Exploring the Asymmetrical Influence of Economic Growth, Oil Price, Consumer Price Index and Industrial Production on the Trade Deficit in China

Abstract

The present study intends to scrutinize the asymmetrical influence of economic growth, industrial production, CPI (consumer price index) and oil price on the trade deficit for the People’s Republic of China’s economy. The Toda–Yamamoto causality, non-linear ARDL method, and quarterly data for 1995Q1 to 2021Q4 have been utilized to investigate the results. The estimated results confirm the uni-directional causality and presence of non-linear co-integration among variables under discussion. However, bound test analysis also reveals the long-run asymmetrical association among TD (trade deficit), IP (industrial production), oil price, and GDP growth, but not the CPI (consumer price index). Further, long-run asymmetrical outcomes highlight that a decrease (increase) in industrial production and an increase (decrease) in oil price and GDP growth rate increase (decrease) the trade deficit. Short-run asymmetrical outcomes reveal a similar trend to the long run, but the impact of all variables in the short run is insignificant, which means that linkages between the trade deficit and the explanatory variables are a long-run phenomenon in People’s Republic of China. Thus, in terms of policy, to reduce the trade deficit, it is necessary to focus on attaining standardized GDP growth, increasing industrial-sector production using advanced technology, and replacing oil-using energy sources with green technology (solar panels, wind farm energy).

1. Introduction

International trade plays a key role in an economy’s industrial and economic expansion. According to traditional and modern economists, a country’s industry can be strengthened, and economic growth can be increased, by boosting international trade [1,2,3]. Over time, universal economies have been interlinked in several ways, including globalization and international trade. Thus, international trade is considered the oldest and most prominent pillar of every country’s foreign financial and political relations. It also plays a fundamental role in developing advanced universal economies [4,5]. The increase in international trade over time among countries has not only developed each country’s economy but has also expanded overall economies. A considerable boost in international trade strengthens the production and services sector, which helps provide goods and services to deprived and underdeveloped economies facing serious comparative disadvantages in producing essential goods and services in their countries [6]. For most of the world’s economies, due to the ease of moving agricultural and capital products, international trade has been considered a tool for industrial and economic growth [7].

Worldwide, international trade is key to building social, political, and economic relations among developed and developing nations. In every era, international trade has gained keen importance because none of the countries can produce everything themselves and strappingly rely on other countries due to socio-economic confines and differences in various factors such as technical capabilities, natural resources, financial resources, and human capital [8]. Generally, international trade is the exchange of goods and services between two or more nations [9]. While comprehensively, under Ricardo’s classical theory of comparative advantage, international trade is deliberated as the difference in the cost of production for similar products produced in different countries [10]. Moreover, neo-classically, Heckscher–Ohlin pronounced that trade among nations had taken place due to differences in factors of endowments [11,12].

The current era’s trade deficit is an emerging challenge that significantly affects developing nations. A trade deficit has been defined as a difference between the exports and imports of a country. A country can be considered to have a trade deficit if its export income is much smaller than its import income [13]. According to the literature, a trade deficit, or import/export discrepancy, harms an economy, severely restricting national output and ultimately diminishing industrial production and the country’s GDP [14]. Generally, when a country cannot produce everything it desires on its soil due to an underdeveloped industrial sector, it purchases the required products from other countries to fulfill its specific needs by paying for imports. If the amount paid for imports exceeds the revenue from exports, this condition is generally known as a trade deficit [15]. Further, a trade deficit also arises when a weak industrial-sector country exports raw materials to a well-developed industrial-sector country at an inexpensive rate and then imports the finished manufactured goods made of the same raw material from that country at a higher rate [13].

Due to upsurges in financial activities and population, oil consumption and imports are increasing daily worldwide. In the last decade of the 20th century, i.e., the period from 1990 to 2000, global crude oil imports were around USD 579.4 billion, which were further increased to USD 2394.1 billion in 2008 and USD 2616.6 billion in 2011 [16]. The importance of the linkage of oil prices with the balance of trade strongly relies on whether the state is an oil exporter or an importer. If a country is an oil exporter, an increase in oil price positively influences its exchange rate, leading to a boost in the trade balance and ultimately causing an appreciation in the country’s currency. However, contrarily, if a state is an oil importer, an increase in the price of oil adversely influences its exchange rate, leading to a trade deficit and causing depreciation in its currency [17].

