The theory that forms the precursor for the model specification in this study is the endogenous growth model.

The major thrust of the endogenous growth model is the underlying dependence of economic growth on endogenous forces and not external factors (Barro 1990). Endogenous growth theory lays claim to the view that human capital investment, innovation and general knowledge are very important in the growth process and hence contribute in no small measure to economic growth. This model further prioritises externalities that are positive and spillover effect of an economy that is knowledge based with the belief that it will engender economic development. Essentially, parts of the postulations of the endogenous growth model suggest that the long-run growth rate of an economy is determined by public policy measures. For example, subsidies, research and development (R&D) or education as the case may be will increase economic growth. According to the theory, expenditure on an incentive for innovation will have a long-run positive effect on economic growth (Bozkurt 2015; Howitt & Aghion 1998; Inekwe 2015; Romer 1986).

In developing countries, the impact of transport infrastructure in stimulating growth is not straightforward (Kauzen, Sun & Frank 2020; Meersman & Nazemzadeh 2017). Meersman and Nazemzadeh (2017) noted that the impact of transport infrastructure differs over regions. Transport investment studies have not always been favoured in South Africa. The effect of investment in R&D on the transport infrastructure of South Africa was studied by the researchers (Rust, Van Wyk, Ittmann & Kistan 2008). An increase in expenditure on R&D into transport infrastructure has recently been noted (Rust et al. 2008). Focus on R&D into transport infrastructure is, however, minimal as far as the national agenda is concerned, through a paucity of innovation (Enns 2018). Nevertheless, Negota (2001) noted that the debate amongst the politicians, economists and policymakers about the role of transport infrastructure in improving lives in the third world has been increasing since the mid-1980s. From our survey of the literature, we found that studies have been published on infrastructure investment in general, but only a few have had a focus on transport specifically. We learn from their findings and apply them to transport infrastructure investments.

Kumo (2012) examined the nexus between infrastructure investment and economic growth in South Africa using data from 1960 to 2009. Granger causality test and vector autoregressive (VAR) were applied for the analysis and the results from the study showed a strong bidirectional relationship between the two.

Again, significant long-run ties were found between the two, and it was confirmed that they both have significant influences on themselves. South Africa according to the results can optimise either of the two and obtain positive results on the other. Egert, Kozluk and Sutherland (2009) assessed the impacts of infrastructure network on sustainable economic growth in the Organization for Economic Cooperation and Development nations. Times series analysis (Bayesian VAR) was applied based on the individual country data. The results indicated that transport infrastructure has a direct and significant effect on the economic growth of these countries. Using the panel data analysis, Vlahinić Lenz, Pavlić Skender and Mirković (2018) found the positive impact of transport infrastructure on economic growth in the case of Central and Eastern European Union member states. The results concur with the finding from Maparu and Mazumder (2017), which find a long-run causal relationship between transport infrastructure and economic development in India when using VAR and Vector Error Correction Model (VECM) to the data collected between 1990 and 2011.

The Bayesian VAR confirmed that the highest contribution to the economic growth was by telecommunication and electricity amongst other infrastructure. The effect on Mexico’s output growth of both public and private expenditures on investment was assessed by Nazmi and Ramirez (1997). According to the findings of these authors, public infrastructure investment spending had an important and positive impact on economic growth. The statistical influence of communal investments on output growth was similar to that of the private capital expenditure.

Using data gathered from a wide range of sources on ports, roads, air transports, railways, electricity and telecommunication, Perkins, Fedderke and Luiz (2005) assessed the long-run effect of economic infrastructure in South Africa on output growth. The results concurred with the findings of the F test conducted by Pesaran and Smith (1995). The results revealed that a vital long-run connection may be found between economic growth and economic infrastructure in South Africa. Cheteni (2013) analysed the combined effects of investments in transport infrastructure and transport sector productivity on the output growth of South Africa from 1975 to 2011. Both the VAR analyses and Bayesian VAR were applied to the study. The results showed that domestic-fixed transport investments, and the real inflation (INF) and exchange rates, have a significant influence on economic growth. In the model, when controlled for INF and exchange rate, the results showed an increased influence of infrastructure investment on economic growth. Furthermore, multifactor productivity and lagged value of the GDP also had significant impacts on South African economic growth.

