Comparative Analysis of VAR and SVAR Models in Assessing Oil Price Shocks and Exchange Rate Transmission to Consumer Prices in South Africa

Abstract

This study compared standard VAR, SVAR with short-run restrictions, and SVAR with long-run restrictions to investigate the effects of oil price shocks and the foreign exchange rate (ZAR/USD) on consumer prices in South Africa after the 2008 financial crisis. The standard VAR model revealed that consumer prices responded positively to oil price shocks in the short term, whereas the foreign exchange rate (ZAR/USD) revealed a fluctuating currency over time. That is, the South African rand (ZAR) initially appreciated against the US dollar (USD) in response to oil price shocks (periods 1:7), followed by a depreciation in periods 8:12. Imposing short-run restrictions on the SVAR model revealed that the foreign exchange rate (ZAR/USD) reacted to oil price shocks in a manner similar to the VAR model, with ZAR appreciating during the initial periods (1:7) and subsequently depreciating in the later periods (8:12). Consumer prices responded positively to oil price shocks, causing consumer prices to increase in the short run, which is consistent with the VAR findings. However, imposing long-run restrictions on our SVAR model yielded results that contrasted with those obtained under short-run restrictions and the standard VAR model. That is, oil price shocks had long-lasting effects on the foreign exchange rate, resulting in the depreciation of ZAR relative to USD over time. Additionally, oil price shocks reduced consumer prices, resulting in a deflationary effect in the long run. This study concluded that South Africa’s position as a net oil importer with a floating exchange rate renders the country vulnerable to short-term external shocks. Nonetheless, in the long term, the results indicated that the economy tends to adapt to oil price shocks over time.

1. Introduction

Since the 2007/08 global financial crisis, the global economic landscape has changed significantly, with emerging market economies such as South Africa being particularly affected (Csomós, 2013). That is, as Rey (2015) pointed out, the world economy has changed as a result of exceptional monetary policies, such as quantitative easing by global central banks, which have caused notable volatility in capital flows and currency fluctuations in emerging markets. For instance, one element that could be attributed to quantitative easing is when central banks buy government bonds and other securities to boost money supply and lower interest rates. This action brought about unprecedented liquidity injections that changed global capital flows (Krishnamurthy & Vissing-Jorgensen, 2011). These changes in global markets have also reached commodity markets, with fluctuations in oil prices triggering currency depreciation in oil-importing emerging markets, resulting in increased domestic inflation through direct and indirect channels (Choi et al., 2018).

South Africa, as an oil-importing country with an inflation-targeting framework, offers a unique case study for investigating these economic dynamics. Figure 1 below highlights how consumer prices in South Africa have fluctuated significantly over the last decade. As a result, between 2009 and 2023, the Consumer Price Index (CPI) experienced significant periods of inflationary pressure, with fluctuations peaking at 8.3% in 2009, followed by more moderate levels in subsequent years. This trend demonstrated the relationship between domestic and international economic factors that influenced price stability in South Africa. That is, given that South Africa relies heavily on commodity exports, particularly precious metals and minerals, global market fluctuations have a direct impact on the South African rand (ZAR)’s strength, which in turn influences the country’s import costs and overall price levels (Loewald, 2022).

Additionally, on one hand, changes in United States (US) Federal Reserve interest rates impact global investor sentiment through their effects on risk appetite and capital flows (Olaberría, 2014). That is, when the Federal Reserve increases interest rates, investors tend to reallocate capital from emerging markets such as South Africa to countries such as the US in pursuit of higher yields and more secure returns (Edwards, 2012). Thus, this movement of capital tends to undermine ZAR and generates inflationary pressures, thereby limiting the effectiveness of the South African Reserve Bank (SARB) monetary policy (Klein, 2012). Domestically, on the other hand, South Africa encounters multiple structural challenges domestically. For instance, Eskom’s energy supply limitations and inflexible labour markets contribute to persistent economic pressures in the country. Therefore, the combination of international factors with domestic challenges results in enduring inflationary pressures that conventional monetary policy tools find challenging to mitigate (World Bank, 2023).

Conversely, Figure 2 below shows the trends in oil prices and the foreign exchange rate (FER) between 2009 and 2023 were highly volatile. That is, the fluctuations in global oil prices, quoted in the South African rand (ZAR), particularly from the post-2008 recovery to peaks, exceeded ZAR 961 per barrel during 2011–2014, as well as the oil price decline in 2014–2015 and the volatility associated with COVID-19 in 2020. These fluctuations in oil prices and exchange rates had a significant impact on South Africa’s trade dynamics and currency valuation (Baffes et al., 2015). The FER, as measured by ZAR/USD, experienced significant volatility during this period, particularly during periods of risk-off sentiment in emerging markets, such as the 2013 taper tantrum and the 2017–2018 concerns about the Chinese slowdown, which resulted in sharp depreciations (Maveé et al., 2016). Thus, the inverse relationship between oil prices and foreign exchange rates is especially visible during major oil market disruptions, particularly in 2020 during COVID-19 lockdowns in many countries worldwide. Therefore, as a net oil importer, South Africa experiences oil price shocks that were typically accompanied by increased pressure on ZAR and a decline in the country’s terms of trade (Kin & Courage, 2014).

The monetary policy framework of South Africa over the years displayed distinct characteristics when compared to other emerging markets. That is, since the 1990s, according to Du Plessis et al. (2007), South Africa’s monetary policy has developed to adopt a more forward-looking and anti-cyclical approach, compared to the absence of such measures in its earlier years. The South African Reserve Bank (SARB) implemented inflation targeting in 2000, establishing a target range of 3–6%, which is comparatively broad in relation to other emerging markets (Baaziz et al., 2013). This targeting framework, as highlighted by Iddrisu and Alagidede (2020), was established with the goal of ensuring price stability, the primary mandate of the SARB. Thus, in order to keep the inflation rate within the target range, the SARB utilises the repo rate as its principal instrument (Merrino, 2022). The SARB also employs a modified Taylor rule framework, considering both the output gap and inflation expectations in its policy decisions (Duke et al., 2023). That is, when inflation surpasses the upper limit of the designated range, the SARB raises the nominal interest rates and lowers the rates when output falls below potential to realign inflation within the target parameters (Baaziz et al., 2013).

Thus, in most cases, the SARB had used its monetary policy tools effectively in the past, adjusting policy in response to global economic crises such as the 2007/08 global financial crisis and the 2020/21 pandemic-induced recession by significantly lowering the repo rate (Merrino, 2022). That is, in the 2007/08 financial crisis, the SARB adopted accommodative actions in order to mitigate the lack of liquidity in the market (Tule et al., 2019). The SARB implemented monetary easing measures. Among these measures, according to Merrino (2022), was strengthening the banking system, such as through lowering the monetary policy rate (repo rate). The impact on the economy was positive, helping to control inflation and maintaining financial stability (Kabundi & Mlachila, 2018). Subsequently, during the 2020/21 pandemic-induced recession, the SARB responded by reducing the repo rate by a total of 300 basis points (five times) over the course of 2020 (Merrino, 2022). That is, according to Mbatha and Alovokpinhou (2021), the reductions in the repo rate were implemented in phases: January was 25 basis points, March was 100 basis points, April was 100 basis points, May was 50 basis points, and July was 25 basis points. Other economic-supporting actions taken by the SARB included promoting bond market liquidity and relaxing lending requirements (Nhamo & Chapungu, 2024). Therefore, by lowering short-term interest rates, the repo rate cut was meant to make it easier for households and businesses to manage and settle their current debt (Mbatha & Alovokpinhou, 2021).

In contrast to other emerging market economies such as China and Russia that utilise managed exchange rates, South Africa employs a floating exchange rate regime (Sui & Sun, 2016). That is, as highlighted by Cheng and You (2024), this method enables market forces to establish the exchange rate autonomously, free from a predetermined position or strict governmental interference. A floating exchange rate in South Africa has been adopted and maintained since the 2000s (Kuttu et al., 2018). This approach facilitates enhanced monetary policy autonomy while simultaneously heightening vulnerability to external shocks. Thus, this flexibility in the exchange rate is accompanied by increased uncertainty and volatility that pose challenges for South Africa. That is, exchange rate volatility may increase production costs, particularly in economies dependent on imported raw materials such as South Africa (Oseni, 2016). This may result in diminished trade volumes and increased prices for consumers (Kayani et al., 2023).

Consequently, South Africa’s experience with oil price shocks and foreign exchange rate fluctuations presents a compelling research opportunity in the post-financial crisis era. While extensive literature exists on exchange rate pass-through and oil price effects in developing economies, South Africa’s distinct position as an emerging market with a sophisticated financial system, yet vulnerable to external shocks, creates a significant research gap (Makrelov et al., 2021). Despite the South African Reserve Bank (SARB)’s inflation targeting framework, persistent inflation pressures and currency volatility continue to challenge policymakers (Loewald, 2022). The existing literature has not adequately addressed how these relationships may have fundamentally changed following the global financial crisis using two distinct econometric models (VAR and SVAR), particularly in the context of South Africa’s specific structural challenges.

Furthermore, this study bases itself on a number of economic theories, including the cost-push inflation theory, exchange pass-through theory, sticky price theory, and the monetary approach to exchange rate determination. Firstly, the cost-push inflation theory predicts that fluctuations in oil prices will have a significant impact on consumer prices, as highlighted by Schwarzer (2018), both directly (by means of transportation costs) and indirectly (by means of increased production costs). That is, this mechanism is particularly essential for energy-dependent sectors, where fluctuations in oil prices have a significant impact on operational costs (Chen et al., 2024). Secondly, exchange rate dynamics are critical in this relationship, as explained by the exchange rate pass-through theory (Herzberg et al., 2003). This theory becomes particularly relevant to South Africa’s small open economy, where currency fluctuations can have a significant impact on domestic prices through import costs (Karoro et al., 2009).

Thirdly, the sticky price theory sheds light on how these relationships develop over time (Kiley, 2006). According to this theory, as explained by McCallum (1986), firms are constrained in their ability to adjust prices immediately, resulting in delayed responses to both oil prices and exchange rate shocks. Lastly, Woo (1985) describes the monetary approach to exchange rate determination as providing interconnections between monetary policy decisions and exchange rate dynamics. This framework describes how monetary conditions influence currency valuation, which in turn affects domestic prices by way of international trade channels (DeJong & Husted, 1993).

