Modeling the Impact of G7 Interest Rates on BRICS Equity Markets: A DLNM Approach Using MSCI Indices

Abstract

This study examines the dynamic and nonlinear effects of global interest rate (based on the G7 market) shocks on equity markets in BRICS countries. A World Interest Rate (WIR) index is constructed using principal component analysis of short-term interest rates from developed economies. The analysis applies Distributed Lag Nonlinear Models (DLNMs) to evaluate the temporal response of each market to positive and negative WIR shocks over a six-period horizon. The results reveal notable asymmetries and heterogeneity. Brazil and Russia experience stronger reactions to negative shocks, while India and China show milder or delayed effects. South Africa stands out for its persistent and symmetric sensitivity to both types of shocks, suggesting deeper exposure to global financial cycles. The DLNM framework allows for a nuanced interpretation of exposure-lag relationships, offering new insights into how global monetary conditions affect emerging markets. These findings highlight that financial integration does not imply uniform vulnerability across countries and that global liquidity shocks can trigger diverse equity market responses. This paper contributes to the literature on international financial linkages and provides relevant implications for investors and policymakers managing portfolio exposure or economic risk in emerging markets.

1. Introduction

The relationship between interest rates and equity prices has long been a central concern in macro-finance. Interest rates, as a measure of the time value of money, are widely recognized as one of the most influential macroeconomic variables affecting stock market valuations (Mishkin, 2008). Changes in interest rates directly influence borrowing costs, corporate profitability, and investor expectations, thereby altering the valuation of firms and shaping portfolio decisions (Alam & Uddin, 2009). While most of the empirical literature documents a negative relationship between interest rate movements and stock returns (Bashir & Hassan, 2017; Bulmash & Trivoli, 1991; Abdullah & Hayworth, 1993), other studies also identify lagged or even positive effects under certain macro-financial conditions (Geske & Roll, 1983).

In an increasingly globalized financial system, emerging markets are no longer isolated from international liquidity cycles. The transmission of global shocks to local markets occurs through capital flows, investor sentiment, and macro-financial linkages (Calvo et al., 1996). Under growing financial integration, investors are now able to diversify internationally, and capital markets in developing economies become more sensitive to global financial conditions (Eichengreen & Gupta, 2015; Bahadir & Lastrapes, 2015). Consequently, understanding how emerging equity markets respond to global interest rate shocks has become vital for both investors and policymakers.

This paper aims to investigate the dynamic and nonlinear response of BRICS equity markets to global monetary shocks, as proxied by a synthetic World Interest Rate (WIR) index. We construct a WIR index derived from the 10-year sovereign bond yields of the G7 economies (the United States, Germany, Japan, the United Kingdom, France, Italy, and Canada). While this index reflects global financial conditions through the influence of G7 markets, we clarify that it does not represent all global economies. Therefore, although we consistently refer to it as the “WIR” index throughout this manuscript, it is based on the influence of G7 markets. The WIR is constructed using principal component analysis over the short-term interest rates of major developed economies, capturing common trends in global liquidity conditions and central bank policies. While previous research has evaluated the effect of the U.S. Federal Funds Rate or developed-country yields in isolation, our approach synthesizes a broader global signal, aligning with the methodology of Bekaert and Harvey (2000) and Mishkin (2008).

To capture the complexity of shock transmission over time and under different market conditions, we employ a flexible modeling strategy based on Distributed Lag Nonlinear Models (DLNMs). While DLNMs have been extensively applied in fields such as epidemiology and environmental sciences, their application in financial economics remains relatively scarce. Our contribution is to extend this framework to analyze how BRICS equity markets respond to lagged shocks in the G7-based WIR. This approach allows us to evaluate both the magnitude and timing of the responses, as well as potential asymmetries between positive and negative shocks (Amarasinghe, 2015).

The contribution of this study is threefold. First, it provides updated empirical evidence on how systemic global financial forces affect the stock markets of BRICS countries—Brazil, Russia, India, China, and South Africa—via a time- and state-varying mechanism. Second, it introduces a novel application of DLNMs in financial research, filling a gap in the modeling of nonlinear, lagged responses to global shocks. Third, by focusing on emerging markets that collectively represent a significant portion of global GDP but remain underrepresented in equity benchmarks (Bekaert & Harvey, 2000), this study contributes to the debate on financial integration and the vulnerabilities of capital flows under global tightening cycles.

The remainder of this paper is structured as follows. Section 2 reviews the related literature on global interest rates and emerging equity markets. Section 3 presents the data and describes the empirical DLNM approach. Section 4 reports the main results for the BRICS countries. Section 5 concludes with a discussion of policy implications and directions for future research.

2. Literature Review

In recent decades, the analysis of global interest rate behavior and its impact on financial markets has gained increasing relevance, especially in the context of emerging economies. The literature has evolved from approaches focused on developed markets to a broader understanding of how global, regional, and idiosyncratic factors interact with macroeconomic and financial variables. In this context, recent studies have sought to identify the mechanisms of financial risk transmission through interest rates, their predictability in different stress scenarios, and their role as a vehicle for economic synchronization or divergence between countries. This review is organized into three thematic sections that address, respectively, (i) the link between interest rates and financial markets, (ii) the response of markets to macroeconomic fundamentals under different monetary regimes and levels of development, and (iii) the construction and dynamics of the world interest rate as an aggregate indicator of risk and global policy.

2.1. Macrofinancial Dynamics and Sensitivity of the BRICS to External Shocks

The analysis of the BRICS economies has gained increasing relevance given their active participation in global capital flows, their weight in global economic activity, and their differentiated exposure to external shocks. In this context, multiple studies have addressed monetary transmission mechanisms, the effects of interest rates, and vulnerability to global risk factors. Waheed et al. (2024) develop a monetary policy reaction function using a Bayesian DSGE approach for the BRICS countries, highlighting the role of credit spreads and fiscal imbalances as significant drivers of inflation, output, and interest rates. These findings reflect the heterogeneity in the response of monetary policies to structural shocks and suggest a country-specific sensitivity to fiscal and credit conditions. In addition, Attílio et al. (2024) employ a GVAR model incorporating not only trade flows but also bilateral financial and investment positions to capture the impact of the US stock market on the BRICS and G7 economies. Their results highlight the increasing sensitivity of BRICS markets to global financial shocks, as well as significant differences in the response of variables such as industrial production, exchange rates, and interest rates.

