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Research Article
Quantile Evidence on Institutional Quality and Economic Growth in a Fragile State: The Case of Afghanistan
expand article infoYang Jingjing, Shah Mir Mowahed, Mariam Reha§
‡ School of Economics and Trade, Hunan University, Changsha, China
§ General Directorate of the Institute of Legislative Affairs and Academic-Legal Research, Ministry of Justice, Kabul, Afghanistan
Open Access

Abs tract

In recent decades, the role of institutions has become a central topic of discussion among scholars and policy makers. This study used time-series data from Afghanistan between 1996 and 2024 to gain new insights into the impact of political instability (POI), corruption (COR) and government effectiveness (GEF) on economic growth. The results of Quantile-on-Quantile Regression and Wavelet Quantile regression reveal that POI, COR, and GEF have adverse and statistically significant effects on GDP growth across all quantiles and over long-term time periods. Event analysis through the interrupted time series technique shows that the key political events, including the Civil War (CW), the First Round of the Taliban Regime (FRTR), U.S.-NATO interventions (USN), the Second Round of Taliban Regime (SRTR), and Regime Changes (RCH), have had a negative impact on Afghanistan’s GDP growth. The immediate impact of the Soviet Union’s war is estimated to be positive. At the same time, Afghanistan’s GDP experienced negative growth during SUW, CW, FRTR, and RCH, while during USN and SRTR, the GDP growth was positive. Based on these findings, the paper discusses possible policy implications.

Keywords

GDP Growth, Institutional Quality, Quantiles Analysis, ITS approach

JEL: O43, C22, P48, D74.

1. Introduction

In recent decades, economists, academics and policy makers have paid significant attention to the relationship between economic growth and institutions. North (1990) and many other researchers (e.g. De Almeida et al., 2024) emphasized the critical role of institutions in shaping national economic growth. To explain cross-country differences in economic development, North identified the underlying factors that contributed to both divergent and convergent economic outcomes. Institutions, on the one hand, can help create a favourable business environment if they reduce uncertainty in transaction costs and foster economic activity. They can also provide political stability, protect property rights, strengthen the rule of law, and rein in corruption (North, 1990; Acemoglu et al., 2001; Corradini, 2021; Heo & Hahm, 2015; Dirks & Schmidt, 2024). On the other hand, fragile institutions — those lacking transparency and accountability —undermine governance quality, fuel political instability, exacerbate inequality, and hinder long-term economic development (Acemoglu et al., 2014; Acemoglu et al., 2001; Brinks et al., 2019; North, 2003).

The concept of “institutions” encompasses several key elements, including the rule of law, control of corruption, government effectiveness, quality of regulation, voice and accountability, stability of political systems, protection of property rights, independence of the judiciary, economic freedom and the size of public sector. The study focuses on the impact of political instability, corruption and government effectiveness on economic growth in Afghanistan.

Over the past fifty years, Afghanistan has struggled to establish state and public institutions. This has been a difficult task due to deep socio-economic crises, poor governance, foreign interventions, civil war and persistent political instability (Beidollahkhani, 2025). Looking further back into the history of Afghanistan, the roots of institutional building can be traced back to the reign of Amunullah Khan, who was credited with securing the independence of Afghanistan from Britain (Chua, 2014). Amunullah was a modernist leader who sought to reform Afghani society and establish a strong state. In 1923 he introduced a constitution and made attempts to establish a robust judicial system within the framework of monarchy (Chua, 2014).

However, despite the relative political stability between 1933 and 1978, the country’s formal institutions were weak, heavily reliant on foreign aid, lacking the administrative capacity necessary to support broad-based economic development. Later political events, including the Soviet invasion and the ensuing civil war, the first and second Taliban regimes, and the U.S.-led intervention, further exacerbated institutional fragility (Alimi, 2025; Rubin, 1995). These events militarized governance, disrupted administrative structures, and contributed to repeated regime changes in 1979, 1992, 1996, 2001, and 2021.

In this war-torn country, discussions about the concept and role of institutions - particularly their ability to help the government provide public services, uphold the rule of law, protect national security and territorial integrity, and safeguard citizens’ rights and freedoms — resumed after the year 2001 (Hakimi, 2024). However, attempts to rebuild institutions and infrastructure failed to achieve sustainable outcomes even with US aid amounting to around $140bn (SIGAR, 2021). The influx of foreign aid, instead of promoting stability, unintentionally strengthened corrupt actors and their networks, thus intensifying conflict, insecurity, and political instability (Dyer, 2016; Shah, 2024; Meng et al., 2025). Furthermore, the combination of large amounts of foreign aid and weak governance created a breeding ground for systemic corruption and collusion between government officials, local elites, and warlords. This also led to the development of a culture of political kleptocracy (Transparency International, 2024; Jodi, 2021; Azizi, 2021; Meng et al., 2025). These interrelated dynamics eroded domestic institutional capacity, undermined the prospects for sustainable development, and ultimately led to the collapse of the republican regime on 15 August 2021.

Based on the information provided and our best understanding, this is the first empirical study of the relationship between institutional quality and economic growth in Afghanistan. Seeking to evaluate this relationship, we will use econometric techniques to answer the following research question:

RQ: How do political instability, corruption, and government (in)effectiveness influence economic performance in a country with a fragile institutional system, such as Afghanistan, in the short, medium, and long term?

By providing an answer to this RQ based on the empirical analysis, our study contributes to the existing literature in several ways. First, in line with most empirical studies, this paper provides evidence that political instability, corruption, and government (in)effectiveness have a negative impact on economic growth in the short, medium, and long term in Afghanistan. Second, our empirical findings show that political instability, corruption, and government effectiveness are not only economically relevant for developed and developing economies, but also have implications for the prosperity of Afghanistan and other less developed and war-torn nations. Third, our findings concerning the impact of corruption on economic growth support the theory of “sanding the wheels”, suggesting that corruption acts as a significant barrier to economic growth in Afghanistan. Finally, in addition to using advanced econometric approaches such as Quantile-on-Quantile Regression (QQR) and Wavelet Quantile Regression (WQR), which capture the effects of the explanatory variables’ quantiles on different quantiles of the dependent variable(s), this study also employs the Wavelet Quantile Correlation (WQC) technique for robustness verification and the Interrupted Time Series (ITS) method for event analysis. Collectively, these methodologies ensure the use of the most appropriate and rigorous econometric tools in order to effectively address the proposed research question (RQ).

The rest of the study is organized as follows: Section 2 reviews the related empirical studies, Section 3 provides information about the data and methodology, Section 4 focuses on the interpretation of the empirical findings, and Section 5 reports the conclusions and policy recommendations.

