Dynamic Spillovers from US (Un)Conventional Monetary Policy to African Equity Markets: A Time-Varying Parameter Frequency Connectedness and Wavelet Coherence Analysis

Abstract

Since the implementation of unconventional monetary policies (UMPs) by the US in response to the global financial crisis (GFC) and the COVID-19 pandemic, there have been increasing concerns that these forward guidance and quantitative easing programmes have had spillover effects on global equity markets. We specifically question whether the implementation of these UMPs have had spillovers to African equities, which have been previously speculated to be decoupled from global markets and shocks. Time-varying-parameter (TVP) frequency connectedness and wavelet coherency methods were used to examine the dynamic time-frequency spillovers between daily time series of the US shadow short rate and African equities returns/volatility between 1 January 2007 and 31 March 2023. On one hand, the TVP frequency connectedness analysis reveals robust long-run spillovers from US monetary policy to African equity markets during specific periods: 2009, 2013, 2020, and 2021. These coincide with instances when the Federal Reserve announced their transition from conventional to unconventional monetary practices and vice versa. On the other hand, the wavelet analysis provides insights into the ‘sign’ of the spillovers, indicating mixed phase dynamics during UMPs responding to the GFC. In contrast, anti-phase or negative co-movements characterize UMPs implemented during the COVID-19 pandemic, implying that these policies increased both returns and volatilities to African equities. Altogether, we conclude that US UMP has increasing deteriorated market efficiency and amplified portfolio risk in African equities whilst during ‘normalization’ periods US monetary policy has little transmission effect.

1. Introduction

Over the last two decades or so, major global crises such as the global financial crisis (GFC) and the COVID-19 pandemic have demonstrated the limitations of traditional monetary policy tools, particularly the manipulation of short-term interest rates, in stabilizing markets and facilitating economic recovery in industrialized economies. When short-term nominal interest rates approach the zero-lower bound (ZLB) amid severe liquidity shortages, the efficacy of conventional monetary policy becomes constrained (Bernanke 2020).

To address these limitations during extreme crises and liquidity shortages, central banks have turned to unconventional monetary policies (UMPs). These unconventional measures include forward guidance and balance sheet operations such as large-scale asset purchases (quantitative easing or QE), maturity extensions, and other programs aimed at supporting bank lending (Umar et al. 2023; Choi et al. 2024).

The implementation of UMPs in developed countries has global implications, affecting stock markets worldwide through channels like portfolio rebalancing, bank credit risk, investor expectations, confidence, asset prices, and market signals (Bernanke 2020). For instance, large-scale asset purchase (LSAP) programs influence asset prices and exchange rates, impacting capital and trade flows (Gagnon et al. 2011; Chodorow-Reich 2014; Faush and Sigonius 2018; Papadamou et al. 2020). Moreover, UMP announcements signal new information about the current state of the economy, hence influencing expectations and confidence of investors which, in turn, can affect portfolio decisions and asset prices by altering the risk appetite of investors (Fratzscher et al. 2018; Plakandaras et al. 2022).

The spillover effects of UMPs have gained relevance, particularly concerning their impact on emerging market economies (EMEs). Concerns have been raised about the potentially more severe spillover effects on EMEs compared to advanced economies (AEs) due to factors like uncoordinated monetary policies, interest rate differentials and vulnerability to sharp capital flows (Lavigne et al. 2014; Estrada et al. 2016; Tillmann et al. 2019). Moreover, countries with less developed equity exchanges are most likely to hold US securities for liquidity purposes, thus making these markets susceptible to cross-border transmission spillovers (Anyikwa and Phiri 2023).

For the case of Africa, several frontier markets have experienced ‘bubble-like’ behaviour and major ‘sell-off’ since the 2007–2008 sub-prime crisis. For instance, Anyikwa and Le Roux (2020) find that African frontier markets such as those in Botswana, Egypt, Côte d’Ivoire, Kenya, Mauritius, Morocco, Namibia, Nigeria, South Africa and Zambia experienced market slumps of between 16% and 52% after most of these markets experienced then-record high equity prices. Ben Yaala and Henchiri (2023) as well as Siyou and Bene (2023) further note some of these equity markets, such as in Botswana, Egypt, Kenya, Mauritius, Morocco, Nigeria, South Africa and Tunisia, experienced some ‘recovery’ after intervention by US monetary policies via quantitative easing (QE), although these exchanges experienced market slumps subsequent to the 2014 ‘taper tantrum’ by US monetary authorities. More recently, several African equity markets, such as those in Mauritius, Morocco, Namibia, Kenya, Nigeria, Tanzania, Tunisia, Ghana, Zambia and Botswana, experienced contractions in stock markets of between 6.5% and 21% during the COVID-19 pandemic (Takyi and Bentum-Ennin 2021) and have since experienced record highs, particularly following the outbreak of the Ukraine-Russia war. The cumulation of these developments raises an important policy question of ‘the extent to which US UMP is responsible for the ‘bubble-burst’ cycles observed in African equity markets’.

Unfortunately, with the exception of South Africa, not much empirical attention has been paid to quantifying the impact of US UMP on African equities, and notably most of these previous studies include African data as part of larger panel of developing and emerging economies without appropriately accounting for heterogeneities in the sample (see Appendix A for summary of previous studies). Moreover, these previous studies present contradictory results, with some works finding a positive effect (Bowman et al. 2015; Fratzscher et al. 2018; Kabundi et al. 2020; Meszaros and Olson 2020; Bhattarai et al. 2021; Abdullah and Hassanien 2022), others a negative effect (Lim et al. 2014; Estrada et al. 2016; Anaya et al. 2017; Gupta et al. 2017; Apostolou and Beirne 2019; Kalu et al. 2020; Ono 2020; Yildirim and Ivrendi 2021), whilst the study by Ntshangase et al. (2023) finds insignificant effects. These features of the literature warrant further investigation into the subject matter.