Regarding financial risk, Sithole and Eita (2023) address the macroeconomic determinants of bank credit risk in BRICS countries, using a Markov switching model. They conclude that weak economic growth, high inflation, appreciated currencies, and high interest rates are associated with increased credit risk, highlighting the nonlinearity in transmission depending on the current economic regime. Likewise, Saliba et al. (2023) analyze how country risk (economic, political, and financial) impacts the level of nonperforming loans in the banking sector. Using quantile regressions, they demonstrate that these risks have a significant impact, especially in economies with high exposure to nonperforming loans, suggesting the importance of the institutional environment for financial stability. From an external perspective, Zhang and Hamori (2022) explore the interconnectivity between BRICS geopolitical risks and US macroeconomic indicators using a TVP-VAR (Time-Varying Parameter Vector Autoregression) model. Their findings show that risks in Russia and Brazil have a greater capacity to affect aggregate volatility and returns, especially in contexts of global crises such as the pandemic, reinforcing the endogenous nature of BRICS-developed country ties.

On the exchange rate front, research such as that by Salisu et al. (2021) and Kerbeg et al. (2025) delves into the relationship between interest rates and exchange rates. While Salisu et al. highlight nonlinear behavior dependent on the economic regime, Kerbeg et al. identify a significant causal relationship between interest rates and exchange rate dynamics using 2SLS (Two-Stage Least Squares) models, confirming the importance of monetary policy in exchange rate stability. Finally, Kumar and Dua (2024) analyze the determinants of portfolio investment flows to the BRICS. Their study reveals that US Treasury bond interest rates have a negative effect on these flows, while factors such as a dynamic stock market, higher interest rate differentials, and credit credibility strengthen capital attraction, indicating the complexity of portfolio decisions under global risk and return contexts.

2.2. Nonlinear Relationships and Macro-Financial Synchronization Under Volatile Conditions

Financial markets in emerging and advanced economies have shown increasing sensitivity to volatile macroeconomic conditions and external shocks. This dynamic has generated lines of research that explore not only the magnitude of the response of financial assets to variables such as interest rates or international prices but also the asymmetry and nonlinearity of these relationships in contexts of macroeconomic uncertainty. Zaidi and Rupeika-Apoga (2021) investigate liquidity synchronization in seven emerging Asian economies, highlighting that such synchronization intensifies in environments of low growth, high inflation, and high interest rates. Furthermore, they show that this comorbidity is determined not only by traditional macroeconomic factors but also by institutional aspects such as weak rule of law, government inefficiency, and investor protection. This liquidity synchronization represents an undiversifiable systemic risk, with significant implications for regional financial stability. In Latin America, Abugri (2008) provides empirical evidence on how macroeconomic volatility, represented by fluctuations in interest rates, industrial production, the exchange rate, and money supply, significantly influences the behavior of stock market returns. Using a VAR model, the author shows that global factors such as the US Treasury rate play a predominant role, although the effects of local factors vary by country, reflecting a heterogeneous risk transmission structure.

At the level of developed markets, Tabash et al. (2024) examine the symmetric and asymmetric effects of macroeconomic fundamentals on the exchange rate in advanced European countries, using a NARDL (Nonlinear Autoregressive Distributed Lag) model. Their findings show that interest rates have an asymmetric effect on the exchange rate in the short and long term, while the price of gold and international reserves also play a stabilizing role. This demonstrates that the market response to fundamentals is not uniform, justifying the use of nonlinear techniques for their analysis. In a more global framework, Martínez-Cañete et al. (2022) propose a nonlinear cointegration approach to assess the relationship between oil prices and the MSCI World Index, finding that this co-mobility intensifies in contexts of near-zero interest rates. By incorporating the shadow rate as a transition variable, the study reveals that in unconventional monetary policy environments, the correlation between equity prices and oil strengthens, reducing the potential for portfolio diversification and amplifying systemic financial risk.

Together, these studies reinforce the need for flexible models sensitive to nonlinearity and asymmetry as key tools for understanding the relationships between macroeconomic fundamentals and financial prices in environments characterized by extreme shocks, unconventional monetary regimes, and increasing international financial synchronization.

2.3. The Role of the World Interest Rate (WIR) in Financial Markets

Interest in understanding the influence of the World Interest Rate (WIR) on financial markets has grown in light of evidence that global monetary conditions transcend national borders. Del Negro et al. (2019) document a sustained decline in the WIR over the past three decades, a phenomenon attributed to the rise in convenience yields for safe assets and slower global economic growth. This trend has had structural consequences on real rates in advanced economies, whose behavior is increasingly converging. From a more structural perspective, Shambaugh and Zhou (2024) use a dynamic factor model with endogenous clustering to construct the WIR for 43 countries, finding that both global and regional factors explain much of the rate dynamics in developed economies, while in emerging markets, idiosyncratic factors still predominate. Capital account openness and the exchange rate regime are key determinants in the transmission of these shocks. In the specific case of emerging markets, Bahadir and Lastrapes (2015) show that debt yields respond gradually to WIR shocks, which supports the hypothesis of partial integration with global capital markets. Furthermore, Battisti et al. (2020) analyze the distributional effects of the WIR and conclude, using the Galor-Zeira model, that a sustained drop in the global rate reduces inequality in poor countries but increases it in rich economies. Taking a more recent, quantile perspective, Joaqui-Barandica et al. (2023) reveal a nonlinear directional pattern in the relationship between the WIR and the Stoxx 600 Banks Index, where the WIR acts as a transmitter of shocks during periods of crisis, especially when European banking is facing extreme conditions. This conditional dependency approach is key to capturing the asymmetric nature of systemic risk. Finally, the effects of US shocks on the WIR are stronger before reaching the zero lower bound, suggesting an environment with lower effectiveness of conventional monetary policy (Shambaugh & Zhou, 2024).