Nonetheless, this study is significant for four reasons. Firstly, South Africa is a unique case study because it combines a modern financial system with typical emerging market vulnerabilities to global economic shocks, making it ideal for studying how international prices affect domestic inflation (Makrelov et al., 2021). This insight is useful for other developing economies that are struggling to keep prices stable during global economic uncertainty. For example, during the global financial crisis, South Africa’s approach to managing inflation through flexible exchange rates and inflation targeting proved effective, with inflation falling from 8.3% to 4.1% between 2009/05 and 2010/05 (Kumo, 2015). Secondly, the global financial crisis fundamentally altered the relationships between crude oil prices, exchange rates, and consumer prices. That is, crude oil now behaves more as a financial asset than a commodity, currency markets react more strongly to oil price changes, and these changes have opened up new channels for oil market shocks to influence domestic inflation by means of exchange rate fluctuations (Mensi, 2019). Thirdly, the rise of digital trading platforms has accelerated these relationships, making price changes in oil, exchange rates, and consumer prices faster and potentially more influential than before (Wei & Guo, 2023). Lastly, to the best of our knowledge, there are few, if any, studies in South Africa that have compared the effectiveness of the VAR and SVAR models with the objective of contributing to the ongoing debate in econometric theory on whether or not imposing restrictions (i.e., SVAR) in a model can yield better results.

Therefore, this study has been structured as follows: Section 2 presents a discussion of the literature review that has been deemed relevant to the current study. Section 3 presents an overview of this study’s methodology, outlining the empirical approach that we employed in this research. Section 4 presents the findings and the analysis of this study. Section 5 will serve as the conclusion of our study, where we summarise the findings and offer policy recommendations and future research directions.

2. Literature Review

This study has its foundation in various theoretical economic literature. Firstly, the cost-push inflation theory states that an increase in production costs, such as wages, raw materials, or import prices, causes an increase in overall price levels within an economy, regardless of changes in aggregate demand (Monfort & Peña, 2008). That is, the traditional cost-push theory emphasises wage increases as a primary factor in raising prices through labour costs; however, a recent empirical study by Romaniello and Stirati (2024) found that external supply shocks and profit margins may also play an important role in explaining cost-push inflation. However, Javed et al. (2011) took it further by arguing that cost-push factors are just as important as demand-pull factors in driving inflation, despite the fact that their research focuses on developing economies. A significant debate in recently published work centres on whether recent inflation episodes are solely driven by cost-push factors or if they also include “profit-push” elements, in which firms use cost increases to increase profit margins (Antonova, 2023).

Additionally, as highlighted by Diaz et al. (2024), the significance of international supply chains and import costs has grown in the analysis of cost-push inflation. Evidence indicates that shocks to intermediate input prices can exercise lasting impacts on domestic prices that are independent of wage increase effects (Romaniello & Stirati, 2024). Antonova (2023) revealed the impact of state-dependent pricing on the transmission of cost-push shocks within production networks. Nonetheless, early theories focused on wage-price escalations. However, a recent analysis acknowledges that cost-push inflation may arise from various factors, such as exchange rates, commodity prices, and supply chain disruptions, which become significant for the current study (Monfort & Peña, 2008). Romaniello and Stirati (2024) observed that in recent European inflation episodes, wage growth has remained moderate despite substantial price increases, thereby challenging conventional cost-push models that emphasise labour costs. Antonova (2023) further noted that the effects of cost-push inflation differ prominently among sectors and are largely influenced by market structure and pricing power. Therefore, the country’s policy responses to cost-push inflation should prioritise supply-side interventions and price controls over conventional demand management by means of monetary policy measures (Romaniello & Stirati, 2024).

Secondly, exchange rate pass-through theory, as highlighted by (Aisen et al., 2021), describes the relationship between fluctuations in the currency exchange rate of a country and their impact on domestic prices. That is, a complete pass-through effect is achieved when changes in the exchange rate result in equivalent changes in domestic prices (Aisen et al., 2021). However, the theoretical framework indicates that exchange rate pass-through, as highlighted by Aron et al. (2014), may be incomplete due to factors such as market competition, strategies related to pricing-to-market, and local distribution expenses. Previous research primarily concentrated on developed economies; however, in recent studies, such as those conducted by Caselli and Roitman (2016), Baharumshah et al. (2017), and Daboussi and Thameur (2014), have broadened their scope to include emerging markets. Their findings suggested that pass-through exchange rates are typically higher in developing countries, although there has been a general decline over time. Thus, in a recent study, Takhtamanova (2024) argued that lower and more stable inflationary environments, which are typically linked to credible monetary policy frameworks, lead to diminished exchange rate pass-through effects.

Nonetheless, there is a lack of consensus in the literature regarding the consistent effects of monetary policy regime changes on exchange rate pass-through effects. Akofio-Sowah (2009) found no significant impact of such changes on exchange rate pass-through in Sub-Saharan Africa. Other empirical evidence indicated that exchange rate pass-through effects may be asymmetric, with certain studies identifying stronger effects during depreciation than during appreciation periods (Mendali & Das, 2023). Therefore, what appears to be a significant gap in the literature pertains to an insufficient understanding of the effects of financial market development and the integration of exchange rate pass-through dynamics in emerging economies (Aron et al., 2014), thus emphasising the significance of accounting for non-linearities in exchange rate pass-through effects, especially in times of increased exchange rate volatility.

Thirdly, the sticky price theory states that certain prices within the economy adjust slowly or infrequently in reaction to fluctuating market conditions (Ball & Mankiw, 1994). As a result, earlier empirical studies suggested that prices generally adjusted only once annually. However, Bils and Klenow (2004) found that prices change more often, with half of the prices lasting 4.3 months or less. Thus, their findings challenged the idea that prices are rigid. Ascari and Haber (2021) illustrated the significant impact of sticky prices on the influence of monetary policy on the economy, particularly indicating that price flexibility increases during high inflation periods. Ball and Mankiw (1994) contend that minor menu costs, which are the costs incurred from altering prices, can lead to considerable price rigidity in the context of imperfect competition.

However, this perspective is contested by recent empirical findings that demonstrated considerable price flexibility across various sectors (Ascari & Haber, 2021). The literature indicates a significant gap in understanding the reasons behind varying levels of price stickiness across different sectors. Bils and Klenow (2004) demonstrated that the frequency of price changes differs markedly among categories, ranging from less than 5% monthly for newspapers and haircuts to over 70% for petrol and fresh produce. De Abreu Lourenco and Gruen (1995) revealed that market structure and the volatility of supply and demand conditions have a significant impact on price flexibility. Therefore, traditional sticky-price models may overestimate inflation rate persistence and underestimate its volatility, especially for goods with infrequent price adjustments (Bils & Klenow, 2004).

Lastly, the monetary approach to exchange rate determination, which emerged in the 1970s, makes the argument that exchange rates are predominantly affected by the relative supply and demand for money across different countries (Boughton, 1988). Thus, this approach suggests that factors such as purchasing power parity (PPP), uncovered interest rate parity (UIP), and stable money demand functions are essential determinants of exchange rates. However, empirical evidence so far has yielded mixed results regarding these assumptions. That is, numerous empirical studies, such as those conducted by Msomi and Ngalawa (2024), Le Huy and Ba (2020), Loría et al. (2010), Uz Akdogan and Dalan Bildir (2009), Chin et al. (2007), and Jimoh (2004), provided evidence for the monetary approach in developing and emerging market economies.

Consequently, Chinn (1991) determined that this approach fails to account for exchange rate behaviour in South Africa. According to Boughton (1988), the approach fails to take into account the importance of relative good prices and portfolio balance effects in determining exchange rates. Msomi and Ngalawa (2024) found that the relationship between exchange rates and monetary variables (such as interest rates, debt differentials, and economic policy) varies across different regime states, thus indicating non-linear dynamics not accounted for by the traditional monetary approach. Crespo-Cuaresma et al. (2005) showed that the monetary model could account for long-run exchange rate dynamics in Central and Eastern European countries but required supplementation with additional factors such as the Balassa–Samuelson effect. Boughton (1988) and Jimoh (2004) recognised that while the monetary approach offers significant insights, its strict application may inadequately account for exchange rate behaviour.

Furthermore, the selected empirical studies that were deemed to be relevant in this study had shown various outcomes. That is, the relationship between oil prices and the inflation rate has changed considerably over time, with studies indicating differing levels of pass-through effects in various economic contexts. For instance, early research had demonstrated robust correlations, as evidenced by Burbidge and Harrison (1984), who recorded notable price level increases in countries that were developing subsequent to the oil price shocks of 1973 and 1979. However, recent studies had arrived at different conclusions as their evidence indicated that this relationship may be evolving. That is, Chen (2009) noted a reduction in the influence of oil prices on inflation in 19 industrial nations and attributed this trend to currency appreciation and specific monetary policies aimed at minimising inflationary pressures.

The extent of oil pass-through effects demonstrated significant variability across different studies and various settings. Cologni and Manera (2008) identified moderate effects in oil-importing Asian and Pacific economies, observing that a 10% increase in oil prices resulted in an approximate 0.5% rise in inflation rate during periods of stable oil prices. In contrast, this finding significantly differs from the estimates provided by Lacheheb and Sirag (2019), who reported a significantly higher pass-through coefficient of 2.7% using a nonlinear ARDL approach in Algeria. Recently, research by Toni (2024) indicated that oil-dependent economies encounter an average inflation rate increase of 0.7% for every 10% rise in oil prices, with notably significant effects observed in the Middle East and North Africa region.

Subsequently, analyses of specific individual countries revealed additional complexities in the relationship between oil prices and inflation. Asghar and Naveed (2015) identified significant effects in Pakistan and noted a positive correlation whereby a 1% increase in oil prices resulted in a 1.88% increase in the inflation rate. Mukhtarov et al. (2019) documented comparable significant effects in Azerbaijan, noting that a 1% increase in oil prices contributed to a 0.58% rise in the inflation rate. Kudabayeva et al. (2024) identified differing sensitivities among oil-importing countries, with Italy and France demonstrating the most sensitivity to fluctuations in oil prices, whereas other nations displayed insignificant impacts. Thus, the variations indicated that domestic economic structures and policy frameworks significantly influence the degree of oil prices’ pass-through effects on the inflation rate. Another aspect of the literature is the evidence for asymmetric effects within the oil prices’ pass-through mechanism. As a result, Ajmi et al. (2015) demonstrated that both positive and negative oil price shocks had a positive impact on inflation in South Africa, with negative shocks resulting in more evident effects on inflation. Lily et al. (2020) also observed this asymmetry in Malaysia, especially after the rationalisation of fuel subsidies. Abu-Bakar and Masih (2018) identified asymmetric effects in India as a result of market concentration, observing that prices increase with rising oil prices but demonstrated minimal downward adjustment when oil prices decline.

Moreover, the differentiation between oil-exporting and oil-importing countries has become a critical factor in analysing the relationship between oil prices and inflation. Tiwari et al. (2019) found that increased oil prices can reduce inflation in oil-exporting countries by means of exchange rate appreciation. Mien (2022) identified two distinct transmission channels in oil-exporting countries, which include the pass-through effect and the Dutch disease effect, with varying susceptibility observed among different countries for each mechanism. As a result, this finding revealed certain inconsistencies in previous literature concerning the influence of oil prices on inflation rate in resource-rich economies. Alternatively, the time-related aspect of oil price pass-through introduces additional complexity to the relationship. That is, Chou and Tseng (2011) identified significant long-run effects with limited short-run impact in Taiwan, whereas Cologni and Manera (2008) reported persistent long-run effects in G-7 countries.