A major concern from the previous literature is that event-based studies and VAR estimates are commonly used to quantify the impact of US UMP on African equity markets. Specifically, event studies face difficulties in choosing ‘an event window’ and can only capture a ‘small number of policy announcements’ whilst traditional and VAR-type methods produce constant coefficient estimates which cannot distinguish between interdependence and contagion effects within financial markets (Rigobon 2019). To circumvent these issues, Diebold and Yilmaz (2009, 2012) devise a connectedness and spillovers framework which relies on the rolling window regressions of the forecast error variance decomposition (FEVD) of a VAR-type model to examine time-varying system-wide connectedness and market-specific net spillover effects amongst a group of financial variables. More recently, Baruník and Křehlík (2018) suggest that the spillovers and connectedness effects can be further disintegrated into different frequency spectrums, which is useful for capturing differences in the heterogenous behaviours of investors and policymakers over different horizon periods. However, since these time-frequency connectedness frameworks only give information on the direction of net spillover effects and not on the ‘sign’ (negative or positive) of these spillovers, we also employ the wavelet coherence method of Torrence and Compo (1998) which uses phase dynamics to identify the ‘sign’ and ‘causal direction’ of the spillover effect in a time-frequency plane. Altogether, these methods allow us to test the following hypothesis:

H1. 

The impact of US UMP on African equity markets is not homogenous across different time-varying and frequency-varying scales.

To capture US monetary policy stance, we use the SSR of De Rezende and Ristiniemi (2023) which is an encompassing measure of the policy announcement dummies; bond yields; US Treasuries, debt and mortgage-backed securities purchases; and other US Federal balance sheet measures of UMP used in previous studies. The SSR uses components of the yield curve to capture the quantitative easing (QE) and quantitative tightening (QT) policies at a hypothetical negative interest rate environment below the lower-bound term structure. During normalization periods, the SSR converges to the Federal Reserve Rate (FFR), and then assumes negative values during periods of UMP. Moreover, the SSR captures both ‘policy announcements’ (i.e., forward guidance) and ‘policy actions’ (i.e., actual purchases of large-scale assets). These features of the SSR, in conjunction with our time-frequency estimation techniques, allow us to test the following three hypotheses:

H2. 

US ‘QE’ and ‘QT’ policy measures exert different spillovers and connectedness effects on African equity markets.

H3. 

US ‘conventional’ and ‘unconventional’ monetary practices exert different spillovers and connectedness effects on African equity markets.

H4. 

US ‘policy announcements’ and ‘policy actions’ exert different spillovers and connectedness effects on African equity markets.

We also use more recent time series and focus on equity markets in 11 African countries/regions (i.e., Botswana, BRVM, Egypt, Kenya, Mauritius, Morocco, Namibia, Nigeria, South Africa, Tanzania, Tunisia) which have the largest market capitalizations in the continent (https://nairametrics.com/2023/12/09/top-10-largest-stock-markets-in-africa-based-on-market-capitalization/ accessed on 31 March 2024). Notably, these countries have different levels of economic development (with South Africa, Botswana, Namibia and Mauritius being classified as high-middle income countries), resource abundance (with South Africa, Botswana and Nigeria being resource-rich countries), and financial systems (with Egypt, Morocco, Tunisia having listing requirements and banking systems which are compliant with Sharia law). Aizenman et al. (2016) and Choi et al. (2024) find that these economic and financial conditions can influence the impact of US UMP in developing and emerging equity markets. Based on these insights, we formulate the following hypothesis:

H5. 

The impact of US monetary policy conduct on African equities is dependent on levels of economic development, resource abundance and type of financial systems.

All in all, our study presents the latest effort amongst a group of recent studies which examine spillovers between UMP and international financial markets using the D-Y connectedness frameworks. Notably, these studies measured UMP using the SSR measure of Wu and Xia (2016) and Krippner (2020), and with the exception of Elsayed and Sousa (2022), include data covering the COVID-19 period in their analyses. For instance, Umar et al. (2023) and Choi et al. (2024) both use the traditional D-Y framework to demonstrate the dominance of US UMP in transmitting systemic shocks to agricultural commodities and Islamic (and to a lesser extent industrialized) equities, respectively. On the other hand, Elsayed and Sousa (2022) and Tiwari et al. (2024) opt to use the TVP framework of Antonakakis et al. (2020) and discover little spillover effect of UMP on cryptocurrency and oil markets, respectively. Collectively, these studies indicate that spillovers from US UMP towards international financial markets is more dominant compared to UMP practised by other industrialized economies. Moreover, the spillover effects of UMP have been found to differ across various crisis periods, with Umar et al. (2023) finding spillovers strongest during the GFC period, whereas Choi et al. (2024) and Tiwari et al. (2024) find stronger effects during the COVID-19 period. Based on these observations, we form our final hypothesis:

H6. 

The impact of US UMP conduct on African equities differs between the GFC and COVID-19 pandemic.

We extend the scope of investigation to African equities which have been recently speculated to be increasingly more vulnerable to global shocks than previously thought (Anyikwa and Phiri 2023). We also methodologically adopt the TVP parameter connectedness framework used by Elsayed and Sousa (2022) and Tiwari et al. (2024), and yet we follow Chatziantoniou et al. (2023) and incorporate it within the frequency connectedness framework to capture a wider spectrum of connectedness and spillover effects which could be hidden by the aggregation of cyclical components in traditional TVP frameworks. Notably, the TVP frequency connectedness has been extensively used in the literature to investigate connectedness amongst various financial markets (Cagli 2023; Huang et al. 2023; Polat et al. 2024; Shen et al. 2024) and yet has not been used in the context of investigating spillovers between US monetary policy and financial markets. For robustness’ sake, we also employ the wavelet coherence analysis to further determine the ‘sign’ on these spillover effects in time-frequency space. Lastly, in differing from previous studies which use the SSR measure of Wu and Xia (2016) and Krippner (2020), we opt for the more recent SSR measure of De Rezende and Ristiniemi (2023) which is not sensitive to the assumed numerical value of the lower bound and has more up-to-date coverage in comparison to other competing measures of SSR. These salient features enhance the precision in capturing US UMP dynamics, and yet these measures are seldom used in the literature.

