Introduction

International trade is regarded as a key determinant of the income level and growth rate of countries. Over the past four decades, international trade has significantly increased country-level economic growth as well as the global GDP. For instance, in the year 2020, international trade contributed almost 52% to the global GDP (World Bank 2021). In addition to its contribution to the global economy, trade between nations supports technological advancements, fosters the efficient use of resources, and stimulates both domestic and foreign markets. These advantages result in maximum productivity and the development of new goods (Cui et al. 2021; Safi et al. 2021).

Given the importance of international trade in boosting the global GDP, it is crucial to investigate its primary determinants. For the purpose of the analysis, the study has relied on the identification of trade exports and its determinants in the context of Pakistan. The bilateral trade of Pakistan with its top five trade partners are taken into consideration. These are the USA, China, UK, UAE, and Germany. This is because since about 50% of Pakistan’s total exports is to countries. The share of trade with each of these countries for the year 2021 is depicted in Table 1.

Table 1 Top five trading partners of Pakistan
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The extensive literature body at present draws attention to the following gaps. First off, studies that use aggregate data to examine the relationship between uncertainty and oil prices suffer from aggregation bias. Second, the relevant research makes the symmetry assumption that oil prices and uncertainty have an equal impact. As far as we are aware, Baek’s study (2020) is the only one to look at the asymmetric effects of oil prices on bilateral trade between Korea and its main trading partners. Because of this, the current article is motivated to investigate the dynamic effects of fluctuating oil prices and uncertainty on Pakistan’s exports to its top five trading partners. The current analysis focuses on the export function because Pakistan’s economy has experienced a significant trade deficit over the past 50 years (Pakistan Economic Survey, 2021).

The present paper contributes to the body of literature in the following ways. First, this is the first study to address the issue of aggregation bias by using monthly data to get more detailed and insightful findings. We anticipated that the monthly series, as opposed to the yearly or quarterly statistics, may more appropriately illustrate the effects of changes in certain series on Pakistan’s exports. Second, this is the first study that, to the best of our knowledge, reveals the dynamic effects of oil prices and the world uncertainty index for Pakistan on Pakistan’s exports to its top five trade partners. Thirdly, this analysis is the first to use Sim and Zhou’s (2015) quantile and quantile (QQ) approach, which can manage the extreme values in the export function, oil prices, and world uncertainty index, in contrast to all previous studies in the relevant literature. Additionally, non-linearities, asymmetries, and time-varying variances are all addressed by the QQ approach (Sohag et al. 2021; Adebayo 2022a, 2022b; Ahyan et al. 2022). Another advantage of the QQ approach is that it handles the problem of model misspecification by individually regressing the quantiles of the explanatory series on the quantiles of the explained series, unlike other methods like quantile regression. Finally, the study uses the quantile-on-quantile Granger causality test to further support the reliability of the results.

Literature review

The literature specific to the determinants of international trade balances can be categorized into three distinct themes. The first category deals with the identification of determinants of international trade using panel-level data. For example, Felmingham (1988) used panel data to demonstrate the necessity of this group by revealing the impact of various macroeconomic factors (such as currency rates, economic growth, etc.) on Australia’s commerce with other countries. Some other studies include Mahdavi and Sohrabian (1993), and Doroodian et al. (1999).

The second category of studies deals with analyzing the bilateral trade flows of countries with their different trade partners in order to address this issue and examine how the trade balance reacts to different macroeconomic variables. The important studies in this regard are Baek (2012), (2011), Ullah et al., (2022), Adebayo et al., (2022a) Bahmani-Oskooee and Wang (2007), and Bahmani-Oskooee and Goswami (2004).

The current body of literature highlights the fact that all the researchers in the previous groups relied on the use of the traditional trade balance modeling proposed by Rose and Yellen (1989), which posited that economic growth and exchange rates are the key determinants of the trade balance. It was later discovered that crude oil has an impact on the trade balance via macroeconomic pathways. Because important determinants like oil prices were excluded from the modeling used in the previously discussed categories, the results may have been biased. Therefore, the third category of studies assesses the oil prices’ macroeconomic implications on the trade balance by relying on aggregate data, contrasting one economy with the rest of the world while raising the possibility of aggregation bias. Select studies in this category are Baek et al. (2019), Gnimassoun et al. (2017), and Allegret et al. (2015). In addition to the potential aggregation bias, another issue that stands out is that all of these studies assume that oil prices have symmetrical effects, meaning that increases in oil prices have a negative influence on the trade balance and decreases will have the opposite effect. But in reality, this presumption might not be accurate. Therefore, it makes more sense to think about how oil prices affect the trade balance in asymmetrical ways.

