Nonlinear Effects of VAT on Household Consumption in South Africa: A NARDL Analysis

2.1 Empirical review

Numerous studies have explored the complex relationship between value-added taxes and household consumption, revealing varied and often contradictory findings. Early contributions, such as those of Tagkalakis (2014), estimated the relationship between VAT revenue and economic activity in Greece using quarterly data from Q1 2000 to Q3 2012. The results suggest that consumption patterns remained largely unchanged, even when lower VAT rates were applied, implying a limited influence of VAT changes on household spending behavior. This aligns with Zídková (2014), who analyzed VAT gaps in the EU using OLS estimations for 2002 and 2006, confirming that the VAT gap increased with higher final consumption. Both studies suggest that VAT policy alone may not strongly alter consumer behavior.

However, other studies contradicted this view. Střílková and Široký (2015), examining Czech households between 2007 and 2014, found that reductions in VAT led to increases in household consumption, suggesting that consumers respond positively to tax relief on their expenditure baskets. Similarly, Van Oordt (2015), through a detailed survey-based analysis of South Africa, argued that increases in VAT significantly affect consumption, particularly among low-income households, reinforcing the regressive nature of indirect taxation.

Further debate emerged in the findings of Erero (2015), who applied a CGE model to South Africa and concluded that VAT increases would not negatively impact poor households, a result that stands in contrast to that of Stacey et al. (2017). Using the same model framework, Stacey et al. demonstrated that VAT hikes during 2010–2011 had a harmful effect on the consumption patterns of low-income households, emphasizing the potential inequity of VAT policies.

Adding to this discourse, Terfa et al. (2017), using stratified random sampling in Ethiopia, found a negative but statistically insignificant effect of VAT on consumption in 2014. This nuanced result suggests potential context-specific dynamics that influence how households adjust to tax changes. Ogneru et al. (2019) further support the argument that VAT may not always translate into reduced consumption is further supported by Ogneru et al. (2019). Their VAR model analysis of Romania (2007–2018) found no direct link between VAT revenue and consumption, contradicting earlier studies that suggested clear behavioral responses to VAT changes. Conversely, Otemu (2020), analyzing data from Nigeria (2000–2018), found strong evidence that VAT influences consumption patterns. These findings echo those of Al Gahtani et al. (2020), who modelled the Saudi Arabian context using an error correction framework (1970–2017), estimating a −0.3% one-time impact of VAT on consumption, suggesting a measurable, though modest, effect of VAT introduction.

More recent studies have reinforced the consumption-suppressing potential of VAT. Roos et al. (2020) confirmed that VAT increases negatively affect household consumption by applying a multiregional model to South Africa. However, Hammour and McKeown (2022) found no significant effect of VAT on consumption in the United Arab Emirates based on survey responses from 2019, suggesting that in higher-income contexts or in the short term, VAT may be less impactful on spending behavior. Notably, Adegbite (2023), using the Autoregressive Distributed Lag (ARDL) model for Nigeria (1990–2021), reported a significant negative relationship between VAT and household consumption, bolstering the argument that VAT erodes disposable income and curbs expenditures. These findings are extended by Omodero et al. (2023), who employed a panel ARDL model for Nigeria and South Africa (1994–2021) and discovered that while VAT has a short-run positive effect on household consumption, its long-run effect is significantly negative, which underscores the temporal complexity of VAT’s impact.

In conclusion, the literature suggests that the relationship between VAT and household consumption is not uniform. While some studies find insignificant or even positive short-run effects, the broader consensus, particularly in developing countries, leans toward the view that VAT increases tend to suppress household consumption, especially among low-income groups.

3.1 Nonlinearity test

The nonlinearity test is one of the crucial tests that needs to be conducted on the time series data before the estimation of the NARDL technique, as it can identify the nature of the relationship between the series (Narayan, 2005; Rahman & Ahmad, 2019). Therefore, this study used the BDS linearity test to check for nonlinearity in the model.