Several novel findings emerge from our analysis. For instance, whilst our results generally concur with those of the prevailing literature which advocates for stronger connectedness and spillover effects during periods of UMP compared to normalization periods (Elsayed and Sousa 2022; Umar et al. 2023; Choi et al. 2024; Tiwari et al. 2024), our findings further suggest that low-frequency spillovers from US monetary policy to African equity markets are most heightened during US policy announcements of intentions to transition from conventional to UMP (i.e., 2008 and 2020) and vice versa from UMP to normalization (2014 and 2021). Moreover, during periods of UMP, QT effects are much stronger than QE, particularly during the COVID-19 pandemic. Overall, these findings imply that US policy announcements around the ‘lower bound region’ compromise market efficiency in African exchanges through equity returns and increase portfolio risks through heightened volatility. However, during periods of normalization experienced subsequent to the Ukraine-Russia war, the US transmit little policy effects towards African equities, which retain their hedging properties and their informational efficiency. These findings are novel for most countries in our study and are relevant for international investors who have included African equities in their portfolios. Moreover, our findings can assist market regulators to discern the sources of financial instability and implement appropriate policy solutions aimed at strengthening African markets.

The rest of this paper is organized as follows: Section 2 deals with the literature review. Section 3 describes the data and empirical framework used to address the objective of this paper. Section 4 presents and analyses the results while Section 5 provides the conclusion and recommendations.

2. Methodology

We begin by outlining our empirical method, which follows three steps. Firstly, we derive the stock returns and volatility. Secondly, we describe the frequency connectedness and wavelet coherence approach, which is then applied in the third step. These empirical frameworks are discussed below.

2.1. Return and Conditional Volatility

We first compute the daily stock return as a natural logarithm of daily closing stock price as follows: $r_t=\ln \left({\displaystyle \frac{P_t}{P_{t-1}}}\right)\times 100$, with $P_t$ representing the closing stock price at time $t$ and $t-1$. Thereafter, we follow the univariate generalized autoregressive conditional heteroscedasticity (GARCH) model developed by Bollerslev et al. (1988) to generate the conditional volatility of stock return. Specifically, we utilized the GARCH (1,1) model which follows the autoregressive (AR) process as follows:

$$r_{it}=\mu +{\phi r}_{it-1}+{\epsilon }_t{\epsilon }_t\left|{\Omega }_{t-1}\right.~N(0,h_t)i=1,2$$

(1)

$$h_{it}^2=\mu +\alpha {\epsilon }_{it-1}^2+{\rho h}_{it-1}^2$$

(2)

Equation (1) is the return equation based on AR(1) and Equation (2) is the conditional volatility process, where $r$ denotes the return from each market, and $\alpha$ and $\rho$ are the coefficient estimates for the ARCH and GARCH parameters. The conditional variance, $h_{it}^2$ provides a measure of the volatility of each stock return. In the second step, we apply the frequency connectedness to the returns and volatility to assess the connectedness and spillover.

2.2. TVP Frequency Connectedness Approach

We use the TVP-VAR-based frequency connectedness approach which is a combination of the frameworks of Antonakakis et al. (2020) and Baruník and Křehlík (2018). The application of this approach is motivated in part by the ability of the model to capture spillovers and connectedness at different frequencies, which is an advantage over the time-domain approach of Diebold and Yilmaz (2012). Importantly, the model decomposes the aggregate spillovers into short duration (high frequency) and long duration (low frequency) which is beneficial for diversification, investment, and hedging strategies (Agyei et al. 2023). However, we follow the same TVP-VAR-based frequency connectedness as in Chatziantoniou et al. (2023) and expressed the TVP-VAR(1) model as follows:

$$Y_t={{\varphi }_{t}Y}_{t-1}+{\in }_t{ϵ}_t\left|{\Omega }_{t-1}\right.~N(0,{\Sigma }_t)$$

(3)

$$vec\left({\varphi }_t\right)=vec\left({\varphi }_{t-i}\right)+{\upsilon }_t{\nu }_t\left|{\Omega }_{t-1}\right.~N\left(0,R_t\right)$$

(4)

where $Y_t$, $Y_{t-1}$ and ${\in }_t$ are $N\times 1$ dimensional vectors for stock market returns/volatility/SSR at time $t$ and $t-1$, and the white noise, respectively. The parameters ${\varphi }_t$ and $\Sigma$ are $N\times N$ dimensional matrices of time-varying coefficients and variance-covariances while $vec\left({\varphi }_t\right)$ and ${\upsilon }_t$ are $N^2\times 1$ dimensional vectors and $R_t$ is an $N^2\times N^2$ dimensional covariance matrix.