Building on four complementary strands of research, we frame our analysis of external-rate shocks to BRICS equity markets. First, the global financial cycle literature shows that U.S./G7 monetary policy shocks co-move financial conditions and asset prices worldwide, limiting domestic monetary autonomy (Miranda-Agrippino & Rey, 2020). Second, a risk-taking channel links tighter global policy to declines in global banks’ leverage and cross-border credit, raising required returns for risky assets—especially in financially open economies (Bruno & Shin, 2015). Third, empirical studies document sizeable and heterogeneous spillovers of U.S. monetary policy to international equity markets and real activity, with transmission shaped by openness, exchange-rate regimes, and financial structure (Ehrmann & Fratzscher, 2009; Georgiadis, 2016). Fourth, factor-based measures of a world interest rate extracted from advanced-economy yields are informative for emerging-market cycles and sovereign risk, underscoring the relevance of external rates for EM dynamics (Bahadir & Lastrapes, 2015; Neumeyer & Perri, 2005; Uribe & Yue, 2006). Against this background, our contribution is to operationalize a G7-based world interest rate (WIR) and to estimate exposure–lag–response profiles with a DLNM, which accommodates nonlinearities and asymmetries in transmission—features that standard linear system models may obscure.

3. Materials and Methods

3.1. Empirical Model

To capture the dynamic and nonlinear influence of global interest rate shocks on the financial markets of BRICS economies, we employ a DLNM, following the framework introduced by Gasparrini (2011). This methodology allows us to simultaneously estimate the nonlinear exposure-response relationship between the WIR and the MSCI equity indices, as well as the delayed effects over a specific lag period. This is particularly useful for financial contexts, where shocks often propagate with temporal dependencies.

Our empirical framework builds on the DLNM; compared with traditional dynamic models such as VAR or TVP-VAR, the DLNM does not require specifying a full system of endogenous interactions and allows the joint estimation of nonlinear and lagged effects through basis functions. While VAR and TVP-VAR are powerful tools to model interdependencies across multiple variables, they generally assume linear dynamics and can become less tractable when allowing for nonlinearities and high-order lag structures (Zhang & Hamori, 2022). By contrast, the DLNM framework is designed to flexibly approximate these dynamics and is therefore well suited to study the transmission of external interest rate shocks to equity markets.

Let Y_t denote the MSCI index for a specific BRICS country at time t = 1, …, T. The model assumes the following structure:

$$g({\mu }_{\mathrm{t}})=\alpha +{\sum }_{\mathrm{j}}{s}_{\mathrm{j}}(x_{\mathrm{t}\mathrm{j}};{\beta }_{\mathrm{j}})+{\sum }_{\mathrm{k}}{\gamma }_{\mathrm{k}}{u}_{\mathrm{t}\mathrm{k}}$$

(1)

where ${\mu }_{\mathrm{t}}$ ≡ E($Y_{\mathrm{t}}$), $g$ is a monotonic link function (e.g., identity or log), and Y follows a distribution in the exponential family. The $s_{\mathrm{j}}$ functions represent the nonlinear relationships (e.g., splines) between the covariates $x$ and the response variable, parameterized by ${\beta }_{\mathrm{j}}$. $u_{\mathrm{k}}$ represents optional control variables with linear effects ${\gamma }_{\mathrm{k}}$. Following the DLNM framework, the dependent variable ${\mathrm{Y}}_{\mathrm{t}}$ is assumed to belong to the exponential family of distributions (Gasparrini, 2011). In our case, ${\mathrm{Y}}_{\mathrm{t}}$ corresponds to the log-returns of MSCI indices, which are treated as approximately normally distributed. Hence, the exponential family formulation reduces to the Gaussian case, providing a consistent likelihood for estimation.

Each nonlinear term $s_{\mathrm{j}}(x_{\mathrm{t}};\beta )$ can be expressed using basis functions as:

$$s(x_{\mathrm{t}};\beta )={z_{\mathrm{t}}}^{\mathrm{T}}\beta$$

(2)

where $z_{\mathrm{t}}$ is the t-th row of the basis matrix Z obtained from transforming $x_{\mathrm{t}}$ with the chosen basis function (e.g., natural splines).

To account for the lagged effects of $x_{\mathrm{t}}$ over time, we extend the model to a Distributed Lag Model (DLM):

$$s(x_{\mathrm{t}};\eta )={q_{\mathrm{t}}}^{\mathrm{T}}C\eta$$

(3)

where $C$ is a basis matrix constructed over the lag dimension (l = 0, …, L), and $\eta$ represents the vector of lag coefficients.

Finally, we incorporate nonlinearities over both the exposure and lag dimensions using a DLNM formulation:

$$s(x_{\mathrm{t}};\eta )={\sum }_{\mathrm{j}}{\sum }_{\mathrm{k}}{r_{\mathrm{t}\mathrm{j}}}^{\mathrm{T}}{c}_{\mathrm{k}}{\eta }_{\mathrm{j}\mathrm{k}}={w_{\mathrm{t}}}^{\mathrm{T}}\eta$$

(4)

Here, $w_{\mathrm{t}}$ is the result of applying a bi-dimensional cross-basis function to $x_{\mathrm{t}}$ and its lag structure. This cross-basis captures how the response changes with both the level of exposure and the time elapsed since the shock. The parameter vector $\eta$ is estimated jointly.

Formally, let $x_{\mathrm{t}}$ denote the WIR shock at time t. The nonlinear transformation of the exposure dimension is obtained through a basis expansion $\beta \left(x_{\mathrm{t}}\right)$, where each column corresponds to a spline basis function evaluated at $x_{\mathrm{t}}$. Thus, the transformed covariates can be expressed as:

$$q_{\mathrm{t}}=[b_1\left(x_t\right),b_2\left(x_t\right),\dots ,b_J(x_t\left)\right]$$

(5)

where $b_J(.)$ denotes the j-th spline basis function, and J is the number of basis functions. Similarly, the lag dimension is represented through another set of basis functions applied over the lag space ($l=0,\dots ,L$):

$$r_{\mathrm{t}\mathrm{j}}=[c_1\left(l\right),c_2\left(l\right),\dots ,b_K(l\left)\right]$$

(6)

where $c_k(.)$ denotes the lag basis function. The cross-basis is constructed as the tensor product $w_t=q_t⨂r_{tj}$, capturing interactions between exposure levels and lag periods (Gasparrini, 2011). The model then takes the form:

$$g\left(E\left(Y_t\right)\right)=\alpha +w_t\eta +\gamma Z_t$$

(7)

where $\eta$ represents the coefficients associated with the cross-basis expansion, and $\gamma$ represents coefficients of additional control variables $Z_t$. The use of natural cubic splines provides flexibility to capture nonlinearities without imposing restrictive parametric assumptions, and it is a standard approach in DLNM applications. The key parameters estimated are therefore the elements of $\eta$, which jointly determine the exposure–lag–response surface.