3.2 The BDS linearity test

The BDS linearity test is an appropriate test to capture nonlinearity in time-series data, as recommended by many authors such as Broock et al. (1996) and Monamodi (2021). The following data-generating process (DGP) was used to demonstrate the BDS linearity test:

Where $Y_t$ is a stationary variable that results from the DGP, $p_{t-1}$ = $(Y_{t-1},$ $Y_{t-p})$ , $\delta$ represents an unobserved set of parameters, $u_t$ is the unmeasured disturbance term that exhibits finite variance and a mean of zero in a normal distribution, and does not rely on $Y_{t-1}$ at every time instance $t$ . As suggested by Monamodi (2021), the BDS model specification includes Equation (2) as part of the DGP:

where $\widehat{u}$ is the estimated residual, ${\delta }_T$ is the consistent estimator of $\delta$ , the limit of ${\widehat{u}}_t$ = $u_t$ is the limit, and is serially independent. ${\widehat{u}}_t$ was normally distributed when ${\delta }_T$ was equal to $\delta$ . In this study, for each embedding dimension $(m$ ), the correlation integral is computed, which measures the probability that two points in the phase space are within a certain distance ( $\epsilon )$ from each other. The correlation integral takes the following form.

Where $I$ is an indicator function that is $1$ if the condition is true and $0$ otherwise, $X_i$ and $X_j$ are points in the phase space, and N is the number of points. Furthermore, the BDS statistic was calculated by comparing the correlation integral for the original time series with that of a surrogate dataset generated under the null hypothesis of linearity (Rahman & Ahmad, 2019).

Where $C_1^m\left(ϵ\right)$ represents the correlation integral for the embedded series with dimension $1$ raised to the power $m$ , and ${\widehat{\sigma }}_{m,ϵ}$ is an estimate of the standard deviation of $C_m\left(ϵ\right)-C_1^m\left(ϵ\right)$ . The null hypothesis is that the time-series data have no significant nonlinearity, while the alternative hypothesis states that there is nonlinearity in the time-series data. A significant BDS statistic with a p-value of less than 5% suggests the presence of nonlinearity in the series (Kim et al., 1998; Mitchell & McKenzie, 2011).

3.3 Data sources

The data for the variables examined in this study were extracted from South African Reserve Bank (SARB) and World Bank databases. Due to the limited quarterly data available in South Africa, this study used annual data from 1994 to 2023 with 30 observations. This study period was chosen to check the impact of value-added tax on household consumption after the first South African democratic election and after the economic devastation caused by the Covid-19 pandemic, hence, using the estimation of the NARDL regression model to check the effect of value-added tax on household consumption during the specified study period.

3.4 Nonlinear stationarity testing

To run a NARDL method, all the conditions within its framework must be met, and all the variables must be integrated either in order I(0) or I(1), or mixed, but not in order I(2), as for the ARDL approach (Ahmad et al., 2018; Ur Rahman et al., 2019). Hence, this study estimated the KSS (Kapetanios et al., 2003) nonlinearity unit root test before applying the NARDL technique.

3.4.1 KSS nonlinear unit root test

Kapetanios et al. (2003) developed a KSS unit root test capable of capturing unit roots in the presence of nonlinear adjustments. Erdas (2019) believes that the KSS nonlinear unit root test is based on the Exponential Smooth Transition Autoregressive (ESTAR) model. Equation (5) represents the ESTAR model:

Where ${\mathcal{Y}}_t$ is the time series variable, $∆$ is the first difference operator, $\gamma$ and $\theta$ are parameters, $p$ denotes the lag structure, and ${\epsilon }_t$ is the residual term. The equation below represents a nonlinear transformation.

To capture the nonlinear adjustment, Equation (6) must be applied for nonlinear transformation to the series. According to Erdas (2019), the model specification used in the KSS nonlinear unit root test can be expressed as follows:

Null hypothesis: the series has a unit root. Alternative hypothesis: the series is nonlinear stationary; therefore,

Kapetanios et al. (2003) suggested that the computed test statistics and critical values must be compared. If the computed t-statistics is less than the critical value of either −2.82 or −2.22 or −1.92 at a significant level of 1%, 5% or 10%, respectively, dismiss the null hypothesis in favour of the alternative hypothesis at the specified significance level.

3.5 NARDL cointegration bounds testing approach

NARDL cointegration bounds testing is essential for determining at least one cointegrating asymmetric vector in the series (Shin et al., 2014; Rezitis, 2019). Kapetanios et al., (2006) believed that the NARDL bounds testing approach is a robust method for detecting cointegration in the presence of nonlinearity. Hence, this study estimates the following asymmetric cointegration equations to capture cointegration before analyzing the asymmetric effects of the VAT tax on household consumption:

The decision rule is that, if the computed F-statistic is greater than the upper bound critical value, the null hypothesis is rejected. Additionally, if the F-statistic is less than the lower-bound critical value, it fails to reject the null hypothesis. If the F-statistic falls between the lower- and upper-bound critical values, the result is inconclusive (Pesaran et al., 2001).