The TVP-VAR model can be transformed into a vector moving average (VMA) as $Y_t={\sum }_{i=0}^{\infty }{\psi }_{it}{\mu }_{t-i}$, with ${\psi }_{it}$ defined as the $N\times N$ dimensional matrix. We applied the TVP-VMA to estimate the H-step-ahead generalised forecast error variance decomposition (GFEVD) which is computed as follows:

$${\Theta }_{ijt}(H)={\displaystyle \frac{{{(\Sigma }_t)}_{jj}^{-1}{\sum }_{h=0}^H({\left({{\psi }_h\Sigma )}_{ijt}\right)}^2}{{\sum }_{h=0}^H{\left({\psi }_h\sum {{\psi }^{\prime }}_h\right)}_{ii}}}$$

(5)

$${\tilde{\Theta }}_{ijt}(H)={\displaystyle \frac{{\Theta }_{ijt}(H)}{{\sum }_{k=1}^N{\Theta }_{ijt}(H)}}$$

(6)

where ${\tilde{\Theta }}_{ijt}(H)$ is the contribution of $j$ market to the forecast error variance of $i$ market at horizon H. Since the row contributions do not sum up to 1, each entry of the variance decomposition matrix ${\tilde{\Theta }}_{ijt}\left(H\right)$ is normalised as ${\sum }_{i=1}^N{\tilde{\Theta }}_{ijt}(H)=1$ and ${\sum }_{j=1}^N{\sum }_{i=1}^N{\tilde{\Theta }}_{ijt}(H)=N$. Based on Equation (6), we compute the total connectedness index (TCI) which measures the degree of connectedness as follows:

$${TCI}_t\left(H\right)={\displaystyle \frac{{\sum }_{i,j=1,i\ne j}^N{\tilde{\Theta }}_{ijt}(H)}{N}}\ast 100$$

(7)

The total directional connectedness or the spillovers transmitted by market $i$ to all $j$ markets, and spillovers received by market $i$ from all $j$ markets, are given as the following:

$${TO}_{it}\left(H\right)={\sum }_{i=1,i\ne j}^N{\tilde{\Theta }}_{ijt}\left(H\right)$$

(8)

$${FROM}_{it}\left(H\right)={\sum }_{j=1,i\ne j}^N{\tilde{\Theta }}_{ijt}\left(H\right)$$

(9)

The net directional connectedness or spillover is the difference between the “TO” and “FROM” which is given by the following equation:

$${NET}_{it}\left(H\right)={TO}_{it}\left(H\right)-{FROM}_{it}\left(H\right)$$

(10)

where $i$ market is a net transmitter if ${NET}_{it}>0$ or a net receiver if ${NET}_{it}<0$. That is, a positive value implies that $i$ market is a net transmitter while a negative value implies that the market is a net receiver.

However, the frequency-domain spillover and connectedness dynamics can be revealed through spectral representation of the variance decomposition based on frequency response to shocks. We assume that the moving average coefficients ${\psi }_h$ computed at $h=1,2,\dots ,H$ horizons are approximately $\psi \left(L\right)$. The frequency response function derived from the Fourier transformation of the coefficients ${\psi }_h$ is expressed as $\psi \left(e^{-i\omega }\right)={\sum }_{h=0}{e}^{-i\omega h}{\psi }_h$, where $i=\sqrt{-1}$. The spectral density of $Y_t$ at frequency $\omega$ is defined as follows:

$$S_Y\left(\omega \right)={\sum }_{h=-\infty }^{\infty }E(Y_t{Y\prime }_{t-h})e^{-i\omega h}={\psi }_t\left(e^{-1\omega h}\right){\Sigma }_t{\psi \prime }_t\left(e^{+i\omega }\right)$$

(11)

The power spectrum $S_Y\left(\omega \right)$ describes the distribution of the variance of $Y_t$ over the frequency component $\omega$. The frequency GFEVD is a combination of the spectral density and GFEVD. We normalise the frequency GFEVD as follows:

$${\Theta }_{ijt}(\omega )={\displaystyle \frac{{{(\Sigma }_t)}_{jj}^{-1}{\left|{\sum }_{h=0}^{\infty }{\left({\psi }_t\left(e^{-i\omega h}\right){\Sigma }_t\right)}_{ijt}\right|}^2}{{\sum }_{h=0}^{\infty }{\left({\psi }_t\left(e^{-i\omega h}\right){\Sigma }_t\right)}_{ii}}}$$

(12)

$${\tilde{\Theta }}_{ijt}\left(\omega \right)={\displaystyle \frac{{\Theta }_{ijt}\left(\omega \right)}{{\sum }_{k=1}^N{\Theta }_{ijt}\left(\omega \right)}}$$

(13)

where ${\tilde{\Theta }}_{ijt}\left(\omega \right)$ represents the portion of the spectrum of the $i$ market at a given frequency $\omega$ that is caused by shocks in the $j$ markets. However, we assess spillover across different frequencies (specifically for short run and long run) rather than at a given frequency; the variance decomposition on a frequency band $d$ is given as $d=\left(a,b\right):a,bϵ\left(-\pi ,\pi \right),a<b,$ and is defined as follows:

$${\tilde{\Theta }}_{ijt}(d)={\int }_a^b{\tilde{\Theta }}_{ijt}\left(\omega \right)d\omega$$

(14)

We compute the frequency connectedness measures to provide information on spillover at a certain frequency range $d$ which are similar the to their time-domain counterpart as follows:

$${TCI}_t\left(d\right)={\displaystyle \frac{{\sum }_{i,j=1,i\ne j}^N{\tilde{\Theta }}_{ijt}(d)}{N}}\ast 100$$

(15)

$${TO}_{it}\left(d\right)={\sum }_{i=1,i\ne j}^N{\tilde{\Theta }}_{ijt}\left(d\right)$$

(16)

$${FROM}_{it}\left(d\right)={\sum }_{j=1,i\ne j}^N{\tilde{\Theta }}_{ijt}\left(d\right)$$

(17)

$${NET}_{it}\left(d\right)={TO}_{it}\left(d\right)-{FROM}_{it}\left(d\right)$$

(18)

where Equations (15)–(17) represent the total connectedness, directional connectedness “TO” and “FROM”, and net directional connectedness at a given frequency band $d$, respectively. Following a study by Chatziantoniou et al. (2023), we decomposed the total frequency band into short run (high frequency) and long run (low frequency).