2. Literature Review

The fundamental drivers of economic growth have been the subject of intensive scholarly debate for a long time. Some scholars emphasise the pivotal role of human capital, which is the key engine for economic performance. This is supported by the work of Barro (2001), Hanushek and Woessmann (2008, 2012) who argue that human capital, especially the human capital of political elites and national business executives, shapes economic outcomes (Jones & Olken, 2005; Besley et al., 2011; Shi, 2024; Shi, 2025). At the same time, a prominent strand of literature posits that institutional quality remains the primary determinant of growth (Acemoglu et al., 2001; Rodrik et al., 2004).

Building upon the institutional perspective, recent empirical studies have increasingly sought to examine how institutional quality and stability influence economic performance across countries. For instance, Acemoglu et al. (2000, 2001, 2014), North (1990, 2003), and Matta et al. (2022) point out that political instability can lead to weak institutions, which, over time, have an unfavorable impact on economic performance. Similarly, studies by Jong-A-Pin (2009), Alesina et al. (1996), Alesina & Perotti (1996), Aisen & Veiga (2013), and Dirks & Schmidt (2024) have demonstrated that political instability has a detrimental impact on economic growth. Empirical studies conducted by Murad and Alshyab (2019), and Assfaw et al (2025), found that political instability impedes economic growth by reducing investment and leading to a loss of physical capital. This was observed in Jordan and Ethiopia respectively. Moreover, political instability is a major vulnerability that causes production disruptions in many developing countries. The precautionary principle motivates investors to reduce both domestic and foreign direct investment, (Asteriou & Price, 2001; Delgado et al., 2014; Gakpa, 2020). This ultimately deters consumption (Bahmani & Nayeri, 2020) and slows productivity (Alexandre et al., 2022; Paulo et al., 2022; Abdelkader, 2017).

Corruption is another significant factor affecting economic performance of a nation, which depends on the quality of institutions and governance. Its impact on economic growth is explained by two competing hypotheses. According to the “greasing the wheels” hypothesis, corruption occurs in economies suffering from weak governance and, by speeding up administrative procedures and overcoming bureaucratic bottlenecks at low cost, stimulates economic activities (Shabbir et al., 2016; Assfaw et al., 2025; Gründler, & Potrafke, 2019; Dokas et al., 2023). Empirical findings by Méndez & Sepúlveda (2006) and Paul (2010) support this theory, indicating that corruption exerts a positive impact on economic growth. Conversely, the “sanding the wheels” hypothesis maintains that corruption in economies with fragile institutional setups causes misallocation of resources, shifting public gains to private profits, thus creating socio-political uncertainty and disrupting economic progress (Méon & Sekkat, 2005; Dokas et al., 2023; Mauro, 1995; Aidt et al., 2008; Cieślik & Goczek, 2018). This hypothesis is supported by recent empirical studies, such as Gründler and Potrafke (2019), Nur-tegin and Jakee (2020), Sharma and Mitra (2019), Paulo et al. (2022), Dirks and Schmidt (2024), and Assfaw et al. (2025). In economies where institutions are not properly enforced, businesspeople, traders, politicians, and administrators often engage in corrupt practices (Acemoglu & Verdier, 2000). Corruption affects GDP by reducing the quality of human capital (Cieślik & Goczek, 2018) and encouraging inefficient allocation of government resources. Corrupt officials seek to maximize their rent-extracting potential (D’Agostino et al., 2016; Montinola & Jackman, 2001), which hinders investment and trade freedoms (Gründler & Potrafke, 2019), and limits funding for innovative activities (Xu & Yano, 2017; Dincer, 2019; Assfaw et al., 2025).

The third factor that poses a threat to the quality of governance and, hence, to economic performance, is institutional fragility. Fragile institutions often lack the ability to enforce laws, provide public services efficiently, and maintain accountability mechanisms. This undermines the overall capacity of the state (De Almeida et al., 2024). By contrast, a strong institutional framework, characterized by political stability, an effective legal system, and robust mechanisms for controlling corruption, contributes positively to economic growth (Asiamah et al., 2022; Mawardi et al., 2024; Correa & Esquivias, 2024). Consequently, good and effective governance plays a crucial role in economic development as it reduces expenses associated with transactions, enforces ownership rights, maintains administrative stability and facilitates various economic activities (Zhou & Feng, 2024; Pang et al., 2024). An effective government fosters trust among investors, promotes technological innovation, and enhances economic performance (Jia et al., 2021). It can facilitate business activities and create a favourable environment for investment and entrepreneurship by reducing administrative hurdles and optimizing public sector operations (Mafimisebi & Ogunsade, 2022). Furthermore, by designing optimal policies, effective governments target high-quality economic development (Kong et al., 2021; Li & Li, 2025). In contrast, weak governments face barriers to meeting public needs and achieving high-quality development. (Zhao et al., 2022; Li & Li, 2025).

The literature emphasizes that weak institutions and corruption hinder economic performance and prevent wider development outcomes. Ear (2016) points out that corruption in Cambodia remains deeply entrenched, with anti-corruption initiatives largely ineffective due to insufficient political will and the persistence of institutional loopholes that undermine enforcement efforts. Similarly, Oyebanji and Omale (2025) regard financial and economic corruption among Nigerian public officials as a systemic reality driven by greed, lack of accountability, political patronage, external influence, and social pressures. They argue that meaningful reform is impossible without addressing the abuse of constitutional immunities by political elites. Complementing these insights, Adelakun et al. (2025) demonstrate that stronger institutional quality can mitigate the migration-induced effects of instability and insecurity, highlighting the importance of governance reform in reducing brain drain in fragile environments. Likewise, Egbetokun et al. (2019) show that institutional quality significantly influences the relationship between economic growth and environmental degradation in Nigeria. This implies that governance effectiveness has a critical mediating effect on sustainable development.

Collectively, these studies confirm that institutional fragility — manifested through corruption, weak governance, and political instability — remains a central barrier to stability and growth in fragile countries. However, despite extensive research into similar contexts, the non-linear effects of political instability, corruption, and government (in)effectiveness on Afghanistan’s GDP growth remain empirically unexplored, which underscores the significance of the present study.

3. Data and Methodology

This section provides detailed information about the econometric model, the dataset, and the steps of the novel empirical technique used in this study. It also explains the justification for this approach.

3.1. Econometric Models and Data

To examine the impacts of political instability (POI), corruption (COR), and government effectiveness (GEF), following Dirks & Schmidt (2024), Alexandre et al. (2022), Dokas et al. (2023), Li & Li (2025), and Assfaw et al. (2025), we employ the following econometric model:

GDPt = f (POIt , CORt , GEFt) (1)

where GDPt is the gross domestic product, POIt denotes political (in)stability, CORt shows control of corruption, and GEFt stands for government effectiveness.