3.6 NARDL model specification

The NARDL framework can be adopted after the BDS linearity test confirms that the relationship between variables is nonlinear (Bahmani-Oskooee & Fariditavana, 2016). This study modified the subsequent model, which was developed by Shin et al. (2014) and applied by Gohar et al. (2022), who examined the short- and long-run effects of income and price changes on consumption expenditures in seven emerging countries over the period 1991 to 2020. The NARDL model specifications are as follows.

where the long-run coefficients are represented by ${\beta }_1$ - ${\beta }_6$ and short-run coefficients are represented by ${\theta }_1$ - ${\theta }_6$ . ${\mathit{IR}}_{\mathit{kt}}$ , ${\mathit{PR}}_{\mathit{kt}}$ , ${\mathit{NI}}_{\mathit{kt}}$ and ${\mathit{CP}}_{\mathit{kt}}$ indicate the interest rate, price, income, and consumption for country $k$ at time $t$ , respectively. ln within each variable denotes that the variables are used with the natural logarithm, whereas $∆$ is the difference operator indicating the short-term impact. This study modified Equation (18) by excluding variables that were not reviewed in the current study, such as $\mathit{NI}$ income and $\mathit{PR}$ prices. To achieve the objectives of the study, these variables were replaced with VAT, household disposable income, and economic growth.

The following variables were used: household consumption is abbreviated as $\mathit{HC}$ , and interest rate as $\mathit{INT}$ . The following section presents the NARDL model, estimated to examine the effect of VAT on household consumption.

In line with Equation (18), the long-run NARDL model estimated in this study to determine the asymmetric and nonlinear effects of VAT on household consumption in South Africa is presented in Equation (19):

After long-run estimation, the following short-run NARDL model was estimated to shed light on the full dynamics of the NARDL framework, especially when the effects of positive and negative changes differ. This study finds it important to not overlook key short-term dynamics.

Where HC stands for household consumption, VAT denotes value-added tax, INT is interest rate, HDI is household disposable income, and GDP signifies economic growth. The NARDL error correction model (ECM) is as follows:

3.7 NARDL long- and short-run asymmetric effects

This study finds that it is crucial to determine the existence of asymmetric linkages among the series. Asymmetry means that the response of one variable to another differs depending on the direction or magnitude of change (Verheyen, 2013; Mosikari & Eita, 2020; Hossain et al., 2021). Not accepting either long-run symmetry or short-run symmetry will result in long- or short-run asymmetry. This study estimated asymmetric cointegration prior to estimating the long- and short-run asymmetries using the NARDL model. After confirming one cointegrating asymmetric vector among the series, the study estimated the long-run asymmetries by examining the coefficients ${\lambda }_2^{+}$ , ${\lambda }_2^{-},$ ${\lambda }_3^{+}$ and ${\lambda }_3^{-}$ :

The estimation of Equation (21) was based on the Wald test to check if ${\lambda }_2^{+}$ = ${\lambda }_2^{-}$ , ${\lambda }_3^{+}$ = ${\lambda }_3^{-}$ . Rejecting the null hypothesis indicates a long-run asymmetry. This study examined short-run dynamics by examining the coefficients ${\alpha }_2^{+},$ ${\alpha }_2^{-}$ , ${\alpha }_3^{+}$ and ${\alpha }_3^{-}$ :

The Wald test was conducted to check if ${\alpha }_2^{+}$ = ${\alpha }_2^{-}$ , ${\alpha }_3^{+}$ = ${\alpha }_3^{-}$ , ${\alpha }_4^{+}$ = ${\alpha }_4^{-}$ . The rejection of the null hypothesis indicates short-run asymmetry. We also estimated the following diagnostic tests to ensure the robustness of the model: the homoscedasticity test, autocorrelation test, residual normality assessment, and Ramsey RESET test.

4.1 Linearity tests

This study used the BDS test for linearity to assess nonlinearity in the variables under review. The estimated BDS Linearity results are listed in Table 1.

In Table 1, the findings from the BDS test for linearity show that the null hypothesis of linearity on household consumption, value-added tax, interest rate, household disposable income, and economic growth are rejected at the 1%, 5%, and 10% levels of significance. In summary, the results of the BDS test for linearity indicate that all the variables under review have nonlinearity characteristics.

It is worth noting that the BDS results provide insights into the appropriate methodology for examining the linkages between household consumption, value added tax, household disposable income and economic growth. This relationship can only be effectively modelled using a nonlinear approach (NARDL).