2.3. Wavelet Coherence

Lastly, we applied the wavelet approach to simultaneously analyse the returns and volatility of African stock markets in response to the UMP in the US across frequency and time domains. One key advantage of this approach is that it offers a way of evaluating the localised variations of power within time series and simultaneously analyses the frequency spillovers between the time series variables at different time periods. Another advantage is that wavelets efficiently adapt to abrupt changes often observed in non-stationary series (Torrence and Compo 1998). We employed the wavelet coherence (WTC) under Morlet’s specification to analyse the connectedness and spillover effects across time and frequency domains. The wavelet is defined as a function of time $t$, and scale $s$ as follows:

$${\psi }_{u,s}\left(t\right)={\displaystyle \frac{1}{\sqrt{s}}}\psi \left({\displaystyle \frac{t-u}{s}}\right)$$

(19)

where the wavelet function $\psi (t)$ is defined over the real axis. The parameters $t$, $s$, ${\displaystyle \frac{1}{\sqrt{s}}}$ and $u$ respectively represent the time position (translation parameter), scale (dilation parameter related to the frequencies), normalisation factor which ensures that the unit variance of the wavelet ${‖{\psi }_{u,s}‖}^2=1$, and the location parameter which indicates the position of the wavelet. We followed the Morlet wavelet which is given by the following equation:

$${\psi }^M\left(t\right)={\pi }^{-1/4}{e}^{i{\omega }_{C}t}{e}^{-1/2{\alpha }^2}$$

(20)

The Morlet wavelet is a complex sine wave with frequency and time given by ${\omega }_C$ and $t$, respectively. A good balance between frequency and time localisation is obtained by setting ${\omega }_0=6$ (Aguiar-Conraria and Soares 2014). We applied the continuous wavelet transform (CWT) for a wavelet $\psi$ which is defined as the convolution of a series as follows:

$$W_x\left(u,s\right)={\int }_{-\infty }^{\infty }x\left(t\right){\displaystyle \frac{1}{\sqrt{s}}}\psi \ast {\displaystyle \frac{\overline{(t-u)}}{s}}dt$$

(21)

where the bar represents the complex conjugate, and $W_x\left(u,s\right)$ is given by projecting the specific wavelet $\psi$. The amplitude of a given time series or its variance at a given time and scale is measured by the wavelet power spectrum (WPS) as ${WPS}_p\left(u,s\right)={\left|W_p(u,s)\right|}^2,$ which measures the variance distribution of the series in the time scale and frequency plane.

The wavelet coherence measures the strength of the relationship between two time series $x\left(t\right)$ and $y(t)$ with the wavelet transforms $W_x(u,s)$ and $W_y(u,s)$ and the cross-wavelet spectrum $W_{xy}\left(u,s\right)=W_x\left(u,s\right)W_y^{\ast }\left(u,s\right),$ is defined as follows:

$$R_{xy}^2\left(u,s\right)={\displaystyle \frac{{\left|S(s^{-1}{W}_{xy}\left(u,s\right))\right|}^2}{S(s^{-1}{\left|W_x\left(u,s\right)\right|}^2)S(s^{-1}{\left|W_y\left(u,s\right)\right|}^2)}}$$

(22)

where S represents the smoothing operator over time and scale, with $0\le R^2\left(u,s\right)\le 1.$ A high value of $R^2$ indicates a higher level of co-movement between the two variables while a low value of $R^2$ indicates a lower correlation between the variables. The graphical plot of the wavelet coherence provides information on the relationship between the variables in the time and frequency space.

3. Data

We analyse daily closing stock prices to calculate returns for eleven major African stock markets, including Botswana, Egypt, Kenya, Mauritius, Morocco, Namibia, Nigeria, South Africa, Tanzania, Tunisia, and the Bourse Regionale des Valeur Mobilieres (BRVM) representing eight West African Economic and Monetary Union (WAEMU) countries (i.e., Benin, Burkina Faso, Côte d’Ivoire, Guinea-Bissau, Mali, Niger, Senegal, and Togo). We use US shadow short rates (SSR) as a proxy for unconventional monetary policy, spanning from 1 January 2007 to 31 March 2023. Data sources include Investing.com for stock market data and Rafael De Rezende’s website for our measure of US SSR (https://www.rafaelbderezende.com/shadow-rates accessed on 31 March 2024).

Table 1. Descriptive statistical properties.