Uncertainty is another crucial factor in determining the trade balance (Liao et al. 2021; Bernanke 1983). Uncertainty has an impact on the firm’s investment choice, which then impacts the manufacturing process and, ultimately, disrupts exports and the trade balance. The majority of research, however (Jia et al. 2020; Tam 2018; Imbruno 2019), use aggregated level data of a country in comparison to its trading partners, and the result is likely to be biased by aggregation. The research on the effects of uncertainty on the trade balance and exports neglects the asymmetries in the uncertainty indices, just like the studies on oil prices. Hence, in this study, we are motivated to include the asymmetrical impact of uncertainty because of this gap.

To sum up, the extensive literature body draws attention to the following gaps. First off, studies that use aggregate data to examine the relationship between uncertainty and oil prices suffer from aggregation bias. Second, the relevant research makes the symmetry assumption that oil prices and uncertainty have an equal impact. As far as we are aware, Baek’s study (2020) is the only one to look at the asymmetric effects of oil prices on bilateral trade between Korea and its main trading partners. Because of this, the current article is motivated to investigate the dynamic effects of fluctuating oil prices and uncertainty on Pakistan’s exports to its top five trading partners. The current analysis focuses on the export function because Pakistan’s economy has experienced a significant trade deficit over the past 50 years (Pakistan Economic Survey, 2021).

The present paper contributes to the body of literature in the following ways. First, this is the first study to address the issue of aggregation bias by using monthly data to get more detailed and insightful findings. We anticipated that the monthly series, as opposed to the yearly or quarterly statistics, may more appropriately illustrate the effects of changes in certain series on Pakistan’s exports. Second, this is the first study that, to the best of our knowledge, reveals the dynamic effects of oil prices and the world uncertainty index for Pakistan on Pakistan’s exports to its top five trade partners. Thirdly, this analysis is the first to use Sim and Zhou’s (2015) quantile and quantile (QQ) approach, which can manage the extreme values in the export function, oil prices, and world uncertainty index, in contrast to all previous studies in the relevant literature. Additionally, non-linearities, asymmetries, and time-varying variances are all addressed by the QQ approach (Sohag et al. 2021). Another advantage of the QQ approach is that it handles the problem of model misspecification by individually regressing the quantiles of the explanatory series on the quantiles of the explained series, unlike other methods like quantile regression. Finally, the study uses the quantile-on-quantile Granger causality test to further support the reliability of the results.

The following sections make up the rest of the article. The variables, their sources, and the approach used for analysis are explained in the second section. The findings are discussed in-depth in the third section. The final section includes a summary of the results, policy implications, and areas for improvement for future research.

Data and methodology

Data

The current study intends to examine the dynamic relationship between oil prices, macroeconomic uncertainty, and Pakistan’s exports to its top five trading partners, namely the USA, China, the United Kingdom, the United Arab Emirates, and Germany, since about 50% of Pakistan’s total exports is to countries. The dataset comprises monthly data from July 2003 to December 2020 for the empirical analysis. The choice of this range was made since monthly data for exports is only available as of July 2003.

Furthermore, the export figures are calculated in thousand US dollars and derived from the State Bank of Pakistan’s official website (2021). Data on monthly average crude oil prices are obtained from the World Bank (2021). Additionally, in order to capture macroeconomic uncertainty, the study has used World Uncertainty Index as a proxy. This is based on the study conducted by Ahir et al. 2018). A five-step method is used (creating the report, editing, second check, sub-editing, and production) to improve the index’s veracity and comparability. The index is also based on quarterly data that is translated into monthly data (2014). The quantile-on-quantile regression (QQR) method is used to calculate the hypothesized nexus among the variables.