The empirical design includes only the WIR index as the explanatory variable. Incorporating domestic macro-financial variables (e.g., GDP, inflation, exchange rates) would confound the interpretation of global spillovers by introducing country-specific effects, thereby limiting the comparability of Brazil, India, China, Russia, and South Africa within a unified global framework. Our parsimonious specification thus focuses on the pure transmission of global interest rate shocks, following the tradition of spillover studies that emphasize single-factor global drivers (Bahadir & Lastrapes, 2015). Future extensions may explicitly incorporate domestic fundamentals to analyze interaction effects between global and local conditions.

3.2. Data

This study uses a database with monthly time series covering the period from January 2005 to June 2025, extracted from the LSEG Refinitiv platform (Equity indices and macro-financial series were accessed via LSEG (formerly Refinitiv) Workspace and Datastream). This window captures relevant episodes of the global economic cycle, such as the 2008 financial crisis, the rise of emerging markets, the COVID-19 pandemic, and the recent phase of monetary tightening in advanced economies. To represent the stock market performance of emerging countries, the MSCI dollar-denominated indexes (price, excluding dividends) for Brazil, Russia, India, China, and South Africa are used, which provide a proxy for stock market performance in each economy. These countries were selected due to their prominence within the BRICS group, which has been widely studied in the literature due to its growing financial integration and exposure to global factors. In the case of Russia, the MSCI Russia Index was suspended in 2022 following the geopolitical conflict with Ukraine and the imposition of international sanctions, which restricted the availability of market data. To maintain consistency in the analysis, we employed the MSCI Emerging Markets EMEA Index as a proxy. This regional index includes Russia along with other Eastern European economies and thus offers an approximate representation of Russian equity performance. We acknowledge that this proxy may dilute Russia’s specific dynamics—particularly in recent years, when its economy showed differentiated trends compared to neighboring countries—and therefore interpret the results for Russia with due caution.

For the G7 developed economies, 10-year sovereign interest rates are used as a proxy for each country’s domestic monetary conditions. These rates are used to construct an aggregate global interest rate index (WIR), estimated from the first principal component of the rates of the United States, Germany, Japan, the United Kingdom, France, Italy, and Canada. This index seeks to capture the common dynamics of benchmark sovereign debt yields in developed markets, acting as a proxy for international financial conditions. Since the start dates of MSCI indices can vary across countries, the effective analysis window for each model is adjusted according to data availability. All series were transformed to obtain monthly returns, and cleaning and time-alignment criteria were applied to ensure consistency in the empirical exercises. The empirical analysis design allows for exploring how global interest rate shocks differentially affect emerging stock markets, depending on the state of the cycle and local conditions. We assess the stationarity of all processed variables entering the models. Specifically, we test MSCI log-returns (Brazil, India, China, South Africa, and Russia) and the global shock ΔWIR (first difference in the G7 10-year PC1). Augmented Dickey–Fuller tests reject the unit root at conventional levels for all series (Appendix A,

Table A1. ADF for processed variables used in estimation (monthly).

Series	Transform	Test	Lag Order	DF Statistic	p-Value	Decision (5%)
ΔWIR (10Y PC1)	first diff (delta_TIM)	ADF	6	−3.9608	0.0116	Stationary
MSCI Brazil	log-return	ADF	6	−6.0936	<0.01	Stationary
MSCI Russia (EMEA)	log-return	ADF	5	−5.6877	<0.01	Stationary
MSCI India	log-return	ADF	6	−5.8064	<0.01	Stationary
MSCI China	log-return	ADF	6	−5.5060	<0.01	Stationary
MSCI South Africa	log-return	ADF	5	−4.8905	<0.01	Stationary

). For completeness, ADF tests on unprocessed levels are reported as diagnostics (Appendix A,

Table A2. ADF on unprocessed levels (diagnostic; not used in estimation).

Series	Level/Transform	Test	Lag Order	DF Statistic	p-Value	Decision (5%)
WIR (10Y PC1, level)	level	ADF	6	−0.2700	0.99	Unit root (non-stationary)
MSCI Brazil (level)	level	ADF	6	−3.5085	0.0427	Stationary
MSCI Russia (level)	level	ADF	5	−2.3445	0.4319	Unit root
MSCI India (level)	level	ADF	6	−2.3016	0.4490	Unit root
MSCI China (level)	level	ADF	6	−3.3341	0.0662	Not reject at 5%
MSCI South Africa (level)	level	ADF	5	−2.6839	0.2917	Unit root

).

4. Results

4.1. Descriptive Analysis of Sovereign Bond Yields in G7 Economies

We present in

Table 1. Descriptive statistics of 10-year government bond yields (2005–2025).

Country	Mean	Median	Min	Max	SD
Canada	2.59	2.53	0.47	4.60	1.06
France	2.15	2.46	−0.39	4.79	1.48
Germany	1.76	1.77	−0.70	4.61	1.51
Italy	3.29	3.71	0.52	6.91	1.42
Japan	0.72	0.68	−0.27	1.97	0.61
UK	2.71	2.64	0.10	5.44	1.49
USA	2.92	2.76	0.56	5.15	1.14

the descriptive statistics of the 10-year government bond yields for G7 countries over the period January 2005 to June 2025. This long-run window captures different global macro-financial environments, including the aftermath of the 2008 financial crisis, the European sovereign debt crisis, the low-interest rate environment of the 2010s, the COVID-19 pandemic, and the recent monetary tightening cycle starting in 2022. The statistics include the mean, median, minimum, maximum, and standard deviation of monthly yields for each country. On average, Italy and the United States recorded the highest long-term bond yields, with means of 3.29% and 2.92%, respectively. Japan, as expected due to its persistent ultra-low-interest rate policy, showed the lowest yields, with an average of 0.72% and a minimum as low as −0.27%. European economies such as France and Germany exhibited negative yields during periods of strong monetary stimulus by the European Central Bank, particularly after 2015, with minimum values of −0.39% and −0.70%, respectively. The highest maximum yield was observed in Italy, reaching 6.91%, reflecting episodes of elevated sovereign risk and market volatility. The standard deviations reveal varying degrees of yield volatility. Germany and France showed the highest standard deviation (1.51% and 1.48%), indicating significant fluctuations despite their relatively low average yields. Conversely, Japan maintained the most stable yield profile (SD = 0.61%).