Jiranyakul (2021) emphasised that these relationships may deteriorate during times of significant oil price volatility, thus indicating that structural breaks are essential in the pass-through mechanism. Moreover, there is evidence from empirical literature to suggest that policy frameworks are essential factors that can influence the transmission of oil price shocks to domestic inflation. That is, Brini et al. (2016) demonstrated that subsidised product prices in MENA countries minimised the effects of the inflation rate, notwithstanding considerable exchange rate influences. Jaffri et al. (2013) highlighted the necessity for monetary policy to account for global energy prices and food inflation, especially in developing economies. Rangasamy (2017) emphasised the significance of the policy by demonstrating that in South Africa, increases in petrol prices have contributed to inflation by means of both direct effects on consumer prices and indirect broader price pressures.

The selected empirical studies highlighted that exchange rate pass-through to domestic prices varies significantly across economies over time. That is, Kemoe (2024) had indicated that developed economies tend to display slow pass-through rates, whereas emerging and developing economies encounter significantly higher rates, which has been supported by robust empirical evidence from various economic contexts. For this reason, Kemoe (2024) revealed that a 1% depreciation results in a 0.22% increase in inflation rate after one year in Sub-Saharan Africa, in contrast to 0.15% in emerging Asia and 0.18% in Latin America. However, a significant trend identified in various studies is the general decline of exchange rate pass-through over time in both developed and developing economies. Thus, researchers such as Volkan et al. (2007) and Usupbeyli and Ucak (2020) had attributed this declining trend to improved monetary policy frameworks and enhanced central bank credibility. Nevertheless, the literature had also revealed notable discrepancies concerning the function of exchange rate regimes. That is, Kemoe (2024) identifies greater pass-through in nations with managed or floating exchange rate regimes when examining bilateral rates. However, Kim et al. (2020) provided opposing empirical evidence that revealed more distinct pass-through effects in countries with fixed exchange rate regimes.

Also, an analysis of specific country cases demonstrated a notable pattern in empirical studies. For instance, Parsley (2012) found that in South Africa, the exchange rate pass-through effects on consumer good prices were relatively low at 16% over two years following exchange rate changes, whereas a higher pass-through was observed for services. That is, this unexpected finding challenges established assumptions regarding sectoral pass-through dynamics. Mushendami and Namakalu (2016) reported a low and incomplete pass-through in Namibia, estimating the exchange rate pass-through elasticity at 0.01–0.04 for consumer and import inflation rates, respectively. Fetai et al. (2016), on the other hand, identified notably higher effects in Western Balkan countries, where a 1% increase in exchange rates resulted in a 1.79% increase in consumer price levels, thus underscoring the considerable regional variations in pass-through dynamics.

Subsequently, the literature indicated a consensus on the asymmetric characteristics of the exchange rate pass-through effects, whereby depreciation consistently had a greater effect on domestic prices when compared to appreciations (Kemoe, 2024). The asymmetry is particularly relevant in developing economies, as evidenced by research conducted on Sub-Saharan Africa, whereby Kassi et al. (2019) analysed 40 sub-Saharan African countries and identified significant asymmetric pass-through effects. This study highlighted those depreciations had a greater impact than appreciations in the short term, particularly in countries within the CFA franc zone. Adekunle and Tiamiyu (2018) found that in Nigeria, over the short term, the pass-through estimates increased when accounting for the asymmetric effects of exchange rate changes. Thus, the variations in the responsiveness of consumer prices to exchange rate appreciation and depreciation were also observed.

Besides, market competition also serves as a significant factor, according to Usupbeyli and Ucak (2020), with less competitive markets generally revealing higher exchange rate pass-through due to firms retaining increased pricing power. As a result, the effectiveness of monetary policy becomes crucial, as central banks with higher credibility demonstrate greater success in anchoring inflation expectations and mitigating the exchange rate pass-through effects (Volkan et al., 2007). Savoie-Chabot and Khan (2015) found that in Canada, a limited fraction of exchange rate fluctuations are reflected in consumer prices, which they attributed to import costs constituting only a minor part of overall supply chain expenses. Alex (2021) highlighted that exchange rate volatility has historically significantly influenced inflation dynamics in Brazil, especially prior to the implementation of inflation targeting in the 2000s. Nonetheless, this impact has diminished over time, particularly following 2008, suggesting a degree of anchoring in inflation expectations (Alex, 2021).

Similarly, other studies conducted on developing economies offer further insights into exchange rate pass-through dynamics. That is, Khodeir (2012) identified substantial evidence of exchange rate pass-through effects in Egypt, indicating that fluctuations in exchange rates significantly influenced both consumer and wholesale prices, with wholesale prices exhibiting a more immediate response compared to consumer prices. In Nigeria, studies such as those conducted by Gidigbi et al. (2018) and Razafimahefa (2012) revealed that the country experiences incomplete yet significant exchange rate pass-through effects, with effects being more significant during the periods of currency depreciation compared to periods of appreciation. Lado (2015) identified unidirectional causality from exchange rates to inflation in South Sudan through Granger-causality tests. However, Madesha et al. (2013) revealed bidirectional causality between exchange rates and inflation in Zimbabwe, indicating mutual influence between the two variables.

Contrary to findings in African economies, Edwards (2006) observed that countries implementing inflation targeting experienced a reduction in exchange rate pass-through to the inflation rate. Thus, his analysis indicated no evidence that inflation targeting heightened exchange rate volatility. Ha et al. (2020) highlighted that exchange rate pass-through effects are significantly influenced by the type of shocks that initiate currency movements, whereby monetary policy shocks are generally linked to greater pass-through than other domestic shocks. Further research also indicated that trade openness and global value chain participation are significant; however, Ha et al. (2020) demonstrated that these structural factors possess diminished explanatory power relative to monetary policy frameworks. Likewise, Revelli (2020) indicated that in Cameroon and Kenya, fixed exchange rate regimes exhibit a higher pass-through effect than flexible regimes.

The on-going development of vector autoregression (VAR) methodologies and their empirical outcomes demonstrates noteworthy advancements in the comprehension of monetary policy and economic shocks. For instance, Primiceri’s (2005) time-varying SVAR study demonstrated that the high inflation and unemployment rates of the 1970s and early 1980s were largely influenced by significant economic shocks rather than changes in monetary policy. His analysis indicated that the volatility of non-policy shocks was significantly higher in the pre-1980s period compared to later years (Primiceri, 2005). This finding redefined previous understandings of the effectiveness of monetary policy. Uhlig (2005) utilised sign-restricted VAR analysis to illustrate that the effects of monetary policy on output are more uncertain than previously understood. His findings indicated that tighter monetary policy might decrease output, increase it, or have no effect at all, typically within a range of 0.2% up or down, and accounted for less than 25% of output variations over a five-year period (Uhlig, 2005). This differed markedly from conventional VAR approaches, which assigned approximately 50% of output variations to monetary policy. Stock and Watson (2001) empirical analysis established that VARs either outperform or match the forecasting accuracy of univariate autoregressions and random walk models. However, their structural analysis revealed significant sensitivity to identification assumptions, indicating that even minor alterations in these assumptions can result in markedly different conclusions regarding the effects of monetary policy (Stock & Watson, 2001). Blanchard and Quah (1988) made a significant methodological advancement by hypothesising that only supply shocks should have permanent effects on output in the long run, which facilitated the differentiation between demand and supply shocks. Their empirical findings demonstrated a significant correlation with historical recession data, although they recognised a lack of precision in measuring the relative contributions of each type of shock.

3. Methodology

This study analysed the effects of oil price shocks and foreign exchange rate transmission on South African consumer prices after the 2007/08 global financial crisis. The study employed both vector autoregression (VAR) and structural vector autoregression (SVAR) models to provide a comparison analysis. Our SVAR model imposed short-run and long-run restrictions. While VAR offers a flexible framework for capturing dynamic relationships, SVAR incorporates theoretical restrictions that could potentially improve the identification of structural shocks. This dual approach allows us to assess whether additional structural assumptions materially affect the results, thus contributing to the ongoing debate in econometrics on whether or not the SVAR outperforms the VAR model. These models have been extensively utilised in previous research, such as that conducted by Wang (2024), Chundama (2022), Rezitis (2015), and Cologni and Manera (2008), that examined the oil prices and exchange rate pass-through effects on consumer prices.

Our standard VAR and SVAR models included three essential macroeconomic variables: the Brent crude oil price in ZAR (OP), the foreign exchange rate (FER) measured in South African cents per USD using middle rates (where 1 South African rand (ZAR) equals 100 cents), and the Consumer Price Index (CPI) excluding food, non-alcoholic beverages, fuel, and electricity for all urban areas. All variables were sourced from the database of the South African Reserve Bank (SARB). The data were collected on a monthly basis from January 2009 to December 2023, resulting in a total of 180 observations. Therefore, this time period was chosen to examine South Africa’s consumer price dynamics in light of changes in oil prices and foreign exchange rates following the 2007/08 financial crisis.

3.1. Unit Root Tests (ADF and PP)

This study employed both the augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) tests to ensure robust results. While ADF handles the simple autoregressive process of order p, PP accommodates general forms of serial correlation and heteroskedasticity, providing complementary information about the series stationarity properties (Phillips & Perron, 1988). The ADF test, formulated by Dickey and Fuller (1979), assesses the presence of a unit root, a characteristic commonly found in non-stationary time series data. Yazdanbakhsh et al. (2017) highlighted that non-stationary series exhibit unpredictable behaviour and can yield erroneous results in various statistical analyses. Hence, it is crucial to perform these unit root tests as they help choose appropriate models and prevent erroneous results, which improves the validity and reliability of statistical findings (Sun & Gao, 2023).