To empirically estimate model (1), this study utilizes a time series dataset for Afghanistan covering the period from 1996 to 2024 (see Panel A of Table 1). The selection of this time frame is primarily driven by data availability, particularly for the institutional quality indicators that serve as the key independent variables in this study. Moreover, during this period Afghanistan underwent multiple governance regimes, most of which were brought to power by force, violence or prolonged military conflicts - often as a result of direct or indirect intervention by major regional or global powers. These dynamics not only hindered the country’s economic development but also intensified political instability, caused widespread corruption, and undermined government effectiveness.

Table 1.

Variables, measurements, and data sources.

Variables Acronyms Definition and measurement
Panel A: Data related to GDP, POI, COR, and GEF will be used for conducting baseline analysis using QQR and WQR techniques, and robustness checks analysis using the WQC technique.
Economic Growth GDP Gross domestic product (constant, US$, 2015)
Political (In)stability Index POI Political instability measures perceptions of the likelihood of overthrow by unconstitutional means or violence and terrorism.
Control of corruption COR Control of the corruption measures the degree to which the government uses its power for personal gain, encompassing both small-scale and large-scale corruption, as well as the “capture” of the state by elites and private interests.
Government Effectiveness Index GEF Government Effectiveness: Standard Error
Panel B: Data related to GDP, SUW, CW, FRTR, USN, and SRTR will be used for conducting event analysis using the ITS technique.
Economic Growth GDP Gross domestic product (constant, US$, 2015)
Soviet Union War SUW The dummy variable takes the value 1 for the war period (1979-1989) and otherwise 0.
Civil War, including the Taliban First Round Regime CW The dummy variable takes the value 1 for the war period (1989-2001) and otherwise 0.
First Round Taliban Regime FRTR The dummy variable takes the value 1 for the war period (1996-2001) and otherwise 0.
United States and NATO Military Presence USN The dummy variable takes the value 1 for the war period (2001-2021) and otherwise 0.
Second Round Taliban Regime SRTR The dummy variable takes the value 1 for the war period (2021-2024) and otherwise 0.

To capture the pre-event economic growth trajectory, the immediate impact of the event, and the subsequent growth trend, this study extends the GDP data from 1996–2024 to 1975–2024 and incorporates several dummy variables (see Panel B of Table 1). The use of GDP data over this extended period is justified because it covers the major political events that led to a decline in institutional quality and hindered Afghanistan’s economic development.

This study uses GDP as the primary dependent variable, while the key independent variables include POI, COR, and GEF. The dataset is sourced from the World Development Indicators (WDI) and World Governance Indicators (WGI) databases. Table 1 provides detailed information about the variables’ names, definitions, and measurements.

Fig. 1 illustrates the annual trends of the targeted variables. The natural log of total GDP trend reveals two critical points: one in 2001, marked by the U.S. invasion of Afghanistan, and the other in 2021, when the Islamic Republic of Afghanistan collapsed and the Taliban took control. Additionally, GDP demonstrates positive growth between these two inflection points and continues to exhibit an upward trajectory following the 2021 regime change. In contrast, political POI, COR, and the GEF have shown a consistent decline over the past three decades (1996-2024).

Fig. 1. 

Annual trends of LnGDP, POI, COR, and GEF from 1996 to 2024.

3.2. Empirical Estimation Strategies

To empirically examine the impact of POI, COR, and GEF on GDP growth, we employ Quantile-on-Quantile Regression (QQR) and Wavelet Quantile Regression (WQR) to estimate the baseline results. For robustness checks aimed at validating the reliability of the QQR and WQR findings, we use Wavelet Quantile Correlation (WQC), and, finally, we apply the Interrupted Time Series (ITS) method to examine the impact of major political events on growth in Afghanistan.

3.2.1. QQR and WQR Techniques

This study examines the non-linear effects of explanatory variables on the dependent variable using Quantile-on-Quantile Regression (QQR) and Wavelet Quantile Regression (WQR). Sim and Zhou (2015) proposed the QQR methodology to capture the non-linear association between the quantile of a dependent variable and the quantile of an independent variable(s). Assuming the X is the primary independent variable and Y is the main dependent variable, the single-variate-based QQR mathematical form for the connection between the quantiles of Y and X can be structured as follows:

(2)

where θ and Φ show the quantiles (0.05–0.95) of the Y and X, and ϵtθ stands for error term with θ — quantiles. Additionally, part (*) of Eq. (2) represents the dependence structure between dependent and independent variables through their respective distributions. Moreover, following Alola et al. (2023) methodology, and assuming Y as the dependent variable and X1, X2, ... Xn as independent variables, the multivariate-based QQR mathematical model can be designed as follows:

Yt=β0(θ,Φ1,Φ2,,Φn)+β1(θ,Φ1)(X1tX1Φ1)++β2(θ,Φ2)(X2tX2Φ2)+βn(θ,Φn)(XntXnΦn)+αθYt1+ϵtθ (3)

where Φ1, Φ2, …, Φn quantify the quantiles of X1, X2, ... Xn, respectively, and the θ shows the quantile of Y. In this paper, the QQR implementation procedure follows the studies by Alola et al. (2023) and Sim and Zhou (2015).

The WQR technique, proposed by Adebayo and Özkan (2024), can capture the impact of X on Y across time scales and quantiles, addressing the drawbacks of Quantile Regression (QR). Following the empirical studies, including Adebayo and Özkan (2024), Liu et al. (2024), and Kumar and Padakandla (2022), this study decomposes the time series data of the response variable (Yt), and explanatory variable (Xt) utilizing the MODWT1 (maximal overlapping discrete wavelet transform). Let X[i] be a signal with a length of T, where T = 2J For an integer J. Then, consider h1[i] as the low-pass filter and g1[i] as the high-pass filter, both defining the orthogonal wavelet. At the initial step, X[i] undergoes convolution with h1[i] to yield the approximation coefficients denoted as α1[i] of length N, and with g1[i] to yield the detail coefficients denoted as d1[i] of length N. These procedures can be defined as follows:

α1[i]=h1[i]s[i]=kh1[ik]s[k] (4)

d1[i]=g1[i]s[i]=kg1[ik]s[k] (5)

Following the same steps, we employ a similar method to filter α1[i], using modified filters h2[i] and g2[i] obtained from the dyadic up-sampling of g1[i] and h1[i]. This recursive process is carried out iteratively. For values of J spanning from 1 to j0 – 1, where J0J, we can calculate the coefficients of the approximate and detailed as follows:

αj+1[i]=hj+1[i]αj[i]=khj+1[ik]αj[k] (6)

dj+1[i]=hj+1[i]αj[i]=kgj+1[ik]αj[k] (7)

In this context, hj + 1[i] = U(hj[i]) and gj + 1[i] = U(gj[i]), where the up-sampling operation is illustrated by operator U. This operation involves inserting a zero value between each consecutive pair of time series.