Figure 1 visually complements these statistics by depicting the monthly evolution of 10-year bond yields for the G7 countries. Figure 1 reveals several key stylized facts. First, the yields across all countries exhibit a clear declining trend from 2005 until around 2015, followed by a sustained low-rate environment, especially in Europe and Japan. After 2021, a notable upward trend is observed across all countries, driven by the surge in inflation and the subsequent response by central banks via interest rate hikes. The divergence in yield levels is also visible. Japan consistently remained an outlier with significantly lower yields, a reflection of its decades-long monetary easing stance. In contrast, Italy and the USA showed sharper swings and higher peaks, particularly during sovereign risk episodes (for Italy) and during post-pandemic monetary normalization (for the USA).

The visual evidence suggests that while G7 countries share common shocks, such as the global financial crisis and the COVID-19 pandemic, the magnitude and persistence of their effects on long-term interest rates vary considerably across countries. These differences underscore the relevance of including global interest rate dynamics as a macro-financial driver in the empirical modeling of emerging market equity returns.

4.2. Construction of the World Interest Rate (WIR) via Principal Component Analysis

To capture a common latent factor driving the co-movement of long-term interest rates in advanced economies, we construct a WIR index based on the yields of 10-year government bonds from the G7 countries. The estimation relies on Principal Component Analysis (PCA) applied to the standardized monthly yields from January 2005 to June 2025. This method allows us to extract the most informative linear combination of these yields that summarizes the global interest rate trend.

The results of the PCA are shown in

Table 2. Principal Components and Variance Explained.

Component	Eigenvalue	% Variance	Cumulative %
Comp 1	6.124	87.49%	87.49%
Comp 2	0.561	8.02%	95.51%
Comp 3	0.204	2.91%	98.42%
Comp 4	0.053	0.76%	99.18%
Comp 5	0.041	0.59%	99.77%
Comp 6	0.013	0.18%	99.95%
Comp 7	0.004	0.05%	100.00%

. The first principal component accounts for 87.5% of the total variance across countries, suggesting a strong common factor in yield movements. The second component adds an additional 8.0%, and the third 2.9%, bringing the cumulative variance explained by the first three components to over 98.4%. This confirms that most of the dynamics in the G7 yield curves can be summarized by a low-dimensional factor space.

While the first component explains the bulk of the variance, interpreting only this dimension would ignore important country-specific contributions that become more visible in subsequent components.

Table 3. Country Contributions to Principal Components (%).

Country	Comp 1	Comp 2	Comp 3	Comp 4	Comp 5
USA	13.06	27.45	15.71	4.29	23.54
Germany	15.93	0.22	5.11	2.52	16.82
Japan	14.31	2.01	46.80	19.95	14.16
UK	15.46	4.23	0.03	45.16	4.77
France	15.82	3.73	0.70	9.06	2.04
Italy	10.47	53.44	27.87	1.75	2.38
Canada	14.95	8.93	3.78	17.27	36.29

reports the percentage contribution of each country to the first five principal components.

The first component presents balanced contributions from most countries, suggesting it captures a global factor. However, higher-order components highlight asymmetries: for instance, Italy dominates the second dimension (53.4%), reflecting idiosyncratic volatility, while Japan heavily loads on the third component (46.8%), likely due to its persistent low-rate regime.

The estimated WIR series, derived from the standardized first principal component and rescaled for interpretability, is displayed in Figure 2. The index reveals several distinct phases in the evolution of global interest rates: a relatively elevated period before the 2008 crisis; a sustained decline during the 2010s under monetary easing; a deep trough around 2020 reflecting the pandemic shock; and a sharp rebound post-2021 in line with inflationary pressures and synchronized monetary tightening. Following the literature on global interest rate indicators (McCracken & Ng, 2016), we apply PCA to the level of the 10-year government bond yields, in order to capture the common dynamics across G7 countries without differencing the series, as the focus is on co-movements rather than stationarity.

4.3. Stock Market Dynamics in BRICS Economies

Figure 3 shows the evolution of the MSCI indices for each BRICS country from January 2005 to June 2025. Significant heterogeneity is evident across markets: Brazil and Russia exhibit high volatility and cyclical behavior, with sharp declines during global crises and partial recoveries afterward. In contrast, India’s index shows a more sustained upward trend over time, with moderate volatility. China and South Africa present more stable paths with limited upward momentum. These patterns reflect both domestic factors and each country’s sensitivity to external shocks.

To better visualize the individual dynamics of each country’s equity index, Figure 4 presents a panel of time series plots, including WIR. This disaggregated view enhances the interpretation of the co-movements and country-specific episodes throughout the period.

Summary statistics for the MSCI indices are reported in

Table 4. Descriptive statistics of MSCI indices (2005–2025).

Country	Mean	Median	Min	Max	St. Dev.
Brazil	2164.4	1944.2	860.0	4728.1	764.7
China	65.9	63.5	26.0	130.0	17.2
India	550.2	499.8	187.4	1163.5	202.3
Russia	2235.5	2206.6	1076.2	3832.6	476.2
South Africa	468.9	468.6	245.8	655.5	65.1

Note: All values are expressed in USD. The MSCI Russia Index was replaced by the MSCI Emerging Markets EMEA Index due to the suspension of the former in 2022 following geopolitical sanctions.

. On average, Brazil and Russia have the highest index levels (2164 and 2236, respectively), consistent with their larger and more mature equity markets in nominal terms. India shows a lower mean (550) but a clear increasing trend in recent years. China exhibits the lowest mean value (66) due to the nature of its index base, and South Africa maintains moderate levels around 469. Standard deviations confirm the high volatility of Brazil and Russia, followed by India, while China and South Africa remain more stable.

Before estimating the distributed lag nonlinear models (DLNM), we evaluated the stationarity properties of the time series involved using the Augmented Dickey–Fuller (ADF) test. This test helps identify the presence of unit roots, which may bias the dynamic relationships under analysis.

Table 5. Results of Augmented Dickey–Fuller Test.

Variable	ADF Statistic	p-Value
WIR	−0.270	0.99
MSCI Brazil	−3.509	0.043
MSCI Russia	−2.345	0.432
MSCI India	−2.302	0.449
MSCI China	−3.334	0.066
MSCI South Africa	−2.684	0.292

summarizes the test statistics and p-values for the variables under study.