4.2 Nonlinear stationarity testing

This study estimates the KSS nonlinear unit root test to check the stationarity of the series. Table 2 presents the findings of the KSS test for nonlinearity in the unit root hypothesis at the level.

It is clear from Table 2 that all the variables–household consumption, value-added tax, interest rate, household disposable income, and economic growth–are nonlinearly stationary at level, with t-statistics of -4.191, -3.980, -5.776, and -4.397, respectively, which are less than the KSS critical value of −2.82 at the 1% significance level. This study did not estimate the KSS nonlinear unit root test at the first difference because all the variables were stationary at level.

Therefore, this study employed the NARDL approach because it is effective when the time series exhibits nonlinear stationarity. In addition, this study is of the view that the data properties that suit the NARDL model are nonlinearity, nonlinearly stationarity, and asymmetric cointegration.

4.3 NARDL optimal lag length selection

Before the empirical analysis of the NARDL model, this study first determines the optimal lag length. The lag section criteria were selected based on AIC and ARDL frameworks, as illustrated in Figure 1. Figure 1 illustrates the lag length suggested by AIC in the NARDL (1, 2, 2, 2, 2, 2, 2) model. The lags remain constant across all positive and negative partial breakdowns of the explanatory and response variables.

Figure 1. Optimal lag structure.

Source: Author’s computation using Eviews 10.

After establishing the optimal lag structure for the model, the NARDL bounds test for asymmetric cointegration is performed using the chosen lag specification.

4.4 NARDL bound test to asymmetric cointegration

As observed in the preceding section, each variable in the NARDL model was evaluated for asymmetric cointegration using endogenous testing methods. This is conducted to identify at least one cointegrating relationship with asymmetry in the series since the NARDL model functions effectively even in the presence of a single asymmetric long-run equilibrium relationship. The results of the NARDL bound tests are presented in Table 3.

In Table 3 there are two asymmetric cointegrating vectors, which are the main model and one of the subsidiary models, with F statistics of 5.820890 and 3.235941, which is above the critical value at the I(1), at the 1% and 10% significance level, respectively. Therefore, this study continues to estimate the NARDL long- and short-run relationships between the variables of interest, as presented in the following section.

4.5 NARDL long-run model estimates

Having determined the existence of two asymmetric cointegration vectors in the previous section and the lag length selection criteria of the NARDL model based on AIC, this study uses the chosen lag length to estimate the long-run relationship between value-added tax and household consumption. The results are presented in Table 4.

In Table 4, a positive change in value-added tax in the long run causes a decrease of 14.47 units in household consumption in South Africa and is statistically significant at the 5% level, since it has a p-value of 2.67%. In other words, in the long run, an increase in value-added tax leads to a decline in household consumption.

In Table 4, a negative change in value-added tax has a negative coefficient of -14.69062, indicating that value-added tax has a negative relationship with household consumption. A negative coefficient indicates that the variables are in the opposite direction. Therefore, a negative change in value-added tax leads to an increase in household consumption, and is statistically significant at the 10% level, with a p-value of 6.50%. This means that a decline in value-added tax results in an increase in household consumption by 14.69 units in the long run. This concurs with Van Oordt (2015), who used a different technique and found that an increase in VAT caused a decrease in household consumption in South Africa. Similarly, Sekwati and Malema (2011) found that VAT has a negative connection with household consumption in Botswana.

In Table 4, a positive change in the interest rate in the long run leads to a decrease of 0.84 units in household consumption in South Africa and is statistically significant at the 5% level, with a p-value of 1.84%. In other words, in the long run, an increase in the interest rate results in a decline in household consumption.

Similarly, Table 4 shows that a negative change in the interest rate is associated with a coefficient of -0.614892, indicating an inverse relationship between interest rates and household consumption. This negative coefficient implies that a decline in interest rate leads to an increase in household consumption. This relationship was also statistically significant at the 5% level, with a p-value of 3.89%. In practical terms, a decrease in the interest rate results in a 0.61-unit increase in household consumption in the long run. These findings are consistent with those of Kozlov (2023) and Ekong et al. (2020), who also found that an increase in the interest rate causes a decline in consumption.

Table 4 clearly shows that a positive change in household disposable income in the long run causes an upsurge of 1.031 units in household consumption in South Africa and is statistically significant at the 1% level, since it has a p-value of 0.24%.