Following the application of a J-level decomposition to Yt and Xt, and the subsequent acquisition of the detail coefficients, we proceed to implement QR on the pair of WQR details, dj(Y) and dj(X), for all levels of J. Consequently, we derive the WQR outcomes for each level of J. Finally, the WQR technique for the dependent variable Y and the independent variable X at a specific decomposition level J, and for a given quantile q, can be rewritten as follows:

ϕ(q)=dj[Y]dj[X])=B0(q)+B1(q)dj[X] (8)

3.2.2. WQC Technique

To verify the reliability of the baseline results, we employ the WQC technique. The WQC technique proposed by Kumar and Padakandla (2022) is based on the quantile correlation method by Li et al. (2015). To calculate the quantile-wise correlation between two time series variables, Li et al. (2015) suggests that Qτ,X = τth quantile of the independent variable, while Qτ,Y = τth quantile of the dependent variable, with the following mathematical expression:

ϕ(q)=dj[Y]dj[X])=B0(q)+B1(q)dj[X] (9)

where qcovt(Yt ,Xt) presents the quantile correlation between the two series.

To extend the described method, following Kumar and Padakandla’s (2022), this study decomposed the modeled series, such as Yt and Xt, using the MODWT technique at Jth level, and obtained the WQC for each J level based on the following mathematical equation.

qcovt(dj[Yt],dj[Xt])=qcovt(dj[Yt],dj[Xt])var(φτ(dj[Yt]Qτ,dj[Yt]))var(dj[Xt]) (10)

Eq. (10) shows the WQC between the modeled series, such as Y and X. This method can handle potential outliers in the data and produce consistent results (Kumar & Padakandla, 2022). Furthermore, WQC captures plausible asymmetries by providing results for different quantiles and presents a comprehensive view of the dynamic relationship over the whole sampled period (Kumar & Padakandla, 2022).

Fig. 2 outlines the sequential empirical analysis framework, from data collection through descriptive analysis, diagnostic tests (Unit Root, BDS), baseline regressions (QOR, WQR), robustness checks (WQC), and event analysis via Interrupted Time Series (ITS). This structured approach ensures a comprehensive and methodologically coherent investigation.

Fig. 2. 

Empirical analysis steps.

4. Empirical Results and Discussions

4.1. Preliminary Time Series Analysis

Before conducting the primary analysis, we performed several preliminary calculations and tests. These included descriptive statistics, correlation analysis, unit root tests for quantiles and the nonlinear BDS test. The purpose of these tests was to capture the characteristics of the variables used in our study.

Table 2 presents descriptive statistics for the variables, including mean and standard deviation, minimum, maximum values, skewness and kurtosis. It also includes the results of Jarque-Berra normality test. Based on these outcomes, GDP exhibits the highest mean and standard deviation, whereas COR and GEF record the lowest mean and standard deviation, respectively, reflecting the variability within the dataset. Table 2 presents descriptive statistics for the variables, including mean, standard deviation, minimum, maximum values, skewness and kurtosis. It also includes the results of Jarque-Berra normality test. Moreover, the Jarque-Bera test and the associated probabilities show that all the variables significantly follow a normal distribution. Fig. 3 shows the correlation coefficients between GDP and all explanatory variables. As shown, POI has the strongest negative correlation with GDP, followed by COR and GEF.

Fig. 3. 

Correlation coefficients heatmap between GDP, POI, COR, and GEF

Table 2.

Descriptive statistics results

Variables GDP POI COR GEF
Mean 23.229 0.303 0.222 0.260
Std. dev. 0.446 0.085 0.069 0.034
Min 22.449 0.208 0.154 0.187
Max 23.773 0.474 0.352 0.331
Skewness -0.301 0.776 0.822 0.167
Kurtosis -1.497 -0.868 -0.908 -0.725
Jarque-Bera 3.150 3.827 4.270 0.772
p-values 0.206 0.147 0.118 0.679
Obs. 29 29 29 29

Fig. 4 presents the quantile unit root test based on the Quantile Augmented-Dickey Filler (QADF) method, respectively, for each variable. Conducting these tests is a crucial step before applying QQR and WQR techniques. This study employs the QADF unit root test proposed by Adebayo and Özkan (2024). Unlike traditional unit root tests, such as ADF, which assume constant distributional properties across the entire range, the QADF test accounts for potential distributional differences across various quantiles of the distribution. Based on the results shown in Figs. 4, all variables exhibit non-stationarity at the level. After taking the first difference of the variables, GDP and GEF exhibit stationarity across all quantiles, while POI and COR show stationarity between 0.35-0.40 and 0.15-0.8 quantiles, respectively.

Fig. 4. 

QADF unit root test

Finally, we performed the BDS test introduced by Brock et al. (1996)2 to examine the non-linear characteristics of the response and explanatory variables. Table 3 presents the BDS non-linearity test results, which indicate that the relationships between GDP and POI, GDP and COR, and GDP and GEF exhibit non-linear behavior, as evidenced by their corresponding p-values being significant at the 1% significance level. These results confirm the suitability of applying nonlinear techniques, such as QQR and WQR.

Table 3.

BDS test results

Dimensions GDP = f(POI) GDP = f(COR) GDP = f(GEF)
Dimensions-II 23.188*** (0.000) 27.585*** (0.000) 10.073*** (0.000)
Dimensions-III 32.399*** (0.000) 38.338*** (0.000) 14.355*** (0.000)
Dimensions-IV 93.995*** (0.000) 120.606*** (0.000) 10.179*** (0.000)
Dimensions-V 120.188*** (0.000) 152.834*** (0.000) 10.415*** (0.000)
Dimensions-VI 25.235*** (0.000) 38.943*** (0.000) 7.859*** (0.000)
Dimensions-VII 27.811*** (0.000) 44.714*** (0.000) 7.497*** (0.000)

4.2. Baseline Results

4.2.1. QQR Results

To evaluate the non-linear impacts of POI, COR, and GEF on GDP in the context of Afghanistan, we used the QQR technique and the results of this method are shown in Fig. 5. Fig. 5(a) illustrates the effect of POI on GDP, indicating that within the lower and middle quantiles (ranging from 0.2 to 0.60), POI has a significant negative impact on GDP. In the higher quantiles (ranging from 0.8 to 0.9), the effect was also negative, but weak. This relationship suggests that POI consistently hinders GDP growth across all quantiles in Afghanistan. These results are consistent with the theories used and can provide practical explanations of the political economy of Afghanistan from different perspectives.