The stationarity tests reveal that among the BRICS equity indices, only MSCI Brazil is stationary at the 5% significance level. The remaining indices—Russia, India, China, and South Africa—exhibit non-stationary behavior, indicating the need for transformation prior to model estimation. Similarly, the World Interest Rate (WIR), constructed via Principal Component Analysis of 10-year government bond yields from G7 countries, also fails to reject the null hypothesis of a unit root.

To address these concerns and avoid issues related to spurious regressions, we applied standard econometric transformations. The equity indices were converted into log returns, a common approach in financial econometrics to induce stationarity and interpret results in percentage terms. The WIR was transformed using first differences (ΔWIR), capturing variations in global interest rate dynamics rather than their absolute levels. Although DLNM does not require explanatory variables to be stationary—provided that trend and seasonality are adequately controlled—differencing the WIR helps focus the analysis on interest rate shocks and simplifies interpretation.

All explanatory variables were standardized to allow for cross-country comparisons of effect sizes. The dependent variables in the DLNM are the log returns of each MSCI index, ensuring compliance with stationarity assumptions required for reliable estimation and inference.

Each DLNM specification is estimated separately for every country, allowing for heterogeneous exposure-lag-response relationships between global interest rate shocks and local equity returns. This country-specific approach captures the unique temporal transmission patterns of financial shocks across emerging markets.

As a robustness check, we reconstruct the world interest rate using G7 short-term (3-month) money market rates from the OECD and re-estimate the DLNM specifications with the resulting shock measure ($\Delta WIR3M_t$). The exposure–lag–response patterns are qualitatively preserved across BRICS—effects remain concentrated at short horizons and show comparable magnitudes without sign reversals—supporting the stability of our findings. Full details and figures are provided in Appendix A (Figure A1, Figure A2 and Figure A3).

4.4. Brazil

Figure 5 displays the estimated exposure-lag-response surface for Brazil, capturing the dynamic and potentially nonlinear effects of standardized global interest rate shocks (WIR) on local equity market returns over a 6-period lag structure. The plot provides a comprehensive visualization of how different magnitudes of interest rate movements—from contractionary (negative WIR values) to expansionary (positive WIR values)—influence stock returns, not only immediately but also with delayed responses.

The color gradient in the figure represents the estimated magnitude of the effect: yellower colors indicate negative responses, and bluer shades indicate positive impacts. A more detailed analysis reveals that moderate to strong negative interest rate shocks (i.e., global monetary tightening) tend to generate small but consistent negative effects on Brazilian equity returns, especially concentrated in the early lags (between 0 and 2). However, these effects are not very pronounced, suggesting a certain level of resilience or absorptive capacity in the Brazilian market.

On the other hand, positive WIR shocks (interpreted as global easing or accommodative monetary conditions) are associated with gradually increasing positive effects, peaking around lag 4. This pattern indicates that the Brazilian stock market reacts to global liquidity expansions with a certain lag, which could reflect the time it takes for capital to reallocate or for investors’ expectations to adjust. It is important to note that the surface shows that the response is not symmetrical: positive shocks appear to generate more persistent and significant reactions than negative ones, indicating an asymmetric sensitivity of Brazilian stocks to global financial conditions.

Figure 6 further explores this relationship by depicting the estimated marginal effects at selected lags (0, 1, 5) and at selected levels of the WIR (quantiles 1%, 50%, 99%) (−0.88, 0.01, 0.99). At Lag 0, the effect of the WIR is nearly linear and slightly negative across the range, with a wider confidence band. At Lag 1, the effect is nearly null and stable, while at Lag 5, the curve becomes more convex, suggesting that Brazil’s equity market reacts positively to expansionary shocks with some delay. The right panels of Figure 6 show how the impact of fixed WIR shocks evolves over time. Notably, a strong negative shock (WIR = −0.88) has a small adverse effect that dissipates quickly, while a large positive shock (WIR = 0.99) produces a delayed positive effect peaking between lags 4 and 5. But it is not significant.

Overall, Brazil’s equity market shows a mild and delayed sensitivity to global interest rate movements, with responses that are more pronounced for positive shocks, suggesting potential global liquidity effects or capital inflows driving equity performance.

Across all countries, the cross-sectional plots follow the same structure: the x-axis labeled ‘Var’ represents standardized quantiles of WIR shocks, while the y-axis ‘Outcome’ denotes the estimated effect on MSCI log-returns. By construction, the median shock (Var = 0) defines the baseline of the model, resulting in a null effect at this point. This explains why the response curves consistently intersect zero at the median across all figures. For clarity of interpretation, we report both the three-dimensional exposure–lag–response surfaces and their cross-sectional slices. While the former offer a comprehensive visualization of the joint effect of magnitude and lag, the latter highlight how effects evolve at specific lags and quantiles. Presenting both views is a common practice in DLNM applications and facilitates the economic interpretation of the results.

4.5. Russia

In the case of Russia, Figure 7 presents the estimated exposure-lag-response surface, the surface highlights that positive global interest rate shocks are associated with notably adverse and immediate effects on Russian equity returns. These negative effects are strongest at shorter lags (around lag 0 to 2), where tightening shocks of moderate to high magnitude lead to cumulative losses exceeding −0.1 in standardized return units. The gradient intensifies in the lower-right quadrant of the plot (high WIR, low lag), suggesting that the Russian market reacts almost instantaneously and disproportionately to global monetary contractions, likely due to its sensitivity to capital flows and risk aversion in global markets.

Conversely, negative WIR shocks (loosening episodes) are associated with mildly positive or neutral effects. The surface indicates a slight increase in returns for low or negative values of the WIR, but these effects are less pronounced and lack statistical prominence beyond lag 2. The relatively flat and shallow gradients in this region of the plot suggest that easing in global rates does not trigger a strong or persistent rebound in Russian equities. Figure 7 reveals an important asymmetry: while global monetary tightening has immediate and substantial negative repercussions for the Russian stock market, monetary easing fails to generate equally strong positive reactions. This pattern is consistent with emerging market vulnerabilities to external financial shocks and capital outflows, particularly in geopolitically exposed or commodity-dependent economies like Russia.