Panel A: Returns	Botswana	BRVM	Egypt	Kenya	Mauritius	Morocco	Namibia	Nigeria	RSA	Tanzania	Tunisia	SSR
Mean	0.007	0.033	−0.033	0.008	0.023	0.007	−0.015	0.060	0.017	0.032	0.051	−1.323
Std. Dev.	0.412	0.806	1.832	0.839	0.702	0.763	3.184	1.081	1.221	1.178	0.526	2.763
Skewness	0.972	0.151	−2.367	0.341	−0.701	−0.630	0.875	0.062	−0.184	0.573	−0.753	1.227
Kurtosis	54.656	7.665	16.849	15.056	43.770	13.275	1641.750	12.727	8.279	57.817	14.672	3.444
Jarque-Bera	660,580	5403	52,955	36,047	411,386	26,493	664,000,000	23,391	6922	1538	743,153	34,239
ADF	−33.807 ***	−40.165 ***	−10.237 ***	−32.055 ***	−46.519 ***	−36.313 ***	−102.321 ***	−32.443 ***	−41.315 ***	−36.395 ***	−36.501 ***	−11.268 ***
PP	−57.865 ***	−59.090 ***	−58.905 ***	−40.005 ***	−48.519 ***	−46.622 ***	102.850 ***	−47.057 ***	−55.293 ***	−68.291 ***	−47.118 ***	−92.204 ***
KPSS	0.30	0.18	0.19	0.23	0.29	0.15	0.15	0.14	0.08	0.13	0.32	0.26
LB(10)	235.010 ***	95.541 ***	302.034 ***	89.911 ***	44.767 ***	60.280 ***	12.137	61.305 ***	84.100 ***	76.046 ***	58.992 ***	--
LB2(10)	1165.30 ***	818.37 ***	1312.20 ***	1182.30 ***	1832.20 ***	2792.10 ***	1099.20 ***	701.66 ***	5613.00 ***	2566.60 ***	2049.90 ***	--
ARCH test(10)	1037.68 ***	586.78 ***	616.598 ***	1174.23 ***	1137.69 ***	1396.98 ***	1189.50 ***	623.978 ***	1579.57 ***	1712.51 ***	1356.15 ***	--
Panel B: Volatility	Botswana	BRVM	Egypt	Kenya	Mauritius	Morocco	Namibia	Nigeria	RSA	Tanzania	Tunisia	--
Mean	0.144	0.572	2.217	0.478	0.406	0.451	41.995	0.847	1.344	1.992	0.211	--
Std. Dev.	0.525	0.606	3.711	1.004	1.447	0.791	705.151	1.716	1.908	8.991	0.433	--
Skewness	13.278	8.260	6.306	18.689	8.580	13.174	27.239	18.146	7.199	12.333	12.992	--
Kurtosis	229.593	118.999	49.479	514.406	93.139	257.734	836.802	451.222	78.076	201.097	246.654	--
Jarque-Bera	12864953	3393239	573265	64988400	2081033	16210080	173000000	49982027	1444346	9849827	14840476	--
ADF	−25.191 ***	−36.150 ***	−8.030 ***	−19.993 ***	−8.427 ***	−13.276 ***	−17.263 ***	−19.096 ***	−9.879 ***	−20.665 ***	−25.385 ***	--
PP	−19.850 ***	−36.283 ***	−7.750 ***	−15.077 ***	−11.323 ***	−18.319 ***	−12.745 ***	−17.667 ***	−8.617 ***	−11.930 ***	−23.208 ***	--
KPSS	0.09	0.28	0.33	0.36 *	0.37 *	0.31	0.12	0.37 *	0.41 *	0.26	0.28 *
LB(10)	148.09 ***	107.060 ***	39.694 ***	95.144 ***	91.010 ***	101.750 ***	11.403	85.576 ***	31.356 ***	46.558 ***	74.586 ***	--
LB2(10)	3.274	9.467	21.344 **	21.790 **	64.846 ***	31.940 ***	0.007	27.120 ***	47.139 ***	0.416	5.361	--
ARCH test(10)	3.237	9.221	21.339 **	21.307 **	61.859 ***	31.787 ***	0.007	27.292 ***	44.491 ***	0.412	5.354	--

Note: ***, **, * denotes significance at 1%, 5%, and 10%, respectively. The ADF and PP respectively represent the Augmented Dicky-Fuller and Philip-Perron test. LB is the Ljung-Box test for serial correlation on standard residual and squared-standard residual, while the ARCH test is autoregressive conditional heteroskedasticity. RSA is Republic of South Africa while SSR is the shadow short rate.

presents descriptive statistics for African stock market returns (Panel A) and conditional volatility (Panel B) alongside US SSR. In Panel A, Nigeria, Tunisia, BRVM, and Tanzania exhibit the highest average daily returns, while Egypt and Namibia perform relatively lower. The average daily SSR is negative at −1.32%, and volatility is highest in Namibia, Egypt, South Africa, and Tanzania. Most returns are positively skewed with leptokurtic distributions, rejecting normality in all cases. The ADF, PP and KPSS tests confirm stationarity in the series, and Ljung-Box tests reveal serial correlation and heteroskedasticity, supporting the use of a GARCH model. In Panel B, Namibia, Egypt, Tanzania, and South Africa show the highest conditional volatility, consistent with unconditional volatility results in Panel A. Unit root tests confirm the stationarity of conditional volatility series, and LB and ARCH tests find no further evidence of serial correlation and heteroskedasticity, confirming the adequacy of the GARCH (1,1) model. Overall, these results support the use of the standard GARCH model to extract the conditional volatility of stock returns and volatility.

4. Empirical Results

4.1. Static TVP Frequency Connectedness Analysis

We begin by presenting our findings from the static Time-Varying Parameter (TVP) frequency connectedness analysis which decomposes aggregated spillover effects into short-run and long-run frequency bands. Following the approach of Chatziantoniou et al. (2023), we classify short-run and long-run as high and low frequency bands (1–5 days and 6 days—infinity period cycles). Our focus is on net spillover effects, particularly identifying net transmitters and receivers of systemic shocks.

The full results of the connectedness table are detailed in Appendix B and Appendix C, with net transmitters and receivers summarized in

Table 2. Summary of net transmitters and receivers at different frequencies.

	Net Receivers	Net Transmitters
Panel A: Returns spillovers
Total	BRVM, Egypt, Kenya, Nigeria, Tanzania, US_SSR	Botswana, Mauritius, Morocco, Namibia, RSA, Tunisia
SR	Botswana, BRVM, Egypt, Mauritius, Morocco, Nigeria, Tanzania, Tunisia	Kenya, Namibia, RSA, US_SSR
LR	BRVM, Egypt, Kenya, Nigeria, US_SSR	Botswana, Mauritius, Morocco, Namibia, RSA, Tanzania, Tunisia
Panel B: Volatility spillovers
Total	Botswana, BRVM, Kenya, Mauritius, Morocco, Nigeria, RSA, US_SSR	Egypt, Namibia, Tanzania, Tunisia
SR	Botswana, BRVM, Kenya, Morocco, Tanzania, Tunisia	Egypt, Mauritius, Namibia, Nigeria, RSA, US_SSR
LR	Botswana, BRVM, Kenya, Mauritius, Morocco, Nigeria, RSA, US_SSR	Egypt, Namibia, Tanzania, Tunisia

Notes: SR—Short-run or high-frequency, LR—Long-run or low-frequency.