Several authors (Bosede, Abalaba & Afolabi 2013; Hong, Chu & Wang 2011; Kayode, Babatunde & Abiodun 2013; Mayekiso 2015; Tripathi & Gautam 2010; Xueliang 2008, 2013; Yu et al. 2012) have used the neoclassical growth model to examine the impact of transport infrastructure on output growth. Apart from the model being widely used, it is fitting to our study. Our model is specified below. Apart from public transport expenditure (PTE), S*PTE, L and S, which are public transport expenditure, the interaction of socioeconomic factor expenditure and public transport expenditure, employment at individual metros, socioeconomic factor expenditure, the INF rate is used to capture the macroeconomic policy, whilst K is proxy for the gross fixed asset of the metros:

We transform Equation 1 into a logarithmic format. This is to allow us to present influential points in an explicit manner; and, on the other hand, correct skewed variables in the appropriate distribution in the direction of normality (Greene 2003).

Equation 2 into a Cobb–Douglas form: Y=AKβ0PTEβ1S*PTEβ2Sβ3Lβ4INFβ5[Eqn 2]

Equation 3 is presented in logarithmic form and transforms it into linear form as follows: lnYit=Ait+β0lnKit+β1lnPTEit+β2lnS*PTEit+β3lnSit+β4lnLit+β5lnINFit+uit[Eqn 3]

Where A_it is the total factor of productivity. The respective coefficients β₀β₁β₂β₃β₄and β₅ represent the output elasticity or parameters to be estimated with respect to each dependent variable. Table 1 presents variables definition, justification why used and their respective measurement.

The secondary data were obtained from the IHS Global Insight Regional (IHS Markit 2017), South African Reserve Bank (SARB), South Africa Statistics, National Treasury (2018) on Local Government.

The method of analysis for the study is divided into two because of the objectives, which delve more on exploring the impact of transport infrastructure using the disaggregated approach. Consequently, both panel data and time series approached were applied. The panel data analysis will come first, and this will be followed by time series analysis of individual metros where necessary.

The choice of this estimation procedure is primarily informed by the fact that the study is interested in disaggregating the analysis, which is a clear departure from what has been carried out in the previous studies. The one-way error component panel regression model has a unique feature of allowing the individual effect of each cross-sectional unit examined during the analysis. The equivalent is the fixed effect least square dummy variable (LSDV), which also gives priority to examine the cross-sectional unit effect in the estimated panel model. The fixed effect within regression is also equivalent to the two, but it does not allow the examination of the individual cross-sectional effect. However, it yields similar results in terms of the parameter estimates of the variables included in the model.

The one way error component panel regression model is expressed in Equation 4: yi,t=α+Xi,t'β+μi,t[Eqn 4]

The unique features of the one-way error component panel regression model are that it paves the way for cross-sectional heterogeneity when it comes to the treatment of the error term in the model as expressed by Equation 5: μi,t=ui+vi,t[Eqn 5]

The error term is now modelled in two forms because of the addition of an unobservable component that captures the individual effect, which is time invariant and white noise error term.

However, the individual effect can also be modelled using the fixed effect. This is called the fixed-effect LSDV. This version of the fixed effect is appealing but care must be taken of the numbers of cross-sectional effects to be estimated.

For example (see Equation 6): K+1+(N−1)=(K+N)[Eqn 6]

Where K is the number of parameters for the original X-regressor (β’s)

Under the regression fixed effects, the cross-sectional effect is still assumed, but they are no longer estimated along with the regression model. The data are demeaned to wipe out the individual effect, and hence only β is estimated, and then the individual effect is calculated.

One of the novelties of this study is that it will explore the impacts of transport infrastructure on the growth of each of the eight metros, especially where necessary, by focusing on the time series data from the concerned metro. This is to determine which of the metros is making optimum utilisation of their transport infrastructures to positively influence their growth. This will enable the government to identify the metros where the synergy between transport infrastructure and growth potentials is weak.