Figure 8 presents the disaggregated effects of standardized global interest rate (WIR) shocks on the Russian stock market. The results reveal a strong asymmetry in the immediate response (lag 0): positive WIR shocks (tightening) are associated with a significant and negative contemporaneous effect on Russian equity returns, just as negative shocks (easing) produce a slightly negative effect. This nonlinear pattern quickly fades, as evidenced by the flat response curves at lags 1 and 5, indicating minimal lagged influence.

The lag-response panels further confirm this dynamic. A large positive WIR shock (+1.07) produces a clearly positive cumulative response, which peaks around lag 2 and gradually declines thereafter. In contrast, a large negative shock (–0.8) generates a modest and statistically less significant impact across the lags. The median WIR value (–0.01) shows no discernible effect across the lag structure, as expected. The evidence points to a nonlinear, time-varying relationship between global interest rate shocks and Russian equity returns. The market appears particularly sensitive to monetary policy tightening shocks, and lagged adjustments likely reflect risk repricing or macrofinancial transmission mechanisms specific to the Russian market structure and its external vulnerability.

4.6. India

Figure 9 displays the estimated exposure-lag-response surface for India. The surface highlights a transient but asymmetric response to global interest rate dynamics, emphasizing India’s relative vulnerability to unexpected loosening cycles rather than to tightening episodes. The results suggest a non-monotonic and lag-dependent relationship. Moderate negative WIR shocks (loosening) appear to produce adverse effects on returns with a short delay—most prominently around lag 2—where a localized region of strong negative response is visible. This pattern may reflect delayed reactions from capital flows or institutional adjustments in the Indian financial market. Conversely, the response to positive WIR shocks (tightening) is more muted and less consistent across lags, indicating weaker sensitivity to global monetary tightening. Interestingly, both ends of the lag distribution (lags 0 and 5–6) show near-zero effects regardless of the shock’s magnitude, suggesting that India’s equity market does not respond instantaneously nor with long-term persistence to external interest rate movements.

Figure 10 provides a disaggregated visualization of the DLNM results for India. The most extreme negative WIR shock (–0.88) produces a rapid but transient drop in yields at the second lag, subsequently recovering through lags 5 and 6, becoming significant. In contrast, the median WIR shock (≈0.01) does not exhibit a statistically significant impact across the entire range of lags, acting as a null baseline. For the extreme positive shock (0.99), the response is also nonlinear: yields decline initially but then show a slight upward trajectory around lags 3–5 before stabilizing. However, this is not significant.

These findings reveal that the Indian market’s response is more pronounced to negative global interest rate shocks, especially at long lags, while reactions to medium or positive shocks tend to be weak. This reinforces the hypothesis of asymmetric transmission of global interest rate cycles to emerging equity markets.

4.7. China

Unlike other emerging economies, the behavior of the Chinese stock market (Figure 11) in the face of global interest rate shocks appears to be governed by a different logic. Analyzing the joint relationship between the magnitude of WIR shocks and the time lags on stock market returns reveals a relatively stable surface, without large fluctuations, suggesting a more contained response dynamic.

Moderate contractionary shocks (WIR < −1) tend to generate slightly negative effects in the short term, especially between the first two lag periods, but without reaching alarming levels. In contrast, when WIR increases, the effects on returns are generally neutral, with a more muted effect in the intermediate lags. This smooth surface is particularly revealing: there are no abrupt areas of gain or loss that dominate the response, which could be linked to the strong regulation of the financial market in China, the role of the State in the economy, and its lesser exposure to international speculative flows.

Beyond the direction of the effects, what stands out is the symmetry and moderation of the response. While other markets show immediate sensitivity or more pronounced cumulative reactions, in China, the transmission of shocks appears to be cushioned or filtered, even in the face of extreme shocks. This pattern could be interpreted as a manifestation of the institutional design of its economy, where external influence is regulated through internal mechanisms, limiting volatility induced by global factors.

In the case of China, the estimated disaggregated lag–nonlinear effects in Figure 12 provide a nuanced understanding of how different magnitudes of WIR influence equity returns over time. At lag 0, the immediate response to either positive or negative WIR shocks remains mild and statistically indistinct from zero, suggesting a limited contemporaneous sensitivity. However, as the time horizon extends, particularly at lags 1 and 5, a slight asymmetry emerges: while mild tightening (negative WIR shocks) appears to generate marginally negative effects, expansionary shocks (positive WIR) are associated with small gains, albeit with overlapping confidence intervals. The lag-response plots on the right panels show that under extreme tightening (quantile 1, WIR = −0.88), returns initially decline slightly but quickly recover and become positive from lag 2 onwards, with a peak near lag 5. In contrast, the response to a neutral shock (quantile 50) is virtually flat across all lags, reinforcing the notion of low baseline sensitivity. When facing a strong expansionary shock (quantile 99), returns display a gradual increase up to lag 4, before tapering off. Overall, the lag-distributed response in China reveals a controlled and dampened dynamic compared to other emerging economies. While the market does exhibit delayed reactions to external interest rate shocks, particularly under extreme scenarios, the magnitude remains modest. These findings are consistent with China’s partially insulated financial system and its managed capital account, which likely buffer the transmission of global financial volatility into domestic equity performance.

4.8. South Africa

Figure 13 illustrates the three-dimensional exposure-lag-response surface for South Africa. Rather than displaying an abrupt or highly asymmetric pattern, the surface suggests a rather attenuated and gradual response. Interestingly, the effects are not concentrated in the immediate term but appear to diffuse slowly across the lags, with the most notable deviations from zero observed around lags 2 and 5. A closer look at the shape of the contour reveals a shallow basin for moderately negative WIR values, especially near lag 2, indicating a delayed vulnerability to adjustment cycles. In contrast, positive WIR shocks produce slightly favorable effects, peaking near the longer end of the lag spectrum. The overall amplitude of the estimated effects remains within a narrow corridor, with values ranging from approximately −0.1 to 0.1, highlighting the moderate nature of the transmission mechanism.

This pattern could reflect the dual nature of the South African financial system: sufficiently open to respond to global monetary trends yet buffered by local institutional factors that cushion extreme reactions. In this sense, the surface captures a slow transmission of global financial conditions to the domestic stock market, with more persistent effects emerging only after a time lag. The results highlight the need to consider both the intensity and persistence of external shocks when analyzing market reactions in partially integrated emerging economies.