. Three key conclusions are drawn. Firstly, the US Shadow Short Rate (SSR) is a net transmitter (receiver) of systemic shocks at higher (lower and total) frequencies. Secondly, BRVM, Egypt, and Namibia (Botswana, BRVM, and Kenya) are net receivers (transmitters) of return spillovers across all frequencies, while volatility spillovers consistently involve Botswana, BRVM, and Kenya (Egypt and Namibia). The remaining equity markets switch between net receivers and transmitters of spillovers across different frequencies. Lastly, during high frequency connectedness, when the US SSR is a net transmitter, Botswana, BRVM, Egypt, Mauritius, Morocco, Nigeria, Tanzania and Tunisia (Botswana, BRVM, Kenya, Morocco, Tanzania, Tunisia) are net receivers of return (volatility) shocks, with other equity markets as net recipients.

Our static analysis holds interesting implications. For instance, without considering frequencies, reliance on ‘total’ TVP connectedness results might lead to the incorrect assumption that the US SSR does not transmit shocks to African equities. The finding that US monetary policy has spillover effects at high frequencies challenges the decoupling hypothesis for African equities in the face of global shocks. However, in similarity to Sugimoto et al. (2014), Boako and Alagidede (2016, 2018) and Mensah and Alagidede (2017), we note that these effects dissipate over long-run frequencies, with African markets being more influenced by spillovers from other African equities. Additionally, our findings suggest South Africa is the only market resilient to both return and volatility net spillovers from US monetary policy during higher frequencies, contradicting previous findings of Kabundi et al. (2020) who found that US UMP affects the South African stock market. Moreover, we observe that the impact of US monetary policy conduct on African equities is not dependent on levels of economic development, resource abundance and type of financial systems as speculated by Aizenman et al. (2016) and Choi et al. (2024). Nonetheless, further dynamic analysis may be needed to confirm these results across different time periods.

4.2. Dynamic TVP Frequency Connectedness Analysis

Next, we conduct our dynamic analysis by firstly examining the time-varying total connectedness index (TCI) across different frequencies. Figure 1 and Figure 2 depict the estimates for returns and volatility series, respectively, with ‘black’ representing total, ‘red’ short-run, and ‘green’ long-run. Interestingly, heightened returns and volatility connectedness are observed at all frequencies during four specific time points: 2009, 2013, 2020, and 2021. At first glance, these periods would seem related to crisis periods such as the global financial crisis and COVID-19 as speculated in the current literature (Elsayed and Sousa 2022; Umar et al. 2023; Choi et al. 2024; Tiwari et al. 2024), and yet the timing of this heightened connectedness appears to be linked to the policy announcements (as opposed to the actual LSAP) of the intention of the US Federal Reserve to change from conventional to unconventional practices and vice versa. For instance, the spikes in 2008 and 2013 coincide with the announcements of QE1 and the taper tantrum in the post-QE3 period, respectively. The 2020 and 2021 spikes relate to the announcement of QE4 in response to COVID-19 and the subsequent announcement of the QT process. In similarity to Choi et al. (2024) and Tiwari et al. (2024), we find that spillovers and connectedness are more pronounced during the COVID-19 period (as opposed to the GFC period), particularly around the tapering phase of UMP. Furthermore, higher frequency connectedness is dominant between 2013 and 2019 for returns series, corresponding to a period when the US Federal Reserve reverted to conventional monetary policy by raising the Federal funds rate, while low-frequency connectedness is predominant across all periods for volatility series.

We further analyse dynamic net directional spillovers for each market, aiming to identify whether individual markets act as net transmitters or receivers of systemic shocks during different periods of conventional and unconventional monetary practices. Time-varying net directional spillover index estimates for each market are plotted in Figure 3 and Figure 4 for returns and volatility series, respectively. Three key results stand out. Firstly, the most pronounced net receiver effects in individual markets occur during the 2009, 2013, 2020 and 2021 periods, particularly for the volatility series. These peak periods generally align with those identified in the time-varying Total Connectedness Index (TCI) and correspond to various announcements of QE and QT policies. Secondly, US monetary policy acts as a transmitter of systemic shocks of high frequency (low frequency) systemic shocks for the returns (volatility series) particularly during the announcements and implementation of QT policies in the 2013–2015 and 2021–2022 periods. Lastly, certain African markets that were mainly net transmitters during QE1–3 become net receivers in QE4, including BRVM, Egypt, Morocco, Nigeria, Tanzania, and Tunisia for returns, and Botswana, BRVM, Mauritius, Nigeria, South Africa, Tanzania, and Tunisia for volatility. This reflects the evolving vulnerability of African equities to global spillovers since the Global Financial Crisis (Agyei et al. 2023; Anyikwa and Phiri 2023; Urom et al. 2023).

4.3. Wavelet Coherence Analysis

We now present the findings from the wavelet coherence analysis performed between (i) the SSR and equity returns (Figure 5) and (ii) the SSR and equity volatility (Figure 6), for each African stock market. The wavelet coherency is represented in heatmaps which describe the phase-dynamics between the variables by providing information on the strength (represented by the colour contours) as well as the sign and direction of causality (represented by arrow orientation) between the series in time-frequency space. On one hand, the warmer (cooler) colours represent stronger (weaker) co-movements, whereas, on the other hand, the arrow orientation produces the following possible outcomes, namely, in-phase (positive) co-movements with SSR leading (lagging) stock returns/volatility as shown by ↑, , →, () or anti-phase/negative co-movements with SSR leading (lagging) stock returns/volatility as shown by ↓, , ← (). The 5% significance levels are denoted by the solid black lines surrounding the contours.