However, the procedure for time series analysis of autoregressive distribution lag (ARDL) is very similar to the panel ARDL approach. The major difference is that instead of pooling the data, the analysis will be carried out for each of the eight metros.

This study is exempt from ethics review as it relies on public data. Issued by the School of Accounting, Economics and Finance; University of KwaZulu-Natal.

This is the first step under panel estimation. It is required to confirm the suitability of the estimating techniques adopted.

It is evident from Table 2 that all the variables are stationary either at levels or after the first difference.

Variables such as the interaction of social infrastructure expenditure and public transport expenditure and public transport expenditure itself are stationary after the first difference. That is, they are the integration of order I(1) for both IPS and augmented Dickey–Fuller (ADF) unit root test methods. Other variables used in the model apart from these two are all stationary at levels. The result implies that all the variables are suitable for inclusion in the panel model analysis.

From the explanation in the methodology, panel data are applied to know the relative effect of public transport expenditure and other output shift factors in the metro on their output growth. The results of the one-way error component panel regression, fixed-effect LSDV and fixed effect regression within are presented in Table 3. They are presented in a single table for the basis of comparison and assessment of consistency in the result.

Table 3 shows the results for the three-panel data analysis used to examine the effect of public transport expenditure on the output growth of the metros in South Africa. The results also show that six of the metros share similarities with regard to the panel presented in the table. This is because the dummy of the two of the metros (BUFF and MAN) are significant whilst the dummy for remaining six are not.

Firstly, the results show that the variables which represent the interactions of social infrastructure expenditure and public transport expenditure have a significant impact on the outputs of the metros. The coefficient from the table of the variable is 0.0196611 and it is significant at 5%. The implication is that the combination of other social infrastructure and public transport expenditures will have positive significant effect on the output of eight metros. Another variable with significant impact on the output growth of the metros is the total expenditure of social infrastructure. Being a derived demand, social infrastructure stimulates the impact of transport infrastructure investment on economic growth. The coefficient is 0.0242986, which shows that social infrastructure has significant positive impact on the output growth of the metros during the period under review. It simply implies that an increase in the expenditure on social infrastructure will bring a significant rise in the output of the metros and vice versa.

Inflation rate is used to capture the effect of macroeconomic policy on the output of the metros. The coefficient of INF in the result is -0.0016917. The value is also significant at 5%. However, the sign is negative, which implies the existence of a significant inverse relationship between the output of the metros and the INF rate.

The implication is that a rise in the level of INF will bring a significant fall to the level of output growth of the metros.

Other variables used in the panel model fail to show significant impact on the output of the metros. However, of them, an important variable out is the public transport expenditure. The result shows that the coefficient is 0.019491. Although the parameter estimates of this variable positive, yet it fails to pass the test of statistical significance at 5%. Therefore, it is concluded that public transport expenditure, in its own right, does not have significant impact on the output of the metros. This may be expected as it is a derived demand. It should, therefore, be considered with other aspects.

The panel result further showed that two of the metros are outliers and this result might not be binding on them because their dummies are significant under both the one-way error component panel regression and fixed-effects LSDV. These metros are BUFF and MAN. The cross-sectional dummy for MAN and BUFF are ‒0.0105391 and 0.0957022, respectively, and they both pass the test of statistical significance at 5%. The implication of this is the likelihood of the results of these two metros, which shows a significant difference from the result of the panel regression presented in Table 3. Furthermore, these two metros can be separately analysed to understand the significant difference in their result from the panel result presented in Table 3.

Normality test is carried out as a post-estimation test on the panel result to examine the validity and the reliability of the estimated panel model. The result is shown in Figure 1.

The results from Figure 1 show that the Jarque Bera statistics is 3.548204 and the probability is 0.169636. The implication of this is that the residuals of the panel regression are normally distributed, and hence, no problem of bias in the estimated panel regression. This result adds value to the estimated panel model.

Following the result from the panel model, it is evident that these two metros are to likely exhibit result that is different from the remaining eight metros. Consequently, ARDL time series regression analysis for the two metros is separately performed to examine this.