Consequently, The ADF and PP tests have been employed in this study under the following two competing hypotheses:

H₀:

$\theta =0$ (i.e., unit root exists, series is non-stationary)

H₁:

$\theta <0$ (i.e., series is stationary, no unit root)

whereby the null hypothesis $H_0$ assumes the presence of a unit root, implying that the data is non-stationary and requires transformation to become stationary. However, the alternative hypothesis $H_1$ proposes the absence of a unit root, implying that the data are already stationary and may be examined without further modification. Therefore, the ADF test is based on the regression equation:

$${∆y}_t={\alpha }_0+{\beta }_t+\theta y_{t-1}+{\sum }_{j=1}^p{\gamma }_j∆y_{t-j}+{\epsilon }_t$$

(1)

The equation consists of a deterministic trend (t), constants ($\alpha$ and $\beta$), lagged difference terms (p) determined using the Akaike information criterion (AIC), autoregressive moving average structure of errors estimated using ${\theta }_j∆y_{t-j}$, and ${\epsilon }_t$ which is the error term. Secondly, the PP test was applied, which is similar to the ADF test but uses a non-parametric method to control for serial correlation when testing for a unit root (Phillips & Perron, 1988). The basic PP test is based on the following regression:

$$y_t=\alpha +{\theta y}_{t-1}+{\mu }_t$$

(2)

where $y_t$ is the variable being tested, t is a modified t-statistic, and ${\mu }_t$ is the error term. This equation generally includes the first difference of the time series, which is regressed on a constant and its own lagged value. The PP test then computes a modified t-statistic that accounts for serial correlation. Thus, transforming Equation (2), the test statistic for the PP test can be expressed as follows:

$$Z_{\theta }=\left(t_{\theta }\right)\left({\displaystyle \frac{\sqrt{f_0}}{\lambda }}\right)-\left({\displaystyle \frac{1}{2}}\right)\left({\displaystyle \frac{{\lambda }^2}{\lambda \sqrt{f_0}}}\right)\left({\displaystyle \frac{T\left(SE\left(\theta \right)\right)}{\lambda }}\right)$$

(3)

where $f_0$ denotes the residual spectrum at zero frequency, which reflects the long-run variance of the residuals and thus addressing potential serial correlation within the data. The term $\lambda$ functions as a consistent estimator of error variance, offering a quantification of the overall variability present in the model’s residuals. The sample size, represented by $T$, represents the total number of observations in the dataset and is essential for determining the statistical power of the test. $SE\left(\theta \right)$ designates the standard error of the estimated coefficient $\theta$, which measures the precision of the parameter estimate and is important for the construction of confidence intervals and the execution of hypothesis tests. Hence, Malec et al. (2024) suggested that an advantage of the PP test is that it eliminates the need to specify the number of lagged difference terms, which can be a challenging task in the ADF test. That is, by employing non-parametric techniques to account for autocorrelation and heteroscedasticity in the error terms, the PP test is resistant to these problems without requiring the explicit inclusion of lagged differences (Hoque et al., 2008).

Nonetheless, the ADF and PP test results were interpreted using a systematic comparison of p-values at a 5% (0.05) significance level. In this analysis, we determined whether the calculated p-value exceeded or fell below the threshold. That is, if the p-value obtained from the ADF and PP tests is equal to or greater than 0.05, we are unable to reject the null hypothesis of a unit root, thus indicating that the time series is not stationary. In contrast, if the p-value is less than 0.05, the null hypothesis can be rejected and the time series is considered stationary.

3.2. Model Specification

Following standard econometric practice, as noted by Zhang et al. (2024), all selected macroeconomic variables (oil prices (OP), foreign exchange rate (FER) and consumer price index (CPI)) were transformed to natural logarithmic variables (denoted as lnOP, lnNEER, and lnCPI) in order to adhere to accepted econometric methods for time series analysis. Thereafter, the basic model to be estimated is represented as follows:

$$lnCPI=f(lnOP,lnFER)$$

(4)

where lnCPI represents the natural logarithmic Consumer Price Index. The lnCPI is the most endogenous variable in the model that responds to both oil prices and exchange rates. lnOP refers to the natural logarithmic oil price, which is the most exogenous variable. The natural logarithmic foreign exchange rate (lnFER) serves as an intermediate variable that transmits external shocks to domestic prices. Then, Equation (4) has been converted into an econometric equation and expressed as follows in order to be estimated:

$${lnCPI}_t={\beta }_0+{\beta }_1{lnOP}_t+{\beta }_2{lnFER}_t+{\epsilon }_t$$

(5)

where ${\beta }_0$ denotes a constant term, ${\beta }_1$ and ${\beta }_2$ denote the parameters to be estimated, and ${\epsilon }_t$ denotes the error term.

3.2.1. Modelling of Cointegration Test

Before comparing the vector autoregressive (VAR) and structural vector autoregressive (SVAR) models, a cointegration test on the relevant variables has to be performed to comply with established econometric standards and ensure robustness against common econometric issues. That is, Gonzalo and Pitarakis (2002) emphasised that cointegration testing is essential for establishing the correct specification of VAR models. That is, the outcome of cointegrating assessment determines the choice of methodology in estimating the VAR model with variables in levels or first differences (Arvanitopoulos & Agnolucci, 2020).

Consequently, Chen et al. (2023) contend that incorrectly specifying the cointegration properties of a time series can lead to model misspecification and produce spurious results. Onatski and Wang (2018), in their study, highlighted the importance of accurate cointegration testing in high-dimensional VAR contexts, where spurious relationships can be made worse. That is, their findings indicated that it is essential to consider both the integration properties of individual variables and any potential common trends among them prior to conducting VAR model estimation and structural analysis.

As a result, following the approach of Wang and Yang (2024), the Johansen cointegration test has been applied, which can be expressed basically as follows:

$$∆{{\rm K}}_t=\pi {{\rm K}}_{t-1}+\pi \left({\Gamma }_j\Delta {{\rm K}}_{t-j}\right)+{\beta }_1{{\rm X}}_t+{\mu }_t$$

(6)

where ${∆{\rm K}}_t$ is a vector comprising the variables of interest, and the test investigates the relationship between changes in these variables ($∆{{\rm K}}_{t-j}$) and their historical values as well as other factors (Enders, 2014). ${\mu }_t$ represents the error term. The matrix $\pi$ is integral to this study. It explains the long-term connections among the variables, which is the central emphasis of cointegration analysis. The ${\Gamma }_j$ matrices denote short-run dynamics, enabling the model to incorporate both long-term relationships and short-term variations.

Thus, by incorporating the variables of interest, Equation (6) is then transformed to be expressed as follows:

$$\begin{gathered} ∆{lnCPI}_t={\pi }_{11}{lnCPI}_{t-1}+{\pi }_{12}{lnOP}_{t-1}+{\pi }_{13}{lnFER}_{t-1}+{\sum }_{j=1}^p({\gamma }_{11j}{∆lnCPI}_{t-j}+ \\ {\gamma }_{12j}{∆lnOP}_{t-j}+{\gamma }_{13j}{∆lnFER}_{t-j})+{\beta }_1{{\rm X}}_t+{\mu }_t \end{gathered}$$

(7)

where $∆{lnCPI}_t$ denotes the change in natural logarithmic consumer prices between the time period. The long-run relationships among variables are represented by the coefficients ${\pi }_{11}$, ${\pi }_{12}$, and ${\pi }_{13}$. The variables (${lnCPI}_{t-1}$, ${lnOP}_{t-1}$, and ${lnFER}_{t-1}$) are incorporated in their lagged level form to account for persistent effects in the model. The coefficients ${\gamma }_{11j}$, ${\gamma }_{12j}$, and ${\gamma }_{13j}$ represent the short-run dynamics that quantify the short-run effects of variations between the variables. The changes in the effects are represented by the lags (${∆lnCPI}_{t-j}$, ${∆lnOP}_{t-j}$, and ${∆lnFER}_{t-j}$) extending up to $j$ periods, with $j$ defined as the optimal lag length for the model. The equation incorporates deterministic components (${\beta }_1{{\rm X}}_t$), including constants or trends to address systematic patterns in the data. Additionally, ${\mu }_t$ denotes the error term, which accounts for unforeseen shocks or deviations that are not explained by the model.

The Johansen cointegration test employs two test statistics. These tests include the trace statistic and the maximum eigenvalue statistic to calculate the number of cointegrating relationships. That is, both tests, according to Lüutkepohl et al. (2000), are based on a maximum likelihood ratio and are essential for identifying the number of cointegrating vectors in a multivariate time series analysis. Thus, trace test statistic is shown in Equation (8) and the maximum eigenvalue test statistic has been expressed in Equation (9):

$${\lambda }_{trace}\left(\pi \right)=-T{\sum }_{i=\pi +1}^{n}ln\left(1-{\lambda }_i\right)$$

(8)

$${\lambda }_{max}\left(\pi ,\pi +1\right)=-Tln\left(1-{\lambda }_{\pi +1}\right)$$

(9)

where $T$ represents the sample size. $\lambda$ denotes ordered measures that quantify the strength of relationships between variables, and $\pi$ indicates the number of long-run relationships present between the variables of interest.

These tests allow us to start by testing the null hypothesis $H_0:\pi =0$ against the alternative null hypothesis $H_1:\pi \ge 1$, assessing the presence of any cointegrating relationships among the variables. Consequently, if we reject this first null hypothesis that indicates the presence of at least one cointegrating relationship, we then proceed to test $H_0:\pi \le 1$ against $H_1:\pi \ge 2$. This second test investigates whether there is at most one cointegrating relationship, rather than at least two. Lastly, if we again reject the null hypothesis, we have to proceed and test $H_0:\pi \le 2$ against $H_1:\pi =3$. This test examines whether there are at most two cointegrating relationships set against all three variables being cointegrated. Thus, as Simpson et al. (2005) pointed out, the results from these tests will collectively suggest the presence of long-term relationships among the variables of interest, thereby confirming cointegration.

3.2.2. Modelling of VAR and SVAR

The main objective of this study is to compare the effectiveness of the standard VAR model and the SVAR model. In order to accomplish this goal, it was necessary to first conduct preliminary assessment of data, which included unit root tests (ADF and PP) and the Johansen cointegration test. The results of these tests were instrumental in the development of our standard VAR and SVAR models for estimation.

In a VAR model, Wang and Wang (2020) highlighted that all variables are generally considered endogenous. That is, this indicates that each variable is treated as a function of its historical values and the historical values of all other variables within the system (Song & Witt, 2006). As a result, the VAR model incorporates lagged values of the variables, which facilitate the capture of dynamic interactions over time (Mao et al., 2023). Lagged values of each variable serve as predictors for the current value of that variable. Thus, the standard VAR eliminates the necessity for structural modelling (Hui et al., 2014).

Therefore, a set of K endogenous variables makes up a VAR model in its most basic form, which can be specified as follows:

$$Y_t=(y_{1t}\dots .,y_{2t,}\dots .,y_{kt})$$

(10)

whereby $k=1\dots .q$.

After that, the VAR (q) process is converted using Equation (10) to read as follows:

$$y_t=Z_1{y}_{t-1}+\dots Z_q{Y}_{t-q}+{\mu }_t$$

(11)

where $Z_i$ are (K × K) coefficient matrices for i = 1… q and ${\mu }_t$ is a k-dimensional process, with E(${\mu }_t$) = 0 and the positive time-invariant specific matrix of covariance E (${\mu }_t{\mu }_t^n$) = ${\mathsf{\Sigma }}_{\mu }$, which indicates a white noise error.