In line with the TVP-frequency connectedness analysis, the wavelet coherence plots reveal (i) greater connectedness and spillovers for volatility series than returns series (Umar et al. 2023), (ii) heightened effects during Unconventional Monetary Policy (UMP) and less during normalization periods (Elsayed and Sousa 2022; Umar et al. 2023; Choi et al. 2024; Tiwari et al. 2024), (iii) increased connectedness and spillover effects during the QE and QT policies implemented in response to the Global Financial Crisis and COVID-19 pandemic.

Furthermore, the wavelets offer insights into the ‘sign’ of the spillover which is important for determining whether US monetary policy stimulates or depresses African equity returns/volatility (Marfatia et al. 2021). For instance, during the QE1–3 period, we find mixed-phase dynamics, with the SSR exerting stimulating (supressing) effect on the returns for Botswana and Tunisia (Namibia) whilst increasing (decreasing) volatility for BVRM, Kenya, Morocco and South Africa (Mauritius, Namibia, Tanzania and Tunisia). Furthermore, during the taper-tantrum and periods eventually leading to normalization, we find that unwinding of the Federal Reserve’s balance sheets had a stimulating (supressing) effect on the returns for Kenya and Tunisia (Namibia and South Africa) whilst increasing (decreasing) volatility for BVRM, Namibia and Tanzania (South Africa). Lastly, during the COVID-19 pandemic, the in-phase or negative co-movements observed between the US SSR and most African equities implies that both returns and volatility in African markets increased in response to lowering of US interest rates below the zero-lower bound.

Overall, we find that US UMP had positive (negative) effects on volatility towards more (less) developed African stock exchanges during the GFC (Giovannetti and Velucchi 2013; Boako and Alagedede 2016) whilst exerting little effect on these equity markets during the normalization periods. However, during the COVID-19 period, most African equity markets were affected by US UMP, and this finding is in line with Anyikwa and Phiri (2023) and Urom et al. (2023) who similarly find contagion effects of global market shocks to a wider range of African stocks during the COVID-19 pandemic. These latter observations can be attributed to three factors. Firstly, African equities have received increasing investor attention over the last decade due to significant financial market reforms which have improved the accessibility and flexibility of trading on African exchange platforms (Boako and Aligedede 2018; Urom et al. 2023). Secondly, during the COVID-19 pandemic there was increased participation of investors in global equity markets due to opportunities presented by the lockdown which increased peoples’ appetites for trading online from home (Chiah and Zhong 2020; Zheng et al. 2022). Lastly, several Central Banks in developing countries have emulated the policy actions of the US Federal Reserve since the COVID-19 period and this has increased the pass-through effects of US monetary policy to domestic markets via the monetary policy transmission mechanism (Huertas 2022; Putniņš 2022).

5. Conclusions

We examine the impact of US UMP on equity returns and volatility of 11 frontier African markets using the TVP frequency connectedness and wavelet coherence applied to daily data of US SSR and equity returns/volatility spanning from 1 January 2007 to 31 March 2023. Notably, both models confirm heightened connectedness during periods of crisis and the unconventional responses of US monetary policy to these crises with stronger spillovers observed during the COVID-19 periods compared to the GFC crisis. However, whilst the frequency connectedness approach is restricted to providing information on net directional spillovers of UMP on equity prices, the wavelet coherence analysis further provides information on the ‘sign’ of the spillover which is important for evaluating whether African stock markets are positively or negatively affected by US monetary policy. To this end, the wavelets reveal that whilst the QE1–QE3 and ‘operation twist’ conducted during the GFC had increased volatility in more developed African equities, the fourth round of QE implemented in response to COVID-19 increased both returns and volatility in most African equities during this period

The main conclusion of our study is that African stock exchanges are not ‘decoupled’ from global shocks experienced during crisis periods, and the observed impact of UMP on African equity returns and volatility has important implications. On one hand, the finding of significant correlations of UMP with African equities returns during crisis periods is a result in violation of the semi-weak form of market efficiency, which hypothesizes that publicly available information such as monetary policy announcements are immediately observed into equity price and cannot be used to attain abnormal profits. On the other hand, the time-varying spillovers from UMP to African equities volatilities is significant for risk management during crisis periods by investors who include African stock within their portfolio. Since African equities are susceptible to volatility contagion effects via US UMPs implemented during crisis periods, then UMPs deteriorated the attractiveness of African equities as a safe haven, hence encouraging long-term/safe investors to decrease their holdings of African equities and encouraging speculators to create short-term holdings of these equities to make quick profit.

Policymakers and market regulators should be interested in our results as they advocate for the use of macroprudential policies in mitigating the risks associated with cross-border transactions during crisis periods. This is more concerning in the post-COVID-19 period where there has been a notable increase in the participation of international investors, with several African equities having experienced 5–10-year record highs within the 2021–2022 period. Whilst the increased participation of international investors in African markets is most welcome, policymakers should safeguard themselves against sharp reversals of capital flows in the form of macroprudential policies aimed at mitigating systemic risk and preventing the build-up of financial imbalances.

Future research could explore the long-term impacts of US unconventional monetary policy (UMP) on African markets, particularly in the post-COVID-19 era. This includes investigating how increased foreign investor participation has reshaped African equities and the potential for sustained volatility transmission. Furthermore, examining the effectiveness of macroprudential policies in mitigating systemic risks from UMP spillovers would be valuable, particularly as African markets become more integrated into global financial systems. Comparative studies on how different African countries manage these risks could provide insights for improving financial stability.

Moreover, studies could focus on the role of information asymmetry in African markets, particularly in the context of UMP and market efficiency. Analysing spillover effects beyond equities, such as bonds and foreign exchange, would offer a more comprehensive view of UMP’s influence. Finally, research on digital and financial innovations, such as fintech, could reveal how these advancements might act as buffers against external shocks, helping African markets decouple from global crises and enhancing their resilience to future monetary policy shifts.