Fig. 5. 

(a). Impact of POI on GDP, (b). Impact of COR on GDP, (c). Impact of GEF on GDP, and (d). Impact of POP

In lower and middle GDP quantiles, where the economy is already weak, POI exacerbates vulnerabilities due to fragile institutions, weak role of low-income groups, and inconsistent policy implementation. This result presents a current image of political economy in Afghanistan, with its fragile institutions and government deficits over the past three decades. Frequent regime changes and contested governance reduce investor confidence, disrupt aid flows and weaken the delivery of government services, collectively hindering the positive dynamics of GDP growth (Jingjing et al., 2025). Moreover, persistent internal conflicts, insurgencies, and external interventions have created a highly risky environment where productive sectors are struggling to operate efficiently. Besides, POI often triggers security breakdowns, which interrupt trade, limit mobility and damage infrastructure, particularly in the sectors with medium to low growth rates. Political instability and inefficient institutions significantly weaken the state’s capacity to absorb resources. This leads to misallocation of resources and economic decline. It is not surprising that Afghanistan heavily relies on international aid for its economic development.

Additionally, POI frequently leads to policy reversals and disrupted long-run development strategies, which prevents the accumulation of human capital, limits technological innovation, and hinders macroeconomic planning and public-private collaboration. Political unrest inhibits foreign direct investment and prevents the local capital holders from externalizing assets. As a result, the base for industrial growth and job creation is shrinking. This is especially true for Afghanistan, whose economy relies heavily on external aid, trading routes, and geopolitical dynamics. These findings are supported by empirical literature, including Aisen & Veiga (2013), Murad et al. (2019), Abdelkader (2017), Okafor (2015), Dirks & Schmidt (2024), and Assfaw et al. (2025).

Moreover, Fig. 5(b) shows that COR adversely influences Afganistan’s GDP growth across all quantiles. The effects are observed at the three levels: low, medium, and high. Within the lower quantile (ranging from 0.2 to 0.4), the negative impact on performance is most significant. In the middle and upper quantiles (from 0.5 to 0.8), the effects are still negative, but they decrease in magnitude over time. These findings are both theoretically and practically sound.

The persistent negative impact of COR on GDP supports the “sanding the wheels” hypothesis, suggesting that COR impedes rather than facilitates growth by increasing transaction costs, lowering institutional efficiency, and degrading public trust. Furthermore, the gradual move toward zero from the medium to the higher quantiles may reflect the growth resilience of the system in the face of COR, but still shows that COR acts as a structural ceiling on Afghanistan’s economic performance.

Afghanistan’s public sector is characterized by weak legal enforcement and limited bureaucratic capacity, where COR deters GDP growth by undermining trust in government and discouraging both domestic and foreign investment. Additionally, COR often redirects government spending from productive sectors, such as infrastructure and education, toward low-return patronage networks (Mauro, 1955), specifically in lower GDP quantiles, where investment is already insufficient. Moreover, COR raises the cost of doing business through informal fees, regulatory uncertainty, and favoritism, which collectively restricts entrepreneurship, diminishes innovation, and erodes the competitive environment (Murphy et al., 2008) even in relatively higher GDP quantiles. Finally, COR frequently results in unpredictable policy changes, making investors and firms reluctant to commit to long-term investments (Olofsgård & Zahran, 2008). These findings are in line with empirical studies by Kaufmann et al. (1999), Rock and Bonnett (2004), Knack and Keefer (1995), Li and Xu (2000), Méon & Sekkat, (2005), Mo, (2001), and Assfaw et al. (2025), but contradict the study by Paul (2010) who concludes that COR is positively associated with GDP growth in Bangladesh.

Fig. 5(c) reveals a counterintuitive, non-linear relationship between GEF and GDP growth in Afghanistan. Contrary to conventional theory, medium-to-high levels of GEF (quantiles 0.30–0.90) have a significant negative influence on growth quantiles. Conversely, in the lowest quantiles of the GEF (0.1–0.2), the effect changes from a weakly negative to a positive one. This paradox is theoretically consistent in the context of Afghanistan, where institutions are characterized by a deep-seated fragility. It suggests that in such a setting, efforts to enhance formal governance — particularly when they are perceived as incomplete or externally imposed — may create friction, raise transaction costs, or disrupt established (if informal) economic networks without providing the corresponding benefits of stability and predictability, thereby stifling growth.

Theoretically, the non-linear relationship between GEF and GDP growth in Afghanistan can be explained through the lens of institutional transition theory and governance traps. The most significant negative impact on GDP is from the middle and high quantile of GEF. At the extremes of the distribution, there are weaker adverse effects. This pattern suggests that partial or fragmented improvements to governance may initially destabilize informal economic arrangements, without delivering the necessary institutional coherence to support sustained economic growth (Auerbach & Azariadis, 2015). Such dynamics are consistent with the concept of the governance trap, in which countries with weak institutional capacities find it difficult to translate their governance reforms into economic benefits (Acemoglu et al., 2014; North, 1990).

In the case of Afghanistan, medium quantiles may represent transition phases, where reforms are often driven externally, disrupting rent-seeking networks and informal governance structures. At the same time, the reforms lack the capacity or legitimacy to replace these structures with functional alternatives. The resulting institutional incoherence can suppress growth by increasing uncertainty, overregulation, and policy inconsistency (Mauro, 1995; Rodrik et al., 2004; Chowdhury et al., 2018). These findings align with empirical studies showing that growth reversals are more likely to occur in countries undergoing a shallow institutional transition, where governance reforms are not supported by credible enforcement mechanisms or inclusive political settlements (Knez & Lokar, 2024). Afghanistan’s experience shows that it is important to sequentially implement reforms and establish institutional credibility before expecting governance improvement to yield consistent economic benefits. Empirical studies by Kinyondo et al. (2021), Yapatake et al. (2022), Chhabra et al. (2023), and Atemnkeng et al. (2024) support the idea that good and effective governance contributes to economic growth and development.

The numerical values of Figs. 5(a), 5(b) and 5(c) are presented in Tables A1, A2 and A3 of the Appendix, respectively.

4.2.2. WQR Results

Building on the confirmed non-linear impacts of POI, COR, and GEF on GDP growth established in the previous section, this paper employs the Wavelet Quantile Regression (WQR) methodology to examine the associations between these explanatory variables and GDP growth in the short, medium, and long term. In contrast to conventional quantile regression (QR), which is effective at handling non-linear relationships, wavelet quantile regression (WQR) offers enhanced flexibility by analyzing the impact of explanatory variables over various time horizons and quantiles. This allows for the capture of a more diverse range of non-linear patterns. The results of the WQR analysis are presented in Fig. 6, using a heatmap visualization where colors progress from dark purple (representing adverse effects) to light green (representing positive effects), in ascending order.