To deepen the interpretation of the estimated exposure-lag-response structure for South Africa, Figure 14 isolates key slices of the surface across both the lag and predictor dimensions. At lag 0, the estimated effect is nearly flat with a slight negative slope, suggesting a minimal and statistically insignificant immediate response to WIR shocks. This already weak response diminishes further at lag 1. By lag 5, a mild upward curvature appears, hinting at a potential delayed adjustment, though the pattern remains within the bounds of statistical uncertainty. The right-hand panels reinforce this subdued interpretation. For extreme negative WIR values (τ = 0.01), the response hovers slightly below zero and traces a shallow U-shape over time, yet without statistical support. At the median (τ = 0.50), the response is effectively flat, indicating no clear sensitivity. Even at the upper tail (τ = 0.99), where a gradual increase up to lag 4–5 is observed, the effect remains weak and fails to reach statistical significance. The results suggest that South Africa’s equity market exhibits no robust or statistically significant reaction to global interest rate shocks. The observed patterns are weak, nonlinear, and lack consistent magnitude across time or quantiles. This highlights the limited transmission of external monetary shocks in this context and underscores the need for cautious interpretation when evaluating global spillover effects on emerging markets.

4.9. Transmission Mechanisms and Country Heterogeneity

Global interest-rate shocks operate through several channels in equity markets. First, a valuation/discount-rate channel, whereby higher world rates raise discount factors and compress present values of cash flows. Second, a risk-premium channel tied to the global financial cycle: tighter external conditions increase required returns for risky assets, particularly where foreign participation is high. Third, a funding/FX channel, as shifts in world rates alter cross-border funding costs and exchange-rate pressures that feed into equity risk premia. Fourth, a policy-reaction channel, insofar as domestic monetary authorities adjust their stance in response to global financial conditions. The strength and timing of these channels depend on country characteristics, including financial openness and foreign investor base, exchange-rate flexibility, market depth and availability of hedging instruments, and sectoral composition (e.g., commodity exposure).

If we analyze country heterogeneity, we find to Brazil, the relatively open equity market with meaningful foreign participation and deep derivatives allows fast repricing via the discount-rate and risk-premium channels. This aligns with the short-lag responses we document: easing (lower WIR) supports valuations, whereas tightening compresses them, with limited persistence as hedging mitigates propagation. India, a larger domestic investor base and capital-flow management make the global cycle transmit more gradually; the responses are milder and materialize with short lags, consistent with a dampened risk-premium channel. In the case of China, capital controls, a managed exchange-rate regime and policy interventions tend to buffer external rate shocks; accordingly, the DLNM surfaces show attenuated and short-lived effects, suggesting policy and segmentation dampen both valuation and risk-premium channels. Russia (proxied by EMEA), here, sanctions and market segmentation since 2022 imply tighter external financing and elevated risk premia; the more immediate adverse reactions to tightening are consistent with funding/FX and risk-premium channels, though results must be interpreted with caution given the EMEA proxy. South Africa. An open—but smaller—market with a flexible exchange rate and commodity exposure exhibits short-horizon effects that are quickly absorbed as FX adjustment and domestic risk premia dominate, yielding weaker persistence.

5. Conclusions

This study provides compelling evidence of the heterogeneous and nonlinear transmission of global interest rate shocks to equity markets in BRICS countries. By applying a DLNM to a standardized WIR index, we unveil differentiated exposure-lag-response dynamics across markets, highlighting the importance of context-specific structures, institutional arrangements, and degrees of financial openness.

Brazil exhibits a delayed yet asymmetric response, with expansionary global shocks (i.e., lower rates) generating gradually stronger and more persistent positive effects on equities. This pattern suggests that Brazil’s market is responsive to global liquidity conditions, possibly due to the attractiveness of its assets during periods of monetary easing in developed economies. Policymakers and investors should therefore consider the role of global easing cycles in stimulating capital inflows and asset revaluation in Brazil, particularly with a lag. Russia, in contrast, demonstrates an immediate and strongly negative reaction to global monetary tightening but little benefit from easing episodes. This asymmetric and fragile pattern reflects the market’s sensitivity to capital outflows, geopolitical risk, and commodity-price linkages. The evidence underscores the vulnerability of highly externally exposed economies to abrupt shifts in global financial conditions—an insight relevant for risk managers and monetary authorities seeking to build buffers against external volatility. It is important to note a limitation regarding Russia: since the MSCI Russia Index was suspended in 2022 due to geopolitical sanctions, we relied on the MSCI Emerging Markets EMEA Index as a proxy. While this choice preserves continuity in the sample, it may dilute country-specific dynamics and should be interpreted with caution. Future research could explore alternative datasets or country-level sources to better capture Russia’s equity market behavior under sanctions. India shows a unique configuration where negative WIR shocks (loosening) elicit more prominent, though delayed, negative reactions. This counterintuitive result may reflect structural features of India’s capital market, such as selective openness and institutional inertia in reallocating capital. The muted response to tightening further supports the notion of partial insulation, yet the delayed adverse effects from easing highlight a nuanced vulnerability that decision-makers should not overlook.

China’s market behavior is the most contained among the BRICS. The surface remains relatively flat, with responses that are mild and symmetric. This stability is likely due to China’s tight capital controls, large domestic investor base, and regulatory mechanisms that insulate the financial system from abrupt external shocks. While this may dampen external volatility, it may also limit the transmission of beneficial global cycles. Policymakers elsewhere may draw lessons from China’s institutional design, although its replicability is limited by broader governance and economic frameworks. South Africa presents a marginal and statistically weak sensitivity to global interest rate changes. The response is neither immediate nor robust, suggesting that its market operates within a moderated global transmission channel. This may be attributed to a hybrid financial architecture—integrated enough to reflect global trends but with domestic stabilizers mitigating excess volatility. For policymakers, this implies that conventional global spillover models may overestimate the risk transmission to South African equities, emphasizing the need for context-specific risk assessments.

Our findings reaffirm that global financial conditions are not transmitted uniformly across emerging markets. The effects depend critically on the structural features of each economy, the composition of market participants, capital mobility, and the degree of regulatory oversight. For international investors, this means that country-specific risk assessments are indispensable when responding to global monetary shifts. For central banks and financial regulators in emerging economies, the results underscore the importance of reinforcing domestic resilience mechanisms to manage the asymmetric and delayed nature of global shock propagation.