On the other hand, a negative change in household disposable income has a positive coefficient of 0.935190, indicating that household disposable income has a positive relationship with household consumption ( Table 4). A positive coefficient indicated that the variables were in the same direction. Therefore, a negative change in household disposable income causes a decrease in household consumption in the long run, as shown in Table 4. In other words, in the long run, a decrease in household disposable income causes a decline of 0.935 units in household consumption in South Africa and is statistically significant at the 5% level, since it has a p-value of 4.50%. Consistent with Sulistyowati et al. (2017) and Aron and Muellbauer (2006), disposable income is found to be positively related to household consumption.

Table 4 indicates that positive changes in economic growth are insignificant, since the p-values are more than the 1%, 5%, and 10% levels of significance in the long run. As indicated in Table 4, negative changes in economic growth are insignificant since the p-values are greater than the significance level in the long run. These results are aligned with those of Koyuncu and Ünal (2020), who find that growth insignificantly affects household consumption.

In Table 4, the R-squared value is 0.991514, which means that about 99.15% of the variance in household consumption is explained by value-added tax, household disposable income, and economic growth in the model. This high value indicated an excellent fit of the model to the data. Furthermore, an adjusted R-squared of 0.968481 means that 96.85% of the variance in household consumption is explained, considering the number of predictors and sample size. The slight decrease from R-squared to adjusted R-squared suggests that the model is still excellent, as shown in Table 4. It is clear from Table 4 that the P-value of the F-statistic is very low, with a value of 0.000018, implying that the overall model is statistically significant at the 1% significance level.

4.6 NARDL short-run model estimates

After estimating the NARDL long-run model, it is conventional to generate the NARDL short-run method and error correction term. Table 5 presents the short-run NARDL results.

In the short run, a positive change in value-added tax shows a significant relationship with household consumption with a probability of 3.63%, below the 5% level of significance, as shown in Table 5. Additionally, a positive change in value-added tax in the short run caused a decline of 11.51 units in household consumption in South Africa. These results are consistent with the long-run outcomes and the empirical literature that includes Alm and El-Ganainy (2013) and Al Gahtani et al. (2020), who found that the value-added tax and consumption of households are negatively related.

It is worth noting that a negative change in value-added tax has a positive coefficient of 15.63948, which means that the value-added tax has a positive relationship with household consumption, as indicated in Table 5. A positive coefficient indicated that the variables were in the same direction. Therefore, a negative change in value-added tax leads to a decrease in household consumption, and is statistically significant at the 1% level, with a p-value of 1.04%. In other words, a decrease in value-added tax causes a 15.63 unit fall in household consumption; these results are contrary to the long-run findings. In the short term, these results could be caused by economic stress, such as a high rate of unemployment in South Africa. Empirical evidence from other countries, such as studies by Obiakor et al. (2015), Ajibola and Segun (2017) and Taiwo and Morufu (2016), is of the view that value added tax and consumption of households are positively related. In South Africa, Omodero et al. (2023) and Erero (2015) find that an increase in VAT would not negatively affect households.

In the short run, a positive change in the interest rate leads to a decrease of 0.43 units in household consumption in South Africa and is statistically significant at the 5% level, as indicated by a p-value of 0.52%, as shown in Table 5. In other words, an increase in the interest rate results in a decline in household consumption in the short term.

Table 5 also shows that a negative change in the interest rate has a coefficient of -0.309456, indicating a negative relationship between interest rates and household consumption. This negative coefficient implies that the variables move in the opposite direction. Therefore, a decrease in the interest rate leads to an increase in household consumption and is statistically significant at the 5% level with a p-value of 1.26%. This means that a decline in the interest rate results in a 0.30 units increase in household consumption in the short run. These findings are consistent with those of Owusu-Sekyere (2017), who also identified a negative relationship between interest rates and household consumption.

Table 5 shows that a positive change in household disposable income causes an increase of 1.180 units in household consumption in the short run, and is statistically significant at the 1% level, since it has a p-value of 0%.

Table 5 indicates that a negative change in household disposable income has a positive coefficient of 1.138582, which means household disposable income has a positive relationship with household consumption, as indicated in Table 5. A positive coefficient indicated that the variables were in the same direction. Therefore, a negative change in disposable income has a p-value of 0.01%, which is statistically significant at the 1% level ( Table 5). In addition, a negative change in disposable income results in a 1.138 unit drop in household consumption in the short run. These findings concur with the long-term results. These results are in line with Habanabakize (2021) and Bohlmann and Inglesi-Lotz (2021), who find a positive link between disposable income and household consumption in South Africa.