Fig. 6. 

(a). Impact of POI on GDP, (b). Impact of COR on GDP, and (c). Impact of GEF on GDP

Fig. 6(a) illustrates the impact of POI on GDP growth in Afghanistan, indicating that in the short and medium term, the effects of POI on GDP are adverse but weak. In the long term, however, POI exerts a more substantial adverse effect. Specifically, the long-term estimated slope coefficients show that POI severely impacts GDP in all the quantiles (0.05–0.95). In contrast, the short-term coefficients indicate that POI’s effect on GDP growth is weak and hovers around zero across the same quantile range.

Similarly, Fig. 6(b) illustrates the impact of COR on GDP, demonstrating that corruption harms GDP growth in Afghanistan in the long term across all quantiles. Notably, within the 0.45–0.75 quantiles of GDP, the medium-term impact of COR remains negative and strong, while its short-term impact is negative but close to zero. Overall, the adverse long-term effect of COR is more severe than its short- and medium-term impacts across all quantiles of GDP.

Finally, Fig. 6(c) displays the relationship between GEF and GDP growth in Afghanistan. The results indicate that the long-term effects of GEF on GDP quantiles (ranging from 0.05 to 0.80) are adverse and strong, while the short- and medium-term effects across all quantiles are adverse but close to zero. The findings from the WQR technique provide theoretical and practical justification for the discussions based on the QQR methodology presented in the previous section.

The numerical values of Figs. 6(a), 6(b) and 6(c) are presented in Table A4 of the Appendix.

4.3. Robustness Checks using WQC Method

To verify the reliability of the findings obtained through the Quantile-on-Quantile Regression (QQR) and Wavelet Quantile Regression (WQR) methodologies, we use the Wavelet Quantile Correlation (WQC) technique. The results concerning the quantile correlation between the response variable (GDP) and the explanatory variables (POI, COR, and GEF) are presented in Fig. 7. Based on the estimated correlation coefficients between POI and GDP shown in Fig. 7(a), we conclude that the relationship between POI and GDP is strongly negative in the long and medium term, notably in quantile 0.50; in the short term it remains negative but weak. This result confirms the primary findings regarding the impact of POI on GDP, as determined by the QQR and WQR techniques.

Fig. 7. 

(a). WQC between POI and GDP, (b). WQC between COR and GDP, and (c). WQC between GEF and GDP.

Fig. 7(b) presents the correlation coefficients between COR and GDP, indicating that the medium- and long-term relationship between COR and GDP is negative and strong. In the short term, the correlations across quantiles ranging from 0.05 to 0.95 remain negative but weak. However, in the quantiles of 0.40 and 0.50, COR exhibits the strongest negative correlation with GDP growth in Afghanistan, in the medium and long term, respectively. This result confirms the robustness of the findings regarding the relationship between COR and GDP growth obtained using the QQR and WQR techniques.

Finally, Fig. 7(c) illustrates the correlation coefficients between GEF and GDP growth across all quantiles. It reveals that there is a consistently negative relationship between them across all time horizons and at all quantile levels. This is particularly true for quantiles 0.4 and 0.5 in the medium-term. These outcomes further validate the main findings on the impact of GEF on GDP growth obtained using the QQR and WQR techniques.

4.4. Event Analysis using Interrupted Time Series (ITS) Model

To further enhance the analysis in this paper, we have examined the impact of several significant political events on Afghanistan’s GDP growth by using data from Panel B of Table 1 and applying the Interrupted Time Series (ITS) method. These events include the Soviet Union War in Afghanistan (SUW), the Civil War (CW), the First-Round Taliban Regime (FRTR), the U.S. and NATO Military Presence in Afghanistan (USN), Regime Changes (RCH), and the Second-Round Taliban Regime (SRTR). The mathematical formulation of these events can be expressed through the following ITS models:

LnGDP t=ϑ0+ϑ1 Time t+ϑ2 Intervention t+ϑ3( Time t Intervention t)+εt (11)

where LnGDP stands for the natural log of total GDP, ϑ0 is the baseline intercept, ϑ1 is the baseline trend (before intervention), ϑ2 is the level change (immediate effect) right after the intervention, and ϑ3 slope change (trend effect) during the intervention.

Table 4 presents the estimated effects of major political events — including the Soviet Union War (SUW), Civil War (CW), First-Round Taliban Regime (FRTR), U.S. and NATO military presence (USN), Second-Round Taliban Regime (SRTR), and Regime Changes (RCH) — on Afghanistan’s GDP performance. The results across all panels confirm a positive trend in GDP growth prior to each event, whereas GDP growth during these events is generally estimated to be negative, except for the USN period. Furthermore, the immediate impacts of events such as the SUW and RCH are found to be positive, while those of the CW, FRTR, USN, and SRTR exhibit adverse immediate effects on GDP growth.

Table 4.

Event analysis results using the ITS approach.

Variables Coefficient t-statistic P >|t|
Variables Coefficient t-statistic P >|t|
Panel A: The Impact of the Soviet Union-Afghan War on Afghanistan’s GDP.
Pre-SUW-G 0.027*** 9.922 0.000
IE-SUW 0.305* 1.788 0.080
GD-SUW -0.026 -1.187 0.241
Adj-R2 0.713
F-Statistics 41.480
Prob. 0.000
Obs. 50
Panel B: The impact of the Civil War on Afghanistan’s GDP.
Pre-CW-G 0.023*** 13.456 0.000
IE-CW -0.075 -0.499 0.499
GD-CW -0.036*** -2.727 0.009
Adj-R2 0.835
F-Statistics 83.620
Prob. 0.000
Obs. 50
Panel C: The Impact of the First Round of the Taliban Regime on Afghanistan’s GDP.
Pre-FRTR-G 0.024*** 11.829 0.000
IE-FRTR -0.175 -0.772 0.444
GD-FRTR -0.055 -0.825 0.414
Adj-R2 0.756
F-Statistics 51.540
Prob. 0.000
Obs. 50
Panel D: The Impact of USN military presence on Afghanistan’s GDP.
Pre-USN-G 0.016** 7.032 0.000
IE-USN -0.270*** -3.342 0.000
GD-USN 0.046*** 7.406 0.000
Adj-R2 0.863
F-Statistics 104.100
Prob. 0.000
Obs. 50
Panel E: The Impact of the Second Round of the Taliban Regime on Afghanistan’s GDP.
Pre-SRTR-G 0.025*** 16.541 0.000
IE-SRTR -0.114*** -2.891 0.706
GD-SRTR 0.017 -0.293 0.872
Adj-R2 0.693
F-Statistics 37.830
Prob. 0.000
Obs. 50
Panel F: The Impact of RCH on Afghanistan’s GDP.
Pre-RCH-G 0.026*** 10.993 0.000
IE-RCH 0.314 1.364 0.179
GD-RCH -0.116** -2.010 0.050
Adj-R2 0.722
F-Statistics 43.360
Prob. 0.000
Obs. 50