The stability of a VAR(q) process is a fundamental characteristic. This suggests that, with appropriate initial values, it generates stationary time series characterised by constant means, variances, and covariance structures over time.

Therefore, following Sims (1980), our reduced-form VAR can be written as follows:

$$y_t=c+{\sum }_{i=1}^p{\phi }_i{y}_{t-i}+{\epsilon }_t$$

(12)

where $y_t=\left[\begin{array}{c}{lnOP}_t\\ {lnFER}_t\\ {lnCPI}_t\end{array}\right]{;\epsilon }_t=\left[\begin{array}{c}{\epsilon }_{lnOP,t}\\ {\epsilon }_{lnFER,t}\\ {\epsilon }_{lnCPI,t}\end{array}\right]$.

Thus, $y_t$ is the vector of endogenous variables, c is the (3 × 1) vector of constants, ${\phi }_i$ are (3 × 3) matrices of coefficients, p is the optimal lag length determined by information criteria, and ${\epsilon }_t$ is a vector of reduced-form residuals with variance–covariance matrix $\mathsf{\Sigma }$.

Additionally, in contrast to standard VAR models, SVAR models enable the identification of economic theory-based structural shocks, which aids in comprehending the overall impacts of unforeseen shifts in variables such oil prices in the economy (Abildgren et al., 2018). That is, Özlale and Pekkurnaz (2010) highlighted that SVAR models offer a good empirical fit that is comparable to that of other vector autoregression models, but they also have the benefit of being able to detect structural shocks. Unpredictable changes are broken down into orthogonal components with economic interpretations using SVAR models (Qiu et al., 2012). They are adaptable to different identification strategies and can be used with a variety of datasets and small open economies such as South Africa (Dungey & Vehbi, 2015).

Therefore, the structural form of the SVAR model is expressed as follows:

$${Zy}_t=Z_1^{\ast }{y}_{t-1}+\dots +Z_q^{\ast }{y}_{t-p}+{\delta \epsilon }_t$$

(13)

$$y_t={A^{-1}Z}_1^{\ast }{y}_{t-1}+\dots +A^{-1}{Z}_q^{\ast }{y}_{t-p}+A^{-1}{\delta \epsilon }_t$$

(14)

whereby the coefficient matrices $Z_i^{\ast }$ for i = 1… q are structural coefficients that generally differ from their reduced form counterparts, assuming that the structural errors ${\epsilon }_t$ are white noise errors. The restrictions that have been put in place are shown in Equation (15) where k is the number of variables in the model:

$${\displaystyle \frac{k(k-1)}{2}}$$

(15)

where ${\displaystyle \frac{3(3-1)}{2}}$ = 3 (i.e., number of restrictions to be imposed).

Therefore, in our SVAR model identification, we impose the following recursive structure for short and long restrictions, which has been justified in the current section below:

$$\left[\begin{array}{ccc}1& 0& 0\\ a_{21}& 1& 0\\ a_{31}& a_{32}& 1\end{array}\right]\left[\begin{array}{c}{∆\mathrm{l}\mathrm{n}OP}_t\\ {∆lnFER}_t\\ {∆lnCPI}_t\end{array}\right]=\left[\begin{array}{c}{\in }_{OP,t}\\ {\in }_{FER,t}\\ {\in }_{CPI,t}\end{array}\right]$$

(16)

Thus, this structure requires restrictions mentioned in Equation (15) for identification. As a results, this specification yields the key equation that captures how consumer prices (natural logarithmic consumer price index) are influenced by changes in oil prices (natural logarithmic oil prices) and foreign exchange rates (natural logarithmic foreign exchange rates (ZAR/USD)), while accounting for their contemporaneous relationships:

$$∆{lnCPI}_t={-a}_{12}{∆lnOP}_t-a_{13}{∆lnNEER}_t+b_{11}{\in }_{CPI,t}$$

(17)

According to Equation (12), changes in the oil price (${∆lnOP}_t$), changes in the foreign exchange rate (${∆lnFER}_t$), and its own structural shocks (${\in }_{\mathit{C}\mathit{P}\mathit{I},\mathit{t}}$) all have a direct impact on changes in the Consumer Price Index ($∆{lnCPI}_t$). The impact of consumer price-specific shocks is measured by scaling the structural shock (${\in }_{CPI,t}$) by $b_{33}$. The oil price pass-through effect occurs when changes in global oil prices are passed on to domestic consumer prices through a variety of channels, such as transportation costs and energy-intensive production processes, and is captured by the coefficient ${-a}_{12}$. Oil prices, as denoted by $b_{11},$ are affected by their own shocks.

The economic rationale behind this methodological approach indicates that the exchange rate pass-through, represented by the coefficient $-a_{13}$, captures the process by which fluctuations in foreign exchange rates can affect consumer prices. Although the actual directional effects rely on the estimated coefficient values, the reduced-form equation’s negative signs (−) show the inverse relationships that surface after the system is solved. $b_{22}$ denotes that foreign exchange rates are affected by their own shocks. Therefore, this study only concentrated on the direct effects of these external factors on domestic consumer prices because the model is based on the idea that the CPI does not have contemporaneous feedback effects on oil prices or exchange rates (thus the zeros in the structural matrix).

To achieve this study’s objective, we used impulse response functions (IRFs) with both VAR and SVAR specifications. That is, to identify distinct shock patterns, the variables are ordered as lnOP, lnFER, and lnCPI. This ordering is based on the assumption that oil prices are the most exogenous variable, followed by foreign exchange rates, and consumer prices that are most endogenous. Therefore, due to this hierarchical structure, changes in oil prices are assumed to have an impact on all variables at the same time.

Subsequently, the IRFs are estimated over a 12-period horizon to capture both short-term and medium-term dynamics. For the standard VAR, we employed the Cholesky decomposition to orthogonalise the shocks. The SVAR specification incorporates contemporaneous restrictions (short and long run) informed by the economic theory presented in this study. The matrix presented in Equation (16) exhibit contemporaneous relationships and is subject to restrictions, as indicated by the number of restrictions in Equation (15). As mentioned above, this study utilised a SVAR model that incorporates three fundamental restrictions that are grounded in established economic theory and empirical literature. These restrictions are imposed in the short and long run. Firstly, we assume that oil prices are exogenous in the short term and are not simultaneously influenced by foreign exchange rates (ZAR/USD) or consumer prices. This restriction aligns with the small open economy assumption, which indicates that South Africa acts as a price taker in global oil markets (Gupta & Modise, 2013). That is, South Africa accepts global oil prices as fixed and does not have influence over them. Thus, this assumption is supported by studies conducted by Al Jabri et al. (2022), Tiberti et al. (2018), and Proença and Aubyn (2013). The studies indicated that fluctuations in global oil prices, which are dictated by international oil markets, tend to have a direct effect on small open economies (such as South Africa), with no reverse impact on global oil prices (Gupta & Modise, 2013).

Secondly, we had imposed a restriction that the foreign exchange rate (ZAR/USD) responds to oil price shocks in real time but does not respond to consumer price shocks in the short term. This restriction is in line with the research conducted by Nusair and Olson (2018), Basher et al. (2012), Sasaki et al. (2022), and Fisher and Huh (2019). According to these studies, the exchange rate is more vulnerable to oil price shocks compared to consumer price shocks in the short term.

Lastly, we had imposed a restriction that indicated consumer prices may respond simultaneously to shocks in both oil prices and the foreign exchange rate (ZAR/USD) in the short run. This assumption appears to be consistent with studies conducted by Bigerna (2023), Sasaki et al. (2022), Elsayed et al. (2021), and Cavalcanti and Jalles (2013). That is, these studies demonstrated the pass-through effects from external factors, such as oil prices and foreign exchange rates, which can influence domestic prices swiftly in small open economies. Ngalawa and Viegi (2011) implemented comparable restrictions in their SVAR analysis of the transmission of South African monetary policy. Thus, these studies emphasised the direct and indirect impacts of oil prices and exchange rates on consumer prices, with no feedback mechanisms.

For long-run restrictions, we follow the approach of Blanchard and Quah (1988), by imposing three restrictions that are similar to those imposed in the short run. Firstly, for the purpose of this current study, we assume that oil price shocks can have permanent long-term effects on all variables (foreign exchange rate and consumer prices). This assumption reflects the persistence of oil price fluctuations in small open economies since they tend to be price takers in global markets, as indicated by Abubakar et al. (2024) and Chebbi (2019). That is, these studies demonstrated that fluctuations in oil prices can have a long-term influence on small open economies, which usually follow a random walk characterised by irreversible shocks (Alba et al., 2020).

Secondly, foreign exchange rate (ZAR/USD) shocks are restricted in a way that they do not have a permanent effect on oil prices, but they can have a permanent impact on consumer prices. This assumption is based on research conducted by Malik and Umar (2019), Hussain et al. (2017), and Atems et al. (2015), who found that fluctuations in the exchange rate do not have a long-lasting impact on the price of oil. Additionally, research undertaken by Kim et al. (2024) and Bems et al. (2021) has shown that exchange rate shocks can have a lasting effect on consumer prices by directly and indirectly affecting the domestic pricing of goods and resource materials. Lastly, we imposed a restriction that indicates that consumer prices are limited to responding solely to the permanent effects of oil prices and foreign exchange rates, without any feedback effects. This assumption indicates that consumer prices are mainly reactive rather than influential, which may be relevant in a small open economy such as South Africa (Myers et al., 2018).

Consequently, these restrictions that we imposed, in the short and long run, are essential for the identification of structural shocks, as substantiated by economic theory and empirical evidence highlighted in this discussion. That is, the short-run restrictions illustrate the immediate transmission of shocks in a small open economy such as South Africa, whereas the long-run restrictions represent the permanent features of various shocks. Therefore, this integration of short-run and long-run restrictions facilitated the precise identification of structural shocks and their transmission mechanisms over different time horizons in South Africa.

3.3. Diagnostic Tests Applied

In order to evaluate model validity, this study used three primary diagnostic assessments, which include the Portmanteau test for autocorrelations, serial correlation Lagrange multiplier (LM) testing, and a normality test. Firstly, the residual autocorrelations in time series models were assessed using the Portmanteau test (Box & Pierce, 1970). Secondly, the autocorrelation LM tests are intended to detect serial correlation in residuals (Breusch, 1978). The LM test is particularly effective at detecting higher-order serial correlations. Lastly, the normality test determines whether model residuals follow a multivariate normal distribution (Jarque & Bera, 1987). This assumption is critical for many statistical techniques, particularly hypothesis testing and confidence interval estimation.

4. Results and Discussion

4.1. Discussion of Unit Root Test (ADF and PP) Results

This section presents the findings of our study, which starts with the results of the stationarity analysis using the Augmented Dickey–Fuller (ADF) test and the Phillips–Perron (PP) test.