Methodology

The following econometric analyses and methods are used for analysis. We first use the BDS test to validate the non-linearity of the chosen series. Second, the described series’ stationarity is confirmed using the ADF test, KSS asymmetric unit root testing, and quantile unit root test. Thirdly, the quantile cointegration test is used to reveal any long-term relationships between the selected series. Fourthly, we examine quantile-wise impacts using the QQR technique. Last but not least, the quantile granger causality test and a comparison of the QQR outcome with conventional quantile regression serve to demonstrate the robustness of the results.

Quantile unit root test

The presence of a unit root that results in an erroneous regression is among the time series data’s most dominant characteristics. As a result, finding stationarity in the modeled series is crucial before using the econometric technique. The results of common unit root tests may be deceptive when examining the integration order since the chosen series exhibit aberrant variances due to local linearities. As a result, tests for asymmetric unit roots using KSS and the ADF are also used. In order to address the asymmetric distribution of data, Koenker and Xiao (2004) created the “quantile autoregressive (QAR) unit root test,” which was later expanded by Galvao (2009). (Sohag et al. 2021). The following highlights several notable advantages of the QAR test over regular tests. First off, the Galvoa (2009) expanded version of QAR can take into account both the linear time trend and covariate stationarity. In contrast to standard unit root tests, it can also test the integration order or unit root for each quantile individually (Godil et al. 2021; Sharif et al. 2017a). Our modeled series has noticeable oscillations and temporal patterns, hence QAR is used to examine local stationarity at various quantiles. This is due to the limited global stationarity that the traditional tests offer. We use Galvao (2009) as our guide to estimate the the conditional quantile function of y as follows:

$${Q}_{\tau }^{y}\left({~}^{{y}_{t}}\!\left/ \!{~}_{{I}_{t}^{y}}\right.\right)= {\mu }_{1}\left(\tau \right)+{\mu }_{2}\left(\tau \right)t+\alpha \left(\tau \right){y}_{t-1}+\sum_{i=1}^{p}{a}_{i}\left(\tau \right)\Delta {y}_{t-i}+{f}_{\mu }^{{-1}_{(\tau )}}$$
(1)

\({f}_{y}\left({~}^{.}\!\left/ \!{~}_{{I}_{t}^{y}}\right.\right)\) is the distribution of \({y}_{t}\) while conditioning the \({I}_{t}^{y}\). \({Q}_{\tau }^{y}\) indicated the \(\tau\) th quantile of y which is conditioned on \({I}_{t}^{y}\). \({y}_{t}\) shows the stationarity of the given lag information, i.e., \({I}_{t}^{y}=\left({y}_{t-1},{y}_{t-2},\dots ,{y}_{t-s}\right)\acute{\varepsilon }\). \({f}_{\mu }^{-1}\) is included to show the inverse of the errors of the common distribution. Additionally, QAR test uses t-statistics to detect the stationarity and the null hypothesis is \({H}_{0}\left(\tau \right)t=1\).

Quantile cointegration

The present study has used Xiao’s quantile cointegration method to analyze the long-term co-movement of the chosen series (2009). Although there are cointegration tests that identify the long-term relationship between the variables (Engle and Granger (1987)), these models treat the cointegration vectors as constants. Contrary to the conventional cointegration tests, quantile cointegration is a special advanced technique that makes the assumption that the coefficients vary in each quantile. In addition, the main goal of assuming the variable coefficients (i.e., \(\beta ={\beta }_{1},{\beta }_{2},\dots ,{\beta }_{i}\) in each quantile is to account for the effects of shock (Sharif et al. 2017b; Sharif et al. 2020a, b).

Quantile cointegration divides the error term into two parts—one with pure innovation and the other with the correlation of leads and lags in \(\Delta {x}_{t}\).—is another impressive aspect of the method. In this case, \({v}_{t}= \Delta {x}_{t}\) with a zero mean stationary order of (n + 1). The standard cointegration equation can be written as:

$${y}_{t}= \alpha + {{\acute{\beta}}_{t}}{x}_{t}+\sum_{i=-n}^{n} {{\Delta \acute{x}}_{t-i}}{\Pi }_{j}+{\varepsilon }_{t}$$
(2)