The SUW, which lasted from 1979 to 1989, is considered a pivotal political episode in Afghanistan’s economic history (see, for details, Bloch, 2021). This period was marked by intense military conflict, the destruction of economic infrastructure, and profound human suffering, including approximately 1.2 million deaths, 2.0 million internally displaced persons, 5.9 million refugees to Pakistan and Iran (Ghaussy, 1989), and nearly 1.5 million individuals disabled (Maley, 2002). Additionally, the prolonged conflict weakened the Soviet Union’s political and economic standing, contributing to its eventual collapse in 1991 (Reuveny et al., 1999).

Similarly, the CW constrained investment opportunities, hindered entrepreneurial activity, disrupted supply chains, destroyed infrastructure, triggered brain drain, and led to capital flight, all of which contributed to the decline in GDP performance in this war-torn country. Empirical studies, including Giustozzi (2008, 2009), D’Souza and Jolliffe (2012a, 2012b), and Ciarli et al. (2010), support the findings of the event analysis for Afghanistan.

The adverse effects observed during both periods of Taliban rule (FRTR and SRTR) are plausible, as these periods were characterized by violent conflict through which the Taliban consolidated power by seizing provinces via armed confrontations with rival groups. Their regime inherited a country devastated by war, subject to international sanctions, and marked by the collapse of formal institutions, as well as severe restrictions on trade, education, and women’s participation during the first round (Haqpal, 2025). During the second round, however, the Taliban gained control over all provinces primarily through negotiations and political settlements. In the SRTR period, major cities, including the capital, remained largely intact, and the regime inherited administrative and physical infrastructure from the preceding Islamic Republic. These conditions enabled the Taliban to exercise greater control over key economic levers, such as the exchange rate, inflation, taxation, trade, and the management of mineral and natural resources, thereby facilitating a degree of relative economic recovery (see, for details, Hamoon et al., 2025).

Between 1975 and 2024, Afghanistan experienced multiple regime changes, nearly all of which occurred through assassinations or coups d’état, with the notable exception of the transition from President Burhanuddin Rabbani to President Hamid Karzai, which was achieved through the Bonn political agreement (see Mark and Ramsha, 2011, for details).

To determine whether the observed effects of each event on GDP growth were influenced by unobserved factors or random noise, a placebo test was conducted. As shown in Fig. 8, the estimated coefficients follow an approximately normal distribution centered around zero, indicating no statistically significant relationship between GDP growth and randomly assigned intervention points. The actual estimated GDP growth during the event period (denoted by the vertical blue line) derived from the Interrupted Time Series (ITS) model lies well outside this distribution of placebo effects. This finding provides strong evidence that the observed positive or negative impact is not the result of random chance but reflects a genuine causal relationship.

Fig. 8. 

Placebo test for the event analysis, including SUW, CW, FRTR, USN, SRTR, and RCH, respectively. The red curve represents density, the green dot plot represents P-values, and the blue vertical lines indicate the GDP growth rate during the event

Finally, Fig. 9 illustrates the event analysis by depicting the trends of observed GDP (blue line), predicted GDP with the event (red-dashed line), counterfactual GDP without the event (green-dashed line), the impact area (pink-shaded region), and the event’s start date (vertical black-dashed line).

Fig. 9. 

ITS plot for the event analysis. (a). ITS plot for SUW, (b). ITS plot for CW, (c). ITS plot for FRTR, (d). ITS plot for USN, (e) ITS plot for SRTR, and (f) ITS plot for RCH

5. Conclusion and Policy Recommendations

In this paper, we have examined the impact of Political Instability (POI), Corruption (COR), and Government Effectiveness (GEF) on Afghanistan’s GDP performance. Using time series data from 1996 to 2024 and implementing Quantile-on-Quantile Regression (QQR) and Wavelet Quantile Regression (WQR) models, we found that POI, COR, and GEF had an adverse effect on GDP growth across all quantiles, in the long term. The results of the QQR and WQR techniques were confirmed by the Wavelet Quantile Correlation (WQC) model, indicating that POI, COR, and GEF are negatively correlated with GDP across all quantiles in the short, medium, and long term. Moreover, the event analysis revealed that, during the Soviet Union War (SUW), Civil War (CW), First Round Taliban Regime (FRTR), and Regime Changes (RCH), Afghanistan’s GDP growth had declined. During the U.S.-NATO military presence and the Second Round of the Taliban Regime (SRTR), Afghanistan’s GDP experienced positive growth.

Based on these empirical findings, the following policy recommendations can be discussed: Afghanistan must prioritize institutional reform to address the persistent adverse effects of political instability, corruption, and weak governance on GDP growth. Strengthening the rule of law through independent anti-corruption agencies, enhancing judicial transparency, and promoting merit-based recruitment in the public sector can significantly improve government effectiveness. These reforms would not only restore public trust but also attract foreign investment and foster a more stable economic environment, as evidenced by the consistent negative impact of POI, COR, and GEF across all GDP quantiles.

In light of the significant economic disruptions caused by past conflicts and regime changes, Afghanistan needs to adopt policies that are resilient to conflict. This includes designing reconstruction plans that prioritize infrastructure development, job creation, and regional equality, especially in post-conflict zones. Establishing a sovereign stabilization fund and aligning development initiatives with peacebuilding efforts can help to shield the economy from future political shocks. Such strategies are essential for breaking the cyclical relationship between conflict and economic decline, as highlighted by the results of the events analysis.

Finally, the observed positive growth of GDP during the Second Round Taliban Regime (SRTR) suggests that even under constrained political conditions, economic stabilization is possible. Policymakers and international stakeholders should consider pragmatic engagement with de facto authorities to ensure continuity in essential services and macroeconomic management. Encouraging decentralized governance and linking international aid to measurable improvements in transparency and service delivery can foster short-term stability and promote long-term development. This approach strikes a balance between the need for economic recovery and the imperative of promoting accountable governance.

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Appendix

Table A1.