The results are presented in

Table 1. Unit root tests results (probability values).

		Levels		First Difference
Variables	Test	Intercept	Intercept and Trend	Intercept	Intercept and Trend
lnOP (logged oil prices)	ADF	0.28	0.35	0.00	0.00
	PP	0.23	0.29	0.00	0.00
lnFER (logged Foreign exchange rate)	ADF	0.90	0.05	0.00	0.00
	PP	0.93	0.17	0.00	0.00
lnCPI (logged Consumer Price Index)	ADF	0.22	0.67	0.00	0.00
	PP	0.15	0.55	0.00	0.00

Source: authors’ estimates.

, which includes the corresponding probability values of the ADF and PP tests. Both tests function under the same principle, assessing whether a data series is stationary or non-stationary, which is a crucial aspect of time series analysis (Brooks, 2019). As a result, the ADF and PP tests were interpreted by comparing p-values at 5% (0.05). This method of interpreting unit root test results is based on the work of Majenge et al. (2024). That is, when the ADF and PP tests yield p-values equal to or greater than 0.05, we cannot reject the null hypothesis of a unit root, indicating that the time series is not stationary. When the p-value is below 0.05, the null hypothesis is rejected and the time series is stationary.

The results of the ADF and PP unit root tests revealed that the three natural logarithmic variables (oil prices (lnOP), Consumer Price Index (lnCPI), and foreign exchange rate (lnFER)) demonstrated non-stationarity at levels, as evidenced by p-values exceeding the 5% significance threshold, with the exception of lnFER PP test results of intercept and trend (0.05). This aligns with economic theory suggesting that macroeconomic variables often exhibit random walk behaviour (Gujarati & Porter, 2009). Nevertheless, following first differencing, all variables demonstrated stationarity behaviour, as indicated by p-values of 0.00, which led to the rejection of the null hypothesis of non-stationarity. Therefore, the results indicated that these variables are mostly integrated of order one, I(1), which is consistent with standard macroeconomic time series behaviour.

4.2. Correlation Analysis

Table 2. Correlation analysis between oil prices, consumer prices, and the foreign exchange rate.

Correlation Probability	lnOP	lnFER	lnCPI
lnOP (logged oil prices)	1.00
	---
lnFER (logged Foreign exchange rate)	0.40	1.00
	(0.00)	---
lnCPI (logged Consumer Price Index)	−0.19	−0.13	1.00
	(0.01)	(0.08)	---

Source: authors’ estimates.

presents the results of the correlation analysis, which indicated noteworthy relationships among South African consumer prices, oil prices, and the nominal effective exchange rate after the post-2007/08 financial crisis period.

The findings revealed a positive (0.40) correlation between oil prices and foreign exchange rates, which is statistically significant at 1%. This finding aligns with the study conducted by Beckmann et al. (2020), which demonstrated that oil price fluctuations significantly affect exchange rates. Likewise, the analysis shows a negative correlation (−0.19) between oil prices and consumer prices, which is statistically significant at 1%. Similarly, foreign exchange rates had a negative correlation (−0.13) with consumer prices. These findings contrast with those of Gao et al. (2019), who found a significant negative correlations in their cross-country analysis. Their findings revealed that while oil prices have a direct impact on exchange rates, their effect on consumer prices is more complex. According to Chen and Chen (2007), this complexity may result from intervening factors such as monetary policy and market structures. As a result, recent empirical studies (Tiwari et al., 2019) suggest that the observed negative correlations with consumer prices could be attributed to potential economic stabilising mechanisms.

4.3. Discussion of Johansen Cointegration Test Results

The results of the Johansen cointegration test for the natural logarithmic variables of interest (lnCPI, lnOP, and lnFER) are shown in

Table 3. Johansen cointegration test results.

Trace Test Outcomes
Hypothesised no. of cointegrated equations	Eigenvalue	Trace Statistic	0.05 critical value	p-value
None	0.082954	25.68223	29.79707	0.1385
At most 1	0.050605	10.52769	15.49471	0.2423
At most 2	0.008194	1.439924	3.841466	0.2302
Maximum Eigenvalue Outcomes
Hypothesised no. of cointegrated equations	Eigenvalue	Max-Eigen Statistic	0.05 critical value	p-value
None	0.082954	15.15454	21.13162	0.2782
At most 1	0.050605	9.087763	14.26460	0.2789
At most 2	0.008194	1.439924	3.841466	0.2302

Source: authors’ estimates.

. The interpretation of the results in Table 3 had followed the standard econometric interpretation. That is, when the trace test and maximum eigenvalue tests yielded p-values equal to or greater than 0.05 (5%), we cannot reject the null hypothesis of a unit root, indicating that the variables in the long run are not cointegrated. Similarly, when the p-value is below 0.05, the null hypothesis is rejected, indicating that the variables are cointegrated.

Nonetheless, comparing the trace and max-eigen statistics has also been used to support the p-value interpretation. If the results of these tests fall below the 0.05 critical value, the null hypothesis cannot be rejected, indicating the non-cointegration of the variables. However, long-term cointegration will be indicated if the tests produce results above the 0.05 critical value, which will reject the null hypothesis.

Firstly, the trace test results at all scenarios (none, at most 1, and at most 2) revealed that none of the variables indicated cointegration in the long run at the 5% significance level. This conclusion is supported by p-values that exceeded 0.05 (0.1385, 0.2423, and 0.2302) and trace statistics that fell below their corresponding critical values. For example, the first trace statistics (25.68223, 10.52769, and 1.439924) are less than the 0.05 critical values (29.79707, 15.49471, and 3.841466). Consequently, this implies the absence of a stable long-term relationship among the variables of interest.

Secondly, the maximum eigenvalue test results further confirm this finding. All three scenarios that were tested (none, at most 1, and at most 2) produced p-values that are greater than 0.05 (0.2782, 0.2789, and 0.2302), and the test statistics were below their critical values. For example, the max-eigen statistics (15.15454, 9.087763, and 1.439924) are less than their critical values (21.13162, 14.26460, and 3.841466) for all the tests. Thus, these findings also imply that the variables are not cointegrated over the long term.

Therefore, these results have important consequences from an economic point of view. They suggest that consumer prices, oil prices, and foreign exchange rates will not be affected by one another over the long run. This can be interpreted in a manner that suggests when policymakers make decisions about the economy in the long run, they cannot depend on a stable and predictable relationship between these variables. That is, they cannot assume that fluctuations in oil prices will result in proportional changes in consumer prices and exchange rates in the long run.

For that reason, now that we know our variables of interests appears to not have the ability to cointegrate over the long term, meaning that they do not share a long-term equilibrium relationship. Now, we are ready to perform our VAR and SVAR models. But, before doing that, we performed a lag selection assessment to ensure that our models have the appropriate lag.

4.4. Lag Selection

The lag selection analysis offers essential insights for optimal model specification in time series analysis. That is, the lag length criteria, in other words, aid in determining the proper lag length, which is necessary for appropriate model specification (Shahrabi et al., 2013). Adom-Dankwa et al. (2024) argue that lag length selection influences model performance in a time series. They also suggest that lower values in the lag length criterion indicate a better model fit. Thus, choosing the appropriate lag length can ensure model resilience and subsequently avoid producing erroneous results (Yang & Koondhar, 2024).

As a result, the findings presented in

Table 4. VAR lag order selection criteria results.

Lag	LogL	LR	FPE	AIC	SC	HQ
0	−56.20529	NA	0.000400	0.688434	0.743332	0.710707
1	784.4663	1642.242	2.52 × 10−8	−8.982167	−8.762574 *	−8.893072 *
2	795.6057	21.37196	2.46 × 10−8 *	−9.007043 *	−8.622755	−8.851127
3	802.9777	13.88693	2.51 × 10−8	−8.988113	−8.439132	−8.765377
4	806.8514	7.161762	2.66 × 10−8	−8.928505	−8.214828	−8.638948
5	812.9606	11.08177	2.76 × 10−8	−8.894890	−8.016520	−8.538513
6	825.9191	23.05417 *	2.63 × 10−8	−8.940920	−7.897855	−8.517722
7	831.4771	9.694196	2.75 × 10−8	−8.900897	−7.693137	−8.410878
8	833.4766	3.417737	2.99 × 10−8	−8.819496	−7.447042	−8.262655

Notes: * indicates lag order selected by the criterion; (LR) sequential modified LR test statistic (each test at 5% level); (FPE) final prediction error; (AIC) Akaike information criterion; (SC) Schwarz information criterion; (HQ) Hannan–Quinn information criterion. Source: authors’ estimates.

highlight diverse recommendations derived from various information criteria. That is, SC (Schwarz) and HQ (Hannan–Quinn) recommend one lag, while the AIC (Akaike information criterion) and FPE (Final Prediction Error) suggest two lags. The sequential modified LR test statistic shows significance at lag 6, suggesting the presence of higher-order dynamics. Consequently, Ng and Perron (2001) highlighted that such divergence in lag selection often arises in empirical analysis and requires careful interpretation based on economic theory. Thus, lag 2, AIC, was selected in accordance with Lütkepohl’s (2005) argument that shorter lag structures generally improve out-of-sample forecasting performance.

4.5. Justification of Not Differencing the Variables

We acknowledge that the handling of non-stationary variables in economic time series analysis appears to spark a debate among economic researchers. For a long time, economists have traditionally held the belief that time series data displaying non-stationary qualities necessitate transformation. In most cases, this has been performed by means of differencing the variables in question. However, over the years, although not popular, a different approach has emerged, contesting this conventional wisdom. Sims et al. (1990) fundamentally transformed how researchers approach data analysis. They argued persuasively that automatically differencing time series data was often unnecessary and could potentially destroy valuable economic information (Ngalawa & Viegi, 2011). Instead, they proposed that the decision to transform data should depend on the specific research questions and hypotheses that are being investigated.

Monetary policy researchers such as Bernanke and Mihov (1995) have since demonstrated compelling reasons to maintain variables in their original levels and not difference the variables. Their research showed that level specifications can provide more consistent estimates, particularly when variables are potentially interconnected. This approach preserves crucial long-term relationships between economic indicators, which are often of importance in understanding complex economic systems. Interest rates, for example, are one variable that has demonstrated the no-need-for-differencing approach. Studies such as those conducted by Taylor (1994) and Clarida et al. (1999) highlighted that interest rates are naturally bounded and tend to fluctuate around an equilibrium. Unlike other economic variables that show consistent growth trends, interest rates are already expressed as percentages and demonstrate mean-reverting behaviour. This characteristic makes them particularly suitable for level analysis within economic frameworks.

