a negative significant relationship between public debt and taxation in the long run [10, 24]. Inflation as one of the control variables indicates a positive insignificant relationship between taxation.

In the short run, inflation is the only significant variable at 5% (see **Table 2**). The coefficient of the speed of adjustment is �0.83 implying that deviation from long-run inflation expectations and public debt in taxation is corrected by 83% of the following period. This means the system can adjust by fluctuating, and this fluctuation will decrease in each period and return to equilibrium. The speed of adjustment confirms the existence of a stable long-run relationship [23, 24]. **Table 3** displays the results of Granger causality to determine the direction the relationship that the series takes.

In **Table 3**, there is unidirectional causality between inflation expectations and taxation. Inflation expectations have a positive impact on taxation at a 1% level of significance. This leads to the rejection of the null hypothesis since a unidirectional relationship exists between inflation expectations and taxation. The results are like findings in the study by [27]. There is also a unidirectional relationship between taxation and public debt. Taxation Granger causes public debt at a 1% level of significance. This concedes with the findings of [28], who revealed that a unidirectional relationship exists between taxation and public debt in South Africa. The results further indicate that inflation Granger causes taxation; hence, there is a unidirectional relationship between inflation and taxation in South Africa. This coincides with the findings by [28].

*The Impact of Inflation Expectations and Public Debt on Taxation in South Africa DOI: http://dx.doi.org/10.5772/intechopen.107389*


#### **Table 3.**

*Granger causality computed from E-views 12.*

**Figure 1.** *CUSUM computed from E-views 12.*

**Figure 2.** *CUSUM of squares computed from E-views 12.*

The series was subjected to diagnostic and stability tests. All variables were free of heteroskedasticity and correlation as the probability of the variables was insignificant. The Kurtosis of 3.5 indicates that the series follows a normal distribution [18]. In addition, the CUSUM, as well as the CUSUM of squares, shows that the model is stable as illustrated in **Figures 1** and **2** by the blue line inside the red lines.

#### **5. Conclusion and recommendations**

The study investigated the relationship between inflation expectations and public debt on taxation, a proxy of personal income tax, capital gains tax, and profits in South Africa from 2000 quarter 3 to 2020 quarter 4. To achieve the objectives that are stated in Section 1, the study used secondary time series data gathered from the South African Reserve Bank. The ARDL and Granger causality methods have been employed in the analysis. To scrutinize the order of integration among the variables, the study used the Augmented Dickey-Fuller (ADF) test and Phillips Perron (PP).

The results revealed that there are different orders of integration since taxation, inflation expectations, and public debt are integrated at I (1) for both methods while inflation is integrated at I (0). Hence, the study adopted the ARDL techniques. The study found out that inflation expectations and public debts are the two main macroeconomic variables that have an impact on taxation in South Africa, in the long run. The results revealed that there is a positive significant relationship between inflation expectations and taxation in the long run. However, the study found a negative correlation between public debt and taxation in the long run, but positively related in the short run. The pairwise Granger causality tests found that inflation expectations Granger cause taxation. There is a unidirectional relationship between inflation expectations and taxation. A causal relationship also existed from taxation to public debt.

Policymakers have long understood the importance of communication strategies and the importance of managing economic expectations; therefore, they must always communicate or inform economic participants (households and firms) about the changes in inflation expectations that might occur in the future. Using monetary policy tools can help policymakers to strive to anchor inflation expectations at roughly 3–6%, which is the inflation target rate in South Africa. This is to help inflation expectations to remain stable. There must be a balance between financing public debt through borrowing and taxation. An increase in taxation may place slow pressure on inflation, which will, in turn, enable the Reserve Bank to keep up with high-interest rates. Hence, there is a need for coordination between fiscal and monetary policies to achieve stability in the economy.

#### **Conflict of interest**

The authors declare no conflict of interest.

*The Impact of Inflation Expectations and Public Debt on Taxation in South Africa DOI: http://dx.doi.org/10.5772/intechopen.107389*

#### **Author details**

Thobeka Ncanywa\* and Noko Setati Walter Sisulu University, Butterworth, South Africa

\*Address all correspondence to: tncanywa@wsu.ac.za

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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#### **Chapter 6**