In Eq. 2, introduce \(\tau\) th quantile of \({\varepsilon }_{t}\) is inserted. This term represents quantiles of \({y}_{t}\), conditioning the \({I}_{t}^{y}\). It can be denoted as \({Q}_{\varepsilon }(\tau )\) while \({f}_{t}=({x}_{t}, {\Delta }_{t-1}, {\forall }_{i})\). The equation will now be,

$$\left({~}^{{y}_{t}}\!\left/ \!{~}_{{I}_{t}^{x}}\right.\right)= {a}_{1}\left(\tau \right)+{b}_{2}{(\acute{\tau} )}t+\alpha \left(\tau \right){y}_{t-1}+\sum_{i=-n}^{n} {{\Delta \acute{x}}_{t-i}}{\Pi }_{j}+{f}_{\mu }^{{-1}_{(\tau )}}$$
(3)

Following Xiao (2009), Eq. 4 is introduced to check the stability of the cointegrating coefficient.

$${Q}_{\tau }^{y}\left({~}^{{y}_{t}}\!\left/ \!{~}_{{I}_{t}^{x}}\right.\right)= {a}_{1}\left(\tau \right)+{b}_{2} {(\acute{\tau} )}{x}_{t}+\gamma {(\acute{\tau} )}{x}_{t}^{2}\sum_{i=-n}^{n}{{\Delta \acute{x}}_{t-i}}{\Pi }_{j}+\sum_{i=-n}^{n}\Delta {x}^{\acute{2}}{\Pi }_{j}{r}_{j}{f}_{\varepsilon }^{{-1}_{(\tau )}}$$
(4)

The final iteration of quantile cointegration is shown by the equation above. In addition, the 1000 Monte Carlo simulation is used to obtain the critical values of \(\left|\widehat{{V}_{n}}(\tau )\right|\). \({\beta }_{\tau }=\beta\) denotes the acceptance of H0, suggesting no long-lasting relationship.

QQR model

The dynamic relationship between oil prices, macroeconomic uncertainty, and Pakistan’s exports to its top five trading partners is analyzed using the QQR approach proposed by Sim and Zhou (2015). The following factors serve as the basis for the application of this technique. First, the early tests show that the selected series, which includes oil prices and other macroeconomic factors, have asymmetries in their distributions. QQR is able to handle these distributions in a suitable manner. Second, this method uses non-parametric features to address OLS regression and standard quantile regression’s drawbacks (Sohag et al. 2021; Meo and Karim 2021). Thirdly, to provide the slope coefficients for each quantile and to address the interdependence issue, QQR regresses the various quantiles of the predictor series on the pertinent quantile of the predicted series. This method provides comprehensive information on each quantile. Fourth, given that the majority of the selected series are asymmetrically distributed, as shown by the values of kurtosis, skewness, and Jarque–Bera, it appears that the QQR technique is appropriate for the analysis (Sohag et al. 2021; Suki et al. 2020; Khan et al. 2019).

The likelihood of model misspecification is reduced because the QQR approach is a bivariate technique in which we can only use one independent series and examine its dynamic impacts on dependent series. Thus, we can examine each of the independent series one at a time. Thus, the two variables chosen for the current article are the price of oil and macroeconomic uncertainty. Although both of these variables have recently increased, less focus has been placed on them. For analysis, the \(\tau\)-quantile of \({EXPUSA}_{t}\) (Pakistan’s exports to USA) is introduced, making it the function of oil prices (\({OP}_{t}\)) that is expressed as:

$${EXPUSA}_{t}={\beta }^{\tau }{OP}_{t}+{u}_{t}^{\tau }$$
(5)

In Eq. 5, there are two unknown terms. Firstly, \({\beta }^{\tau }\) is an unknown term since its value depends on the nexus between EXPUSA and OP, which is still unknown. Secondly, \({u}_{t}^{\tau }\) is an error term with zero quantiles. In order to transform Eq. 1 into linear form, 1st order Tylor expansion of \({\beta }^{\tau }(,)\), around the \({OP}_{t}\) can be written as:

$${\beta }^{\tau }{OP}_{t}\approx {\beta }^{\tau }{OP}^{\theta }+{\beta }^{{\acute{\tau} }}\left({OP}^{\theta }\right)\left({OP}_{t}-{OP}^{\theta }\right)$$
(6)