Empirical studies have demonstrated the value of this more flexible approach. For instance, Brischetto and Voss’s (2000) research on Australian monetary policy showed how minimal transformations—such as applying logarithmic transformations to most variables while keeping them in levels—could provide robust and insightful analyses. Ngalawa and Viegi (2011), despite finding that their variables were non-stationary, I(1), chose to estimate their structural vector autoregressive (SVAR) model using the variables in levels rather than differencing them. This decision was primarily supported by the influential work of Sims et al. (1990), who demonstrated that transforming non-stationary data to make them stationary through differencing or cointegration operators is unnecessary, as the statistics of interest typically have distributions unaffected by non-stationarity.

The findings of Sims et al. (1990) have become widely accepted in the SVAR literature. Thus, this approach has been demonstrated in studies such as Bernanke and Mihov (1995), Piffanelli (2001), and Dungey and Pagan (2000). The preference for using levels is further justified by concerns about imposing potentially incorrect restrictions through transformation, with studies such as those conducted by Kim and Roubini (2000), and Becklemans (2005) that argued that such restrictions can lead to incorrect inferences. Additionally, Bernanke and Mihov (1995) point out that level specifications produce consistent estimates regardless of cointegration, while difference specifications can be inconsistent when variables are cointegrated. Likewise, Enders (2014) presented empirical evidence indicating that transforming data to attain stationarity may obscure significant relationships between variables and potentially misrepresent the model dynamic structure. Ashley and Verbrugge (2009) conducted rigorous Monte Carlo simulations demonstrating that VARs in levels outperform differenced specifications, even in the presence of non-stationary data. Gunasinghe et al. (2019) theoretically demonstrated that estimating SVARs in levels permits implicit cointegrating relationships, thereby eliminating the need for explicit modelling. That is, Arefeva and Arefyev (2024) further highlighted that cointegrated relationships can be captured when SVARs are estimated using non-stationary data in levels without converting the data to stationarity. This technique works particularly well for locating long-term structural shocks.

Additionally, the use of lagged variables in VAR models offers an alternative to differencing the data, which is commonly used to achieve stationarity (Qiu et al., 2024). This is due to the fact that the lagged structure naturally takes into consideration the trends and temporal relationships in the data (Geng et al., 2023). That is, incorporating a lagged structure allows us to mitigate unit root problems in the original data by destabilising autocorrelation patterns that are typical of non-stationary series (Faisal et al., 2023). Therefore, our VAR and SVAR models incorporated lags that may demonstrate qualities that are comparable to a stationary series in the model.

4.6. Empirical Results: Comparing VAR and SVAR

This section of the study presents the empirical results from utilising the standard VAR and SVAR models, respectively. Given the outcome of estimating the Johansen cointegration test discussed in Section 4.3 above, we concluded that our variables of interest are not cointegrated. That is, these variables do not share a stable long-run relationship. Then, the results obtained from estimating the standard VAR in this study had to be interpreted as the effects that occurred in the short run. However, in our SVAR model, we had imposed short- and long-run restrictions.

Therefore, given the above discussion, our models (VAR and SVAR) have been estimated without differencing the variables, irrespective of the results obtained from performing the unit root testing. That is, this approach follows the argument made in the discussion above (Section 4.6), which highlighted the potential benefits against the transformation of non-stationary data in econometric models. That is, our approach is consistent with Magubane and Nzimande (2024), Ngalawa and Viegi (2011), Bernanke and Mihov (1995), and Sims (1992). These studies highlighted that differencing variables may eliminate significant long-term information from the data, which could result in misspecification. Hamilton (1994) reinforced the argument by demonstrating that VARs incorporating non-stationary variables yield consistent parameter estimates and valid inference methodologies.

As a result, the empirical findings of this study had compared the results received from performing the impulse response function (IRF) estimated using the standard VAR model, as shown in Figure 3, with the results of the structural impulse response function (SIRF) estimated using the SVAR model, as shown in Figure 4 (imposing short-run restrictions) and Figure 5 (imposing long-run restrictions).

Following Sims (1980), the variables were ordered as lnOP, lnFER, and lnCPI to identify the distinct patterns of shocks, with oil prices considered the most exogenous, moving to the foreign exchange rate and consumer prices regarded as the most endogenous. As noted above, this ordering reflects the assumption that changes in oil prices can simultaneously affect all other variables. Subsequently,

Table 5. Diagnostic test results.

Types of Test	Null Hypothesis	Model	T Statistic	Probability	Decision (i.e., Reject or Accept the Null Hypothesis)
Portmanteau Test for autocorrelations	No residual autocorrelations	VAR	60.10	0.26	Null hypothesis accepted
		SVAR	60.10	0.26	Null hypothesis accepted
Serial correlation LM tests	No serial correlation	VAR	9.12	0.43	Null hypothesis accepted
		SVAR	9.12	0.43	Null hypothesis accepted
Normality test (Jarque-Bera)	Residuals are multivariate normal	VAR	434.80	0.00	Null hypothesis rejected
		SVAR	339.69	0.00	Null hypothesis rejected

Source: authors’ estimates.

provides results received from conducting diagnostic test on both models.

As a result, Figure 3A–I, Figure 4A–I, and Figure 5A–I provide illustrations of the impulse response functions (IRFs) obtained from estimating the standard VAR, SVAR imposing short-run restrictions, and SVAR imposing long-run restrictions, respectively. The IRF results are interpreted by observing the blue lines, which represent the point estimates, while red lines indicate the 95% confidence bands. That is, when the confidence bands contain zero (crossing both positive and negative regions), the response is considered uncertain. However, when the confidence bands are either above or below zero, then the response is considered certain.

For instance, Figure 3A reveals that oil prices demonstrated a significant response to their own shocks, as evidenced by confidence bands remaining strictly above zero. The coefficients accumulate from an initial 0.092786 and increase to 0.893329 by period 12. This suggests that oil price shocks have lasting impacts on future oil price movements in South Africa. This effect corresponds with the findings of Cologni and Manera (2008), which indicated a significant impact of oil prices on oil-importing economies. Figure 3B reveals that oil prices’ response to exchange rate shocks was uncertain, as evidenced by the confidence bands (red lines) crossing the zero line, though the point estimate suggests a small negative effect (approximately −0.01). This supports Chen’s (2009) findings of diminished external factor impacts on oil prices in industrialised countries. Figure 3C also demonstrates an uncertain negative response to consumer price shocks (from 0 to −0.152625 by period 12).

Additionally, Figure 3D illustrates the reaction of foreign exchange rates to oil price shocks with a response that is uncertain, whereby the response pattern shifts from initially negative to marginally positive after period 7. Consequently, this is in line with the findings of Duke et al. (2023) regarding the relationship between oil prices and exchange rates. Thus, the economic consequences for South Africa derived from this result may suggest that as oil prices shock, the value of the South African rand (ZAR) is likely to appreciate against USD due to oil price fluctuations (from −0.002136 to −0.004712 by period 7). That is, it may now be less expensive to purchase one barrel of Brent crude oil, as fewer ZAR is required to exchange for USD for this transaction. This will eventually appreciate ZAR currency against the globally recognised trading currency (in most cases, USD). In the latter part (from period 8 to 12), this relation appears to change positive by period 12. This positive feedback might indicate that ZAR depreciates against USD when there are shocks in oil prices (from 0.004029 to 0.057115 by period 12). That is, during this period, the increasing demand for USD in the market increases the supply of ZAR, thereby increasing USD’s value (ZAR depreciates against USD).

Figure 3E indicates a significant positive persistence in exchange rate reactions to their own shocks (accumulating from 0.032201 to 0.436000), which is consistent with Kemoe’s (2024) findings regarding exchange rate dynamics in developing economies. Nonetheless, Figure 3F, although uncertain, highlights that the foreign exchange rate (ZAR/USD) responded negatively to consumer price shocks, with confidence bands spanning zero throughout the horizon. That is, this negative outcome for South Africa may indicate a depreciation in the exchange rate (weakening of ZAR currency against USD). This finding may appear to suggest that the rise in inflation reduces confidence in ZAR currency, causing investors to dispose of ZAR-denominated assets. Consequently, as ZAR depreciates, it can be speculated that the cost of imported goods and local products that rely on imported materials increases, as these are priced in USD in most cases. This situation creates a cycle in which rising consumer prices contribute to further ZAR depreciation, which leads to additional price increases by means of the exchange rate pass-through effect. This appears to align with the findings of Iddrisu and Alagidede (2020) as well as Salvucci and Tarp (2024), who highlighted that depreciation of the exchange rate has a greater impact on consumer prices in Sub-Saharan Africa (including South Africa) compared to currency appreciation.

Although uncertain, as demonstrated by the confidence bands (red lines) crossing the zero line, Figure 3G reveals that consumer prices respond positively to oil price shocks. This is shown by the blue line consistently remaining above zero throughout the period (from 0.002574 to 0.206851). This indicates a relative transmission of oil price shocks to consumer prices in the short run. That is, this outcome appears to support the theory of cost-push inflation as described by Monfort and Peña (2008) and the observations regarding price adjustment processes highlighted by Ball and Mankiw (1994). Thus, this finding appears to suggest that that changes in oil prices around the world have a direct impact on the price of goods and services for consumers in South Africa. Therefore, this observation is consistent with the study of Mao et al. (2023), who highlighted that increased production and transportation costs brought on by rising oil prices are frequently passed on to customers in the form of higher prices for goods and services.

Figure 3H illustrates that the response of consumer prices to foreign exchange rate shocks shows a progressively increasing negative trend that is statistically uncertain, as indicated by confidence bands crossing zero. This is consistent with the finding observed in Figure 3F about the negative relationship that exists between the foreign exchange rate and consumer prices. This supports the findings of Parsley (2012) regarding the relatively low pass-through of exchange rates to consumer prices. Figure 3I demonstrates that consumer prices significantly responded positively to their own shocks (from 0.050705 to 0.51796), which is consistent with the observations of Ball and Mankiw (1994) regarding price rigidity and persistence in consumer prices.

Therefore, since South Africa is a net oil importer, there are economic consequences that may be of interest for policy makers. The impulse response function results from performing the standard VAR model had revealed that fluctuations in oil prices and foreign exchange rates have an impact on consumer prices. That is, the IRF outcomes indicate that external shocks appears to have a short-term effect on domestic inflation, which could lead to a decrease in purchasing power of the South African rand (ZAR), especially for households with lower incomes who subsequently bear the cost.

Figure 4A–I highlight the findings that were revealed when we imposed short-run restrictions on our SVAR model. By imposing these short-run restrictions, we were interested in how shocks to oil prices affect the foreign exchange rate and consumer prices. As a result, similar to our VAR interpretation, the confidence bands (red lines) crossing the zero line indicated that IRFs showed uncertain short-run movements caused by shocks. However, certain movements are demonstrated by both confidence bands that are below or above zero. For instance, Figure 4A indicates that oil price shocks demonstrated an increasing response to their own shocks (from 1.00 to 9.627817 by period 12). That is, when there is a shock to oil prices, it quickly leads to further increases in oil prices. This can be attributed to increased investments in oil exploration and drilling activities as a result of fluctuations in oil prices (Solaymani & Kari, 2013). A positive oil price shock, according to Zoundi (2024), has the ability to boost production, trade surplus, economic growth, and currency appreciation in net oil country exporters.