The results of the unit root test are presented in Table 4 for MAN metro and ADF test is used.

Unit root test result for MAN metro as presented in Table 4 indicates that the variables’ order of integration ranges between order 1 and order 0. The log of social infrastructure expenditure, the log of the interaction between public transport expenditure and social infrastructure expenditure as well as the inflation rate are I(0) which means that they are stationary at their level. The other variables in the model, namely, the growth rate of the metro, labour, and capital are all I(1), which means that they are stationary at first difference. Consequently, the ARDL estimation can be applied. However, first the cointegration test is carried out before the estimation of the ARDL regression.

Table 5 summarises the impacts of transport infrastructure on the output growth of MAN metro.

The result shown in Table 5 is an indication that many of the variables have significant impact on the output growth of the MAN metro.

The results of the MAN metro indicate that many of the variables used as proxy for transport infrastructure have significant impact on the growth of the metro. The social infrastructure expenditure, the interaction of public infrastructure expenditure, and the total expenditure on social infrastructure have significant impacts on the growth of the metro in the short run. However, only the interaction of public infrastructure expenditure that have the impact in the long run. This further justifies the fact that combination of the social infrastructure and public transport expenditure significantly influences the growth of the metro.

Amongst other control variables, labour and capital show significant impact on the growth of the MAN metro during the period under review. In addition, the macroeconomic variable used in the model, that is INF rate, also show significant impact on the growth of the metro. The error correction term coefficient is -0.120434. The coefficient is negative and statistically significant at 5%, which is an indication that the adjustment process is in the right direction and also indicates that when there are disequilibrium, forces that will restore the equilibrium will set in.

Three tests are conducted to assess the validity of the ARDL regression results, namely, the test of serial correlation, the heteroscedasticity test and the normality test. Their results are presented as follows.

The null hypothesis in Table 6 is that no serial correlation is involved. Considering the probability of the F statistics, a noticeable indication no serial correlation problem in the estimated ARDL model exists as the null hypothesis is accepted.

Similarly, the null hypothesis is ‘no heteroscedasticity’ as all the probabilities of the test statistics are greater than 5%, indicating that the null hypothesis is accepted. In this context, it can be concluded that no heteroscedasticity is observed.

The Jarque Bera statistics is used to assess the normality of the estimated ARDL model and the results are presented in Figure 2. The Jarque Bera probability is 0.099628, which shows that the model is normally distributed. The implication is that the inferences drawn from the ARDL estimated model are valid.

The ADF test is applied to ascertain the order of integration of each variable in the model.

The results of the unit root test indicate that two of the variables are stationary, whilst others are non-stationary (see Table 8). However, the ones that are non-stationary eventually become stationary after the first deference, thereby they are integrated with order I(1). Only INF rate and social expenditure infrastructure are stationary at levels. The findings under the unit root test show that ARDL approach conditions are satisfied. The next is the integration test.

The time series estimation using the ARDL approach for BUFF metros is explained under this section.

The results from the BUFF metro are presented in Table 9, which show that all the variables virtually have significant impacts on the growth of BUFF. Public transport expenditure, social infrastructure expenditures and the interaction between the two all have significant impact on the growth rate of BUFF metro. For instance, the coefficients are 0.034802, 0.034105 and 0.025074, respectively, and they are all individually significant at 5%.

Other variables, such as labour which is proxy for total labour cost and capital which is proxy for the value of fixed assets, all have significant impact on the growth of BUFF metro during the period under review. However, INF failed to show significant impact on the output of the metro. These may be because of South Africa’s INF target.

Apart from the fact that there is a long-run relationship amongst the variables, all the variables that have significant impact in the short-run are also significant in the long-run. It implies that public transport expenditure, social infrastructure expenditure and other variables, all have sustainable impact on the growth of the BUFF metro.

The error correction model coefficient is negative and significant. The value of the error correction is ‒0.123417 and it is significant at 1%. This is an implication that the adjustment to equilibrium in BUFF is in the right direction; and whenever there a disequilibrium, forces that restore the equilibrium will set in.