Equation 6 demonstrates the double indexing of \({\beta }^{\tau }{OP}^{\theta }\) and \({\beta }^{\acute{\tau }}\left({OP}^{\theta }\right)\) in \(\tau\) and \(\theta\). It indicates that \({\beta }^{\tau }{OP}^{\theta }\) and \({\beta }^{\acute{\tau }}\left({OP}^{\theta }\right)\) are the functions of \(\tau\) and \(\theta\). Thus, the equation can be expressed as:

$${\beta }^{\tau }{OP}_{t}\approx {\beta }_{0}(\tau ,\theta )+{\beta }_{1}(\tau ,\theta )\left({OP}_{t}-{OP}^{\theta }\right)$$
(7)

To obtain the final version of the equation, we put Eq. 7 into Eq. 5 as:

$${EXPUSA}_{t}=\underbrace{{\beta }_{0}(\tau ,\theta )+{\beta }_{1}(\tau ,\theta )\left({OP}_{t}-{OP}^{\theta }\right)}+{u}_{t}^{\tau }$$
(8)

The component in \(\underbrace{}\) denotes the \(\tau\) th conditional quantile of EXPUSAt. Additionally, the component \(\underbrace{}\) expresses how exports to the USA react to oil prices, taking into account the whole distribution of both series. In addition, unlike the typical quantile regression \({\beta }_{0}\) and \({\beta }_{1}\) are indexed in\(\tau\), and \(\theta\).

We can move forward with the following equations if we perform the same exercise for EXPUSA against the second independent series, macroeconomic uncertainty (MEU):

$${EXPUSA}_{t}={\beta }^{\tau }{MEU}_{t}+{u}_{t}^{\tau }$$
(9)
$${\beta }^{\tau }{MEU}_{t}\approx {\beta }^{\tau }{MEU}^{\theta }+{\beta }^{\acute{\tau }}\left({MEU}^{\theta }\right)\left({MEU}_{t}-{MEU}^{\theta }\right)$$
(10)
$${\beta }^{\tau }{MEU}_{t}\approx {\beta }_{0}(\tau ,\theta )+{\beta }_{1}(\tau ,\theta )\left({MEU}_{t}-{MEU}^{\theta }\right)$$
(11)
$${MEU}_{t}=\underbrace{{\beta }_{0}(\tau ,\theta )+{\beta }_{1}(\tau ,\theta )\left({MEU}_{t}-{MEU}^{\theta }\right)}+{u}_{t}^{\tau }$$
(12)

Similar to Eq. 8, Eq. 12 is the final iteration of the QQR model, except for the relationship between MEU and EXPUSA. To investigate the dynamic relationship between oil prices, uncertainty, and exports, QQR regression models for the other four trading partners—China, UK, UAE, and Germany—can be created using the same methodology.

Robustness check of QQR estimations

Two methods are used to assess the validity of the QQR findings. First, the results of classical quantile regression are compared with those of the QQR estimations. This is done by calculating the average QQR parameters that the conventional quantile technique is unable to obtain. The equation can be expressed mathematically as follows:

$${y}_{1}\left(0\right)\equiv \overline{\widehat{\beta } }\left(0\right)=\frac{1}{s}\sum_{\tau }\widehat{{\beta }_{1}}\left(\tau ,\theta \right)$$
(13)

In Eq. 13, \(\overline{\widehat{\beta } }\)= QQR regression’s parameters’ average.

We use the quantile granger causality test to determine the effects of OP and MAU on exports because we believe that Pakistani policymakers and authorities may combat the fluctuations in oil prices and macroeconomic uncertainty by implementing new policies and practical measures. This technique is another measure to check the reliability of QQR results.

Results and discussion

Exports to the USA (EXPUSA), Exports to China (EXPC), Exports to Germany (EXPG), Exports to the United Kingdom (EXPUK), and Exports to the United Arab Emirates (EXPUAE) are dependent series. Oil prices (OP) and macroeconomic uncertainty (MEU) are independent series. Table 2 shows the descriptive statistics of the series. Regarding the dependent series, EXPUSA, followed by EXPC, EXPUK, and EXPUAE, has the biggest means of Pakistani exports to the USA. The lowest mean for EXPG indicates that Pakistan’s major export markets are the USA and Germany, respectively. On the other hand, compared to MEU, the mean for oil prices is greater. Additionally, the kurtosis values for all the series are larger than 1, indicating a non-normal distribution. The fact that there is a significant discrepancy between the minima and maxima values of every modeled series, indicating the asymmetric distribution of the variables, is another crucial fact (Sharif et al. 2020b; Adebayo et al. 2022a, b, c). The results of the Jarque–Bera test are also used to confirm the mistakes’ normalcy. The probability/t-statistics results support the non-normal distribution of the residuals. Therefore, the QQR technique, which can handle the asymmetrical nexus among the variables, is motivated and justified by the kurtosis values, minima and maxima of the series, and the results of the Jarque–Bera test (Sharif et al. 2019; Pan et al. 2022).