Table 5 shows that positive changes in economic growth are statistically insignificant in the short run. As demonstrated in Table 5, negative changes in economic growth are statistically insignificant, and these results are in line with the long-run findings.

The error correction term has a negative significant coefficient with a p-value of 0%, which is less than the 1% significance level. This implies that the model adjusts substantially toward an equilibrium steady state. This result is satisfactory because the coefficient is negative and statistically significant.

4.7 NARDL long and short run asymmetric effects

The estimated results for the long- and short-run asymmetric linkages are discussed in this section. Table 6 presents the outcomes of the Wald test assessing asymmetry in both long-term and short-term dynamics.

Over the long term, the findings in Table 6 indicate no support for asymmetric impacts on the interplay between value-added tax, household disposable income, and household consumption. In other words, the long-run relationships between value-added tax, household disposable income, and household consumption are revealed in this study as symmetric and well represented within the ARDL model. It is clear from Table 6 that both interest rates and economic growth have asymmetric effects on household consumption in the long run. Table 6 also indicates that the interest rate and economic growth have asymmetric effects on household consumption in the short run. Table 6 shows that the short-run relationship between the value-added tax and household consumption shows evidence of an asymmetric effect. Household disposable income has a symmetric effect in both the short and long run, as demonstrated in Table 6. In the short run, the relationship between value-added tax and household consumption is most effectively modelled using the ARDL specification. The following section presents the estimation of a graphical asymmetric analysis of the value-added tax and household consumption.

4.8 NARDL dynamic multiplier graph

This study used a dynamic multiplier graph, and the results are presented in Figure 2.

Figure 2. NARDL dynamic multiplier graph.

Source: Author’s computation using Eviews 10.

Figure 2 confirms the results in Table 6, which show that the value-added tax has an asymmetric effect on household consumption in the short run since the asymmetric plot is away from zero between periods 1 and 3.5. Hence, it is concluded that the asymmetry effect is significant in the short run, whereas in the long run, the asymmetry effect is insignificant because the asymmetry plot moves close to the zero line starting from period 3.5 15.

Figure 2 indicates that the negative shocks to value-added tax have a positive effect on household consumption, since the negative multiplier line for value-added tax lies on the positive side above the zero line. The positive multiplier line for value-added tax lies below zero on the negative side, as demonstrated in Figure 2, which implies that positive shocks to value-added tax harm household consumption.

4.9 NARDL residuals diagnostics tests

This study ensured the robustness of the NARDL model through diagnostic tests. Table 7 presents the results of the serial correlation, heteroscedasticity, normality, and Ramsey reset test.

Table 7 shows the results of the Breusch-Godfrey test, with a p-value of 29.41%, suggesting that there is no evidence of serial correlation. Consequently, the null hypothesis of no serial correlation could not be rejected at the 5% significance level. It is clear from Table 7 that the Breusch-Pagan-Godfrey test was utilized in this study to check for heteroscedasticity in the model. The findings from the test results in Table 7 indicate that the null hypothesis of homoscedasticity, which asserts that the variance of the residuals is constant, cannot be rejected. This is because the probability of 86.99% exceeded the 5% significance threshold. Furthermore, the normality of the error terms was assessed using the Jarque-Bera test statistic. As shown in Table 7, the p-value for the Jarque-Bera statistic was 57.14%. Thus, we accept the null hypothesis that the residuals follow a normal distribution as the p-value exceeds the 5% significance level.

The results of the Ramsey RESET test displayed in Table 7 indicate no evidence of model misspecification, as the p-value of 44.30% exceeds the 5% level of significance. Thus, the null hypothesis, which asserts that the NARDL model is correctly specified, was not rejected. This test is followed by the CUSUM and CUSUM of Squares tests.

4.10 NARDL dynamic stability test

This thesis also examines the stability of the NARDL model at the 5% significance level. To assess stability, recursive estimations of the NARDL model were performed using the CUSUM and CUSUMQ tests, and the outcomes are presented in Figure 3.

Figure 3. NARDL dynamic stability test results.

Source: Author’s computation using Eviews 10.

The findings presented in Figure 3 indicate that the NARDL model exhibits stability, as evidenced by both CUSUM and CUSUMQ lines remaining within the 5% significance threshold. Consequently, the model instability hypothesis is rejected. The following section presents the analyses of pay as you earn tax and value-added tax on household consumption using the QARDL framework.