Figure 4D reveals that the short-run impact of oil price shocks on the foreign exchange rate (ZAR/USD) appears to be relatively small, whereby the response pattern shifts from initially negative (from −0.023026 to −0.050787 by period 7) and then turns marginally positive after period 7 (from period eight 0.043420 to 0.615554 by period 12). This finding appears to follow the same trend as Figure 3D above. Thus, the economic consequences of this outcome may indicate that the value of the South African Rand (ZAR) is likely to appreciate in the short term due to fluctuations in foreign exchange rates caused by oil price shocks. That is, oil price shocks, from period 1 to 7, ZAR currency appears to appreciate against USD. As a result, fewer ZAR is needed to purchase USD due to fluctuations in oil prices. However, from period 8 to 12, oil price shocks shift the negative effect response into positive responses (from period 8 to 12). These positive responses of the foreign exchange rate (ZAR/USD) could suggest that ZAR currency weakens against USD. That is, more ZAR is needed to exchange for USD due to oil price shocks. Therefore, this mixed reaction of foreign exchange rate (ZAR/USD) from oil price shocks appears to be consistent with the findings of Saidu et al. (2021), who highlighted that ZAR currency tends to depreciate when prices of oil increase and appreciate when oil prices decrease.

Figure 4G highlight that sudden shocks in oil prices appear to have prompted consumer prices to increase modestly but progressively over time (from 0.027742 to 2.229328 by period 12). That is, while this effect is initially small, it grows steadily over the first few periods, demonstrating how oil price shocks gradually feed into overall consumer prices in South Africa. This finding appears to be consistent with the results shown in Figure 3G. This suggests that, in the short run, oil price shocks tend to raise consumer prices in South Africa. This pass-through effect provide support to the cost-push inflation theory.

The results received from Figure 4H appear to support the results we obtained in Figure 3H. That is, shocks in the foreign exchange rate (ZAR/USD) appear to decrease consumer prices over time (from −0.049180 to −2.555252). This can be attributed to ZAR’s appreciation relative to USD. This appreciation typically results in lower costs for imported oil products, potentially leading to a reduction in consumer prices over time as purchasing power increases and thus causes deflationary pressures on imported goods (Orlov, 2015).

Imposing long-run restrictions on our SVAR model revealed results that are in opposition compared to when we had imposed short-run constraints. For instance, Figure 5A demonstrates how oil prices responded to their own shocks, resulting in certain long-term and cumulative effects. The results indicated that these effects continue to accumulate, suggesting that when oil prices fluctuate, the impact tends to persist and increase over time. Figure 4A and Figure 5A differ in the way that the results in Figure 4A are uncertain, indicated by the red lines crossing zero, whereas Figure 5A presents certain results, as the red lines remain above zero. Figure 5D reveals that when there is an oil price shock, it appears to cause the foreign exchange rate (ZAR/USD) to increase upwardly (from 0.008073 to 0.142147). That is, oil price shocks appear to have a long-lasting effect on the foreign exchange rate (ZAR/USD). In other words, this finding can be viewed as the depreciation of ZAR against USD, whereby, in the long run, South Africa will need more USD to purchase the same amount of Brent crude oil (leading to the depreciation of ZAR over time).

Figure 5G illustrates perhaps the most surprising finding on how consumer prices react to oil shocks in the long run. Contrary to what we might expect, when there is an oil price shock, it actually appears to push consumer prices down. That is, consumer prices appear to decrease in the long run. This negative relationship starts small but increases over time (from −0.014208 to −0.113067). As a result, this deflationary effect can be attributed to increased oil supply (or decrease in demand for oil) and effective monetary policy measures (Roudari et al., 2023). That is, it appears that cost pressures in the economy are easing and consumer prices tend to stabilise in the long run. Therefore, oil price shocks that cause inflation to rise in the short run (as shown in Figure 3G and Figure 4G) appear to be short-lived, as long-run oil price shocks cause deflationary effects, as illustrated in Figure 5G.

Figure 5H illustrates different responses of consumer prices to shocks in the foreign exchange rate (ZAR/USD). Initially, foreign exchange rate (ZAR/USD) shocks result in a modest increase in consumer prices (from 0.003859 to 0.002957 by period 5). Thus, this appears to indicate that ZAR depreciates against USD, causing consumer prices to increase from period 1 to 5. This is consistent with studies conducted by Salvucci and Tarp (2024), Bems et al. (2021), and Marcelin and Mathur (2016), which found that currency depreciation in most countries has an immediate and significant impact on consumer prices by increasing the cost of imported goods. Therefore, the depreciation of ZAR relative to USD raises consumer prices and puts pressure on inflation in the domestic economy from period 1 to 5. Nonetheless, this relationship evolves over time, ultimately resulting in a decline in consumer prices (from period 6 to period 12 (−0.000532 to −0.036224)). Thus, this appears to indicate that ZAR appreciates relative to USD, causing consumer prices to decrease from period 6 to 12. This is consistent with research conducted by Charteris and Kallinterakis (2021), who found that imported goods priced in USD would cost less in ZAR as ZAR appreciated, potentially resulting in lower consumer prices. Therefore, due to increased purchasing power caused by ZAR appreciation and lower import costs, consumer prices fall and potentially lead to lower inflation.

4.7. Diagnostic Test Results

Several diagnostic tests were performed to assess the reliability of the study model. As a result, Table 5 presents the findings from diagnostic testing.

As a result, both models revealed similar trends in residual behaviour. The Portmanteau test results, featuring a test statistic of 60.10 and a probability (p-value) of 0.26 for both models, suggested the absence of residual autocorrelations. This finding is consistent with Brooks’s (2019) claim that well-specified VAR models display uncorrelated residuals. The serial correlation LM test statistics of 9.12, with p-values of 0.43 for both models, confirmed the absence of serial correlation. The findings support Hamilton’s (1994) arguments regarding the significance of independent residuals in time series analysis. Thus, the acceptance of the null hypotheses in both the Portmanteau and serial correlation tests indicated the model’s adequacy in capturing dynamic relationships between variables.

Additionally, the results received from the Jarque–Bera normality test (VAR: 434.80, SVAR: 339.69) with p-values of 0.00 rejected the null hypothesis of multivariate normality, which is frequently observed in time series data, as noted by Kim et al. (2020). The finding of non-normality aligns with the results of Samunderu and Murahwa (2021) regarding emerging markets, where persistent non-normal residuals can lead to inaccurate risk measurements. The diagnostic results indicate that the models effectively manage autocorrelation issues; however, they encounter difficulties regarding normality assumptions, a phenomenon attributed to the inherent properties of economic data as noted by Bai and Ng (2005).

5. Conclusions and Policy Recommendations

This study used vector autoregression (VAR) and structural vector autoregression (SVAR) models to investigate the impact of oil price shocks and foreign exchange rates on consumer prices in South Africa following the 2008 financial crisis. To achieve the study objectives, we compared several modelling approaches, which include standard VAR, SVAR with short-run restrictions, and SVAR with long-run restrictions.

The standard VAR model revealed that oil price shocks had an uncertain but generally positive effect on consumer prices in the short term. When the foreign exchange rate was examined, an interesting pattern emerged in which the South African rand (ZAR) initially appreciated against the US dollar (USD) in response to oil price shocks (periods 1:7) before depreciating (periods 8:12). This suggests that the currency’s response to oil price shocks varies over time.

When short-run restrictions were imposed on the SVAR model, the results showed that oil price shocks had more persistent effects on consumer prices than the standard VAR model. This finding is consistent with economic theory about cost-push inflation, in which businesses pass on increased costs to consumers. The foreign exchange rate followed a similar pattern to the VAR model, with initial appreciation followed by depreciation, demonstrating the robustness of this finding across different modelling approaches.

However, the unexpected findings came from the SVAR model with long-run restrictions. In contrast to both the VAR and short-run SVAR findings, this approach revealed that oil price shocks had a deflationary effect on consumer prices in the long term. This unexpected finding suggests that, while oil price shocks may initially raise consumer prices in the short run, long-term economic adjustments such as increased oil supply (or reduced demand) or effective monetary policy interventions will eventually result in price stabilisation or even reduction over time.

The long-run SVAR model findings on foreign exchange rates revealed a few noteworthy dynamics. Initially, foreign exchange rate (ZAR/USD) shocks caused a modest increase in consumer prices (periods 1:5), indicating that ZAR’s depreciation against USD increased consumer prices. However, this relationship changed over time, eventually resulting in consumer price decreases (periods 6:12). These findings indicated that when ZAR depreciates, consumer prices tend to increase, whereas when ZAR appreciates, consumer prices tend to decrease. Thus, in both the short and long run, the impact of foreign exchange rate (ZAR/USD) shocks on consumer prices is not straightforward because it fluctuates over time (from negative to positive responses or the other way around).

Therefore, this study concludes that South Africa’s status as a country that imports oil and has a floating exchange rate system makes it vulnerable to external shocks in the short term. However, in the long term, the results suggest that the economy has developed mechanisms to adjust to oil price shocks over time. This may have occurred through changes in consumption patterns, improvements in energy efficiency, or effective monetary policy responses.

Consequently, based on this study’s findings, several policy recommendations are formulated for policymakers in South Africa. Firstly, the monetary authority (SARB) should monitor global oil price fluctuations due to their certain influence on domestic consumer prices. This may necessitate the development of early warning systems to anticipate and respond to oil price shocks. Secondly, although the SARB’s exchange rate management appears to be significant, the foreign exchange rate (ZAR/USD) pass-through effects suggest that the SARB should avoid overreacting to short-term currency fluctuations as part of its inflation-targeting strategy. That is, ZAR relative to USD changes over time (depreciates/appreciates). Lastly, the government should diversify South Africa’s energy sources to enhance economic stability, thereby reducing dependency on oil imports and minimising vulnerability to oil price fluctuations. This may involve investment in renewable energy sources and enhancements in energy efficiency to mitigate the effects of external shocks on consumer prices.

Limitations of the Study and Future Research

Building on the findings of this study, future research could extend this analysis in several directions. Firstly, future research may investigate these relationships by incorporating additional economic variables that could provide a more comprehensive understanding of external shock transmission mechanisms. Secondly, future research may analyse non-linear relationships that could reveal threshold effects in the oil price–inflation nexus. Thirdly, research should assess how these patterns differ across various sectors of the South African economy. Also, comparing South Africa’s experience with other emerging market economies could provide valuable insights.