Table 2 Descriptive statistics
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Table 3 presents the results emerging from the Brock-Dechert-Scheinkman (BDS) test, which is used to confirm the non-linearity of the series All of the modeled series’ BDS statistics have zero p-values, which indicates non-linearity. Therefore, the results of the BDS test point to the use of a method that can reveal the asymmetric nexus between the series, again supporting the application of the QQR methodology.

Table 3 Brock-Dechert-Scheinkman test
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The results of the ADF and KSS asymmetric unit root test, are shown in Table 4. Due to the fact that all series are stationary at I, we move forward with QAR (1).

Table 4 Unit root tests
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Table 5 also displays the QAR test results that agree with the outcomes of the ADF and KSS tests.

Table 5 Quantile autoregressive unit root test
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Once it is shown that none of the series are I(2), we employ the quantile cointegration test suggested by Xiao (2009) to look for a long-term correlation between the variables we have chosen. The results are shown in Table 5. The results show that cointegration exists for nearly all of the quantiles. Furthermore, we see that the cointegration between each series’ lower and higher quantiles and the dependent series varies. The long-term association between the regressor and regressand variables is seen to be varied, as well. Additionally, the quantile cointegration in Table 5 reveals that the long-run connection between the chosen variables is unequal.

The key findings of the QQR are provided hereby. Pakistan’s exports to the USA generally have negative consequences due to the price of oil (OP). When low to high quantiles (0.01–0.99) of OP interact with moderate to high quantiles (0.3–0.9) of exports, the unfavourable nexus between the two series becomes significantly more intense. It shows that the movement of OP from a low to a high ratio sharply lowers the exports from a medium to a high ratio. It is interesting to note that the third export quantile responds positively to all OP quantiles, indicating that exporting manufacturers benefit when Pakistan’s export ratio is lower than that of the USA. The negative effects are predominant, notwithstanding the varied results.

Furthermore, the exports’ low quantiles (0.1–0.3) show a negative association with the low quantiles of MEU. On the other hand, MEU’s entire quantile range has a positive effect (which is not significant) on the export ratio in the range of 0.2 to 0.6. It means that MEU has non-linear effects on exports. However, due to MEU, the extreme quantiles (low and high) of exports must bear the loss (Table 6).

Table 6 Quantile cointegration test
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In the context of China, the QQR calculations highlight that OP primarily reduces the function of exports. The OP’s quantiles lead to a disruption in the exporters’ ratio (0.1–0.5). Additionally, the highest quantile of exports (0.9) exhibits a negative correlation with all the quantiles of the OP. On the other hand, when we examine the relationship between the high quantile (i.e., 0.8) of the former and the quantiles of the latter, a positive relationship is observed between OP and exports. Additionally, one of the high export quantiles (0.8) has a positive relationship with OP oscillations. In terms of the impact of MEU on exports to China, the findings show that MEU consistently exhibits the negative effects on reducing exports to China. All the quantiles of MEU are directly related to one of the high quantiles (0.9) of exports. This highlights that exporting producers experience the negative effects of MEU when there is a low to high ratio of exports to China and the price of oil is also rising.

In the case of Pakistani exports to the UK the following results emerge. In relation to the relationship between OP and exports, the QQR estimates indicate substantially mixed findings. The quantiles of the 0.3 to 0.6 show that the exporters have a variable reaction to the quantiles of OP. Later, due to oscillations in all OP quantiles, these mixed effects provide noticeably favorable responses, with the mid to high quantiles of exports (0.5–0.7) benefiting greatly. The high quantiles (0.8 and 0.9) of exports, however, are notably negatively impacted by OP’s mid to high quantiles (0.5–0.9).