Impact of POI on GDP using QQR

GDP-Quantiles τ = 0.10 τ = 0.20 τ = 0.30 τ = 0.40 τ = 0.50 τ = 0.60 τ = 0.70 τ = 0.80 τ = 0.90
τ = 0.10 -0.798 -0.942 -0.942 -0.942 -0.942 -0.968 -0.968 0.322 0.322
τ = 0.20 -0.811 -0.855 -0.855 -0.855 -1.016 -0.947 -0.947 -0.168 -0.013
τ = 0.30 -0.620 -0.620 -0.620 -0.652 -0.924 -0.924 -0.874 -0.160 -0.160
τ = 0.40 -0.620 -0.620 -0.674 -0.674 -0.727 -0.727 -0.727 -0.160 -0.160
τ = 0.50 -0.452 -0.526 -0.686 -0.686 -0.754 -0.754 -0.754 -0.157 0.074
τ = 0.60 -0.523 -0.592 -0.598 -0.598 -0.721 -0.721 -0.721 -0.113 0.045
τ = 0.70 -0.548 -0.550 -0.550 -0.550 -0.662 -0.855 -0.855 -0.113 0.043
τ = 0.80 -0.480 -0.492 -0.492 -0.492 -0.820 -0.820 -0.820 -0.098 0.013
τ = 0.90 -0.719 -0.719 -0.719 -0.719 -0.729 -0.719 -0.719 -0.064 -0.064
Table A2.

Impact of COR on GDP using QQR

GDP-Quantiles τ = 0.10 τ = 0.20 τ = 0.30 τ = 0.40 τ = 0.50 τ = 0.60 τ = 0.70 τ = 0.80 τ = 0.90
τ = 0.10 -1.577 -1.577 -1.577 -1.602 -1.602 -1.602 -1.602 0.405 0.405
τ = 0.20 -1.523 -1.523 -1.523 -1.606 -1.606 -1.606 -1.452 -0.294 -0.188
τ = 0.30 -1.525 -1.525 -1.525 -1.525 -1.525 -1.525 -0.716 -0.229 -0.229
τ = 0.40 -1.141 -1.141 -1.141 -0.872 -0.872 -0.848 -0.841 -0.229 -0.229
τ = 0.50 -0.860 -0.860 -0.860 -0.860 -0.860 -0.860 -0.806 -0.214 -0.214
τ = 0.60 -0.910 -0.910 -0.910 -0.910 -0.910 -0.858 -0.823 -0.179 -0.018
τ = 0.70 -0.787 -0.787 -0.835 -0.878 -0.878 -0.878 -0.837 -0.179 0.027
τ = 0.80 -0.784 -0.784 -0.784 -0.806 -0.806 -0.812 -0.867 -0.113 -0.113
τ = 0.90 -0.676 -0.791 -0.791 -0.791 -0.791 -0.791 -0.791 -0.102 -0.102
Table A3.

Impact of GEF on GDP using QQR

GDP-Quantiles τ = 0.10 τ = 0.20 τ = 0.30 τ = 0.40 τ = 0.50 τ = 0.60 τ = 0.70 τ = 0.80 τ = 0.90
τ = 0.10 -0.404 -0.525 -0.525 -0.525 -0.525 -0.178 -0.305 -0.921 -0.921
τ = 0.20 0.065 -1.450 -1.512 -1.619 -1.619 -0.404 -0.108 -0.284 -0.284
τ = 0.30 1.495 -1.615 -1.615 -1.615 -1.615 -1.131 -0.696 -0.174 -0.481
τ = 0.40 1.653 -0.930 -1.033 -1.033 -1.084 -1.102 -1.007 -0.603 -0.603
τ = 0.50 0.566 -0.013 0.081 -0.222 -0.286 -1.313 -1.420 -1.420 -0.728
τ = 0.60 0.215 0.193 0.193 -0.086 -0.086 -0.800 -0.800 -0.938 -1.224
τ = 0.70 0.425 0.423 0.215 0.200 -0.220 -0.532 -0.532 -1.224 -1.657
τ = 0.80 0.565 0.565 0.300 0.300 0.117 -0.563 -0.563 -1.657 -1.657
τ = 0.90 0.588 0.588 0.588 0.487 0.487 -0.072 -1.108 -1.108 -1.108
Table A4.

Impact of POI, COR, and GEF on GDP using WQR

Quantiles Impact of POI on GDP Impact of COR on GDP Impact of GEF on GDP
Short Medium Long Short Medium Long Short Medium Long
τ = 0.05 0.000 -0.078 -0.488 0.029 -0.092 -0.484 -0.067 -0.051 -0.343
τ = 0.10 0.015 -0.055 -0.489 0.016 -0.063 -0.484 -0.067 -0.022 -0.339
τ = 0.15 0.010 -0.062 -0.483 0.011 -0.069 -0.475 -0.023 -0.013 -0.328
τ = 0.20 0.010 -0.032 -0.494 0.006 -0.037 -0.494 0.004 -0.070 -0.328
τ = 0.25 -0.035 -0.030 -0.483 -0.025 -0.032 -0.483 0.025 -0.075 -0.324
τ = 0.30 0.078 0.066 -0.516 -0.006 0.075 -0.506 -0.004 0.077 -0.339
τ = 0.35 -0.060 0.074 -0.521 0.082 0.070 -0.516 0.025 0.051 -0.350
τ = 0.40 0.214 0.078 -0.527 -0.046 0.063 -0.521 -0.015 0.061 -0.363
τ = 0.45 -0.284 -0.116 -0.555 0.257 -0.084 -0.548 0.115 -0.080 -0.343
τ = 0.50 0.009 -0.150 -0.561 0.002 -0.120 -0.554 0.024 -0.112 -0.403
τ = 0.55 0.006 -0.196 -0.563 0.029 -0.073 -0.552 0.006 -0.046 -0.385
τ = 0.60 -0.023 0.063 -0.474 0.020 -0.230 -0.473 -0.029 -0.027 -0.431
τ = 0.65 -0.062 0.072 -0.474 -0.109 -0.155 -0.475 -0.052 -0.078 -0.468
τ = 0.70 0.025 0.105 -0.445 -0.138 -0.212 -0.445 -0.066 -0.109 -0.230
τ = 0.75 -0.007 0.013 -0.453 -0.146 -0.212 -0.456 0.006 0.014 -0.333
τ = 0.80 0.018 -0.028 -0.463 -0.019 0.028 -0.468 -0.026 0.024 -0.260
τ = 0.85 0.027 0.072 -0.469 -0.081 -0.063 -0.473 -0.026 -0.054 0.053
τ = 0.90 -0.011 0.036 -0.434 -0.021 -0.072 -0.440 0.036 0.029 0.059
τ = 0.95 0.018 0.042 -0.437 0.000 -0.053 -0.442 0.000 0.029 0.064

1 MODWT (maximal overlapping discrete wavelet transform) introduced by Percival and Walden (2000).
2 BDS test refers to Brock-Dechert-Scheinkman (1996) independence test.
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