We discover that there is a distinct response from exports to MEU from quantile to quantile regarding the relationship between MEU and exports to the UK. For instance, all of MEU’s quantiles (0.1–0.9) show a significant positive impact on the two low export quantiles (0.1 & 0.2). In quantile 0.6 of exports, this substantial negative association has no effect at all. Once more, the high quantiles of exports (0.8 and 0.9) show a negative relationship with MEU. As a result, in the instance of the UK, the MEU export connections are incredibly variable and non-linear.

The results regarding Pakistan’s exports to the UAE are then examined here. The moderate to high (0.5–0.9) exports quantiles are negatively impacted by all quantiles of OP. However, the second quantile of exports responds favorably to the OP’s quantiles. We see both the good and negative effects of OP when we look at the low quantiles (0.1 & 0.2) of exports. According to the QQR estimations, the large gains for exporting businesses are implied by the high quantiles (0.8–0.9) of exports’ interaction with MEU’s quantiles.

As we turn our attention to the situation of exports to Germany, we find some interesting results. All quantiles of OP are positively but weakly correlated with the low quantiles of exports (0.1 and 0.4). It implies that changes in OP have no impact on exports to Germany during these quantiles. However, the exports’ high quantiles (0.7–0.9) show that OP is having very negative effects. On the whole, OP’s effects on exports continue to be inconsistent. Similarly, all of the MEU quantiles show a negligible influence on the low and high quantiles of exports (0.1–0.3 and 0.6–0.8). On the other hand, all quantiles of OP cause a large loss in low to medium quantiles (0.3–0.7) of exports.

Robustness checks

We use the causality test under the presumption that Pakistan’s economic policy is in line with the direction of the State Bank of Pakistan. Table 7 lists the results of the QGC test. The results back up the QQR projections. We discover a two-way causal link. Furthermore, it is clear that fluctuations in oil prices and unpredictability considerably raise Pakistan’s exports and vice versa in all circumstances, supporting our earlier conclusions.

Table 7 Quantile Granger causality test
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Discussion

Based on the QQR estimations described above, we contend that our findings are unexpected and special in a number of ways. We also look at a new factor, macroeconomic uncertainty, which has a significant impact on Pakistan’s exports to its top five trading partners. According to the findings about the dynamic effects of OP, Pakistan’s export ratio must deal with generally significantly negative effects as a result of oscillations in OP in the case of exports to the USA, China, the United Arab Emirates, and Germany. This empirical result supports our findings and is in line with the literature (Baek et al. 2019; Le and Chang 2013; Bodenstein et al. 2011; Adebayo et al. 2022b). There are a number of ways that OP changes can reduce the ratio of the export. First off, since inflation is a relatively close channel, OP has an impact on how exports function. The exports are frequently halted by this channel, both directly and indirectly. The direct effect of an increase in oil prices is a reduction in the production of items based on petroleum due to high production costs; thus, the volume of exports is decreased by the production process reduction. The indirect result of an increase in OP is that it raises the cost of production, shipping, and heating, which lowers exports.

Second, through altering the supply and demand for raw materials, oil prices can have an impact on exports. The rationale is that unexpected spikes in oil prices raise the cost of producing raw materials since they tend to reduce their supply while simultaneously driving up their prices due to increased demand. High production costs and little exports are the results of this technique. Thirdly, agriculture accounts for the majority of Pakistan’s exports. A decrease in investment in agricultural products as a result of the increase in OP leads to lower production and fewer exports.

The findings indicate that despite an increase in OP, exports to the USA and China are improving, as shown by several of the exports’ quantiles. This distinguishing feature of our findings. It appears that several exporting industries hedge their bets to prevent potential losses brought on by the increase in OP. As a result, those businesses profit throughout this time. The case of the UK is another distinctive feature of the current study. In the instance of Pakistan’s exports to the UK, we notice both the considerable positive and negative effects of OP.

Our study asserts that exports to the top five trading partners must suffer a large loss as a result of macroeconomic uncertainty. The identical results are also disclosed by Novy and Taylor (2020), Tam (2018), Imbruno (2019), and Feng et al. (2017)). The high price ratios, low investment, low demand for raw materials, high employment rates, low expenditures, low demand for raw materials, and low production could all be caused by uncertainty, according to one theory. This mechanism thus hinders exports while also halting economic growth. It is interesting that some export quantiles to the UK and the UAE support the advantages of uncertainty. This is a particular result of the investigation once again.

Conclusion

The current study uses disaggregated (monthly) data of oil prices and uncertainty to examine their dynamic effects on Pakistan’s exports to its top five trading partners for more informative and robust findings, contending that the prior literature suffers from aggregation bias as a result of using the aggregate data. The present study has several contributions to the existing literature. First, this is the first study to address the issue of aggregation bias by using monthly data to get more detailed and insightful findings. We anticipated that the monthly series, as opposed to the yearly or quarterly statistics, may more appropriately illustrate the effects of changes in certain series on Pakistan’s exports. Second, this is the first study that, to the best of our knowledge, reveals the dynamic effects of oil prices and the world uncertainty index for Pakistan on Pakistan’s exports to its top five trade partners. Thirdly, this analysis is the first to use Sim and Zhou’s (2015) quantile and quantile (QQ) approach, which can manage the extreme values in the export function, oil prices, and world uncertainty index, in contrast to all previous studies in the relevant literature. For the analysis, we make use of a number of sophisticated econometric methods. First, according to the quantile unit root test, all of the chosen series have the integration order, and none of them are I(2). Second, the quantile cointegration test’s application verifies that there is long-run relationship among the modeled series. Thirdly, QQR estimations provide a range of intriguing results. According to theory and earlier research, rising oil prices (OP) lead to a decline in exports because of their inverse relationship with exports. Our research suggests that the OP has mixed and non-linear impacts, though. Although our findings support the earlier research in the bulk of the cases, including the USA, China, UAE, and Germany, a strong correlation between the two series is also seen. For instance, certain export quantiles in the USA and China show a noticeably favorable association with OP, showing that the exporting enterprises benefit in these quantiles. Beyond that, the document’s most notable finding is that, in the case of the UK, exports in excess of three quantiles have a detrimental effect on OP. On the other side, because of the rise in OP, the other more than three exports quantiles benefit significantly.

Similarly, uncertainty has conflicting consequences on exports, with the exporting producers experiencing both losses and gains as a result of the uncertainty. Uncertainty is a mixed benefit for Pakistan’s exports, as evidenced by the UAE, UK, and USA cases specifically. The quantile granger causality test, which validates our findings for the USA, China, UK, UAE, and Germany, identifies the bidirectional causal link among the series in all situations.

Pakistan’s exports are highly susceptible to OP and uncertainty. Hence results-based strategies are advised. In most circumstances, OP decreases Pakistan’s exports. The following proposal may mitigate OP’s negative consequences. First, the exporting manufacturer should hedge against oil prices to reduce price risk. This policy may mitigate the OP’s abrupt escalation’s negative consequences on exports. Second, authorities and politicians should subsidize important exporting industries, especially when oil prices are expected to rise. The targeted subsidies may help combat OP’s harmful effects. Thirdly, long-term export contracts between exporting enterprises and trading partners may reduce OP’s negative consequences.

Like oil prices, macroeconomic uncertainty (MEU) always hurts exports. Global economies should address macroeconomic uncertainty since the world has become a village. The COVID-19 epidemic caused worldwide economic growth and trade to decline. In this case, these tips may help. First, “anti-globalization” beliefs may increase global uncertainty. This may hurt local economic development and worldwide trade. Thus, global governments and businesses should reject “anti-globalization” ideas that fuel MEU. Second, to address MEU-related epidemics like COVID-19, international authorities should coordinate fiscal, monetary, and capital flow policies. They also create a plan to stabilize global eco-growth and trade.

The current study also highlights limitations that may lead to new discoveries. First, this article considers Pakistan’s top five trading partners. For greater direction, future study can include other trading partners. Second, adding political risk, trade policy risk, globalization, global chain values, exchange rate, and financial stress to the model should yield more intriguing results. Thirdly, the latest article focuses on Pakistani exports. Thus, researchers can use the same model for the world’s largest exporters to provide policy-oriented conclusions.

Disclaimer

The authors understand that the corresponding author is the sole contact for the editorial process. He/she is responsible for communicating with the other authors about progress, submissions of revisions, and final approval of proofs.