Moreover, an increase in oil price for developing economies causes currency depreciation, increases the trade deficit, and leads to a decline in industrial productivity and GDP growth that directly affect ordinary people’s livelihood by reducing their purchasing power parity (PPP) [18]. A decline in PPP increases external debt, weakens economic development, causes an upsurge in taxes and interest rates, and discourages investment which ultimately diminishes production and ordinary people’s consumption [19]. A reduction in investment and production has a double effect: on the one hand, it reduces GDP; on the other, it creates a severe import/export imbalance that ultimately causes a precarious trade deficit [20].

In the recent two decades, the quick economic expansion of the People’s Republic of China and its amalgamation with the outside globe have turned out to be indispensable. They highlighted economic activity among economists, development policymakers, social thinkers, and scholars from all arenas. Precisely, rapid financial expansion has been strongly linked with a persistent trade surplus, net foreign assets buildups, significant growth of income, an upsurge in the exchange rates, and the overall upsurge in foreign trade [21]. Since China’s opening-up reforms, a rapid expansion in China’s economy has been witnessed, with industrial growth being the most conspicuous element [22]. On the one hand, the expansion of the industrial sector significantly contributes to China’s overall economic growth, while on the other hand, it highlights its production and consumption trends and impacts foreign trade [23]. Moreover, China’s industrial expansion has entailed a structural change to its economy and boosted exports, but at the same time, industrial expansion has also increased China’s oil consumption and domestic GDP. China’s industrial expansion has created a severe trade imbalance due to an increased demand for imported goods, which ultimately increases the payments made for imports [24].

In this modernized age of globalization, technological innovation, and industrial development, capital goods have replaced the labor force to a great extent. However, due to its severe effectiveness, the trade deficit is still a hot issue for most emerging economies, especially in South Asia and Sub-Saharan Africa. Therefore, as per the sensitivity and importance of the trade deficit dilemma, various scholars have described different determinants of trade deficit by utilizing different methods for disparate emerging countries [25]. The influence of oil prices on the balance of trade in 34 states was studied through the PMG ARDL model. Bala, et al. [26] scrutinized the threshold influence of oil prices and export prices on trade deficits in African states associated with OPEC by using a dynamic panel model. Mesagan, et al. [27] explored the dynamic influence of the exchange rate on the trade deficit asymmetrically in South Africa through the NARDL model. Samuel [28] empirically reconnoitered the dynamical impact of the exchange rate, FDI, and inflation on trade balance by employing the econometric method of VECM (Vector Error Correction Model). Moyo and Garidzirai [29] empirically described the association between economic growth and trade balance in African countries by utilizing FGLS (feasible generalized least square) model. In the light of prior literature, it has been noted that inadequate work has been found worldwide that enquires about the association between trade deficit, oil price, industrial production, and economic development in the long run [2,23,30].

Moreover, no study has been extensively found emphasizing the casual and asymmetrical relationship between trade deficit, industrial production, oil price, consumer price index, and economic growth in People’s Republic China. Therefore, the current study’s novelty is an extended effort to fill the above-described gap by investigating the long and short-run asymmetries through the globally recognized non-linear ARDL model and the direction of causality through the Toda–Yamamoto causality test among the above-described variables. In addition, concerning the research gap, the prevailing study intentions to answer the following research questions:

• Is there an asymmetrical relationship between trade deficit, industrial production, oil price, consumer price index, and economic growth in China?

• Is there a bi-directional or one-directional casual association between China’s trade deficit and the explanatory variables?

In line with the above research questions, this paper’s main objectives are as follows:

• To examine China’s asymmetrical relationship between trade deficit, industrial production, oil price, consumer price index, and economic growth.

• To inspect the causal association amid China’s trade deficit, industrial production, oil price, consumer price index, and economic growth.

• To provide policy recommendations, based on the results, to help overcome the significant challenge posed by China’s trade deficit.

Answering these questions in the abovementioned crucial objectives, by utilizing well-reputed statistical tools (NARDL and Toda–Yamamoto causality test), provides a suitable pathway toward policy design, which helps in minimizing the trade deficit issue in the light of outcomes for all the key variables (industrial production, oil prices, GDP growth, and Consumer Price Index) for the People’s Republic China’s Economy.

The remainder of the prevailing study is schematized as follows. Section 2 presents a literature review related to the topic under discussion. Section 3 presents the methodology, including describing the data and constructing a globally acknowledged logical model. Section 4 presents and deliberates on the empirical outcomes. Lastly, Section 5 presents the study’s conclusions, policy recommendations, and limitations, and provides future research directions.

2. Literature Review

In recent times, especially over the last 25 years, owing to industrial advancement and an increase in the use of petroleum products, exploring the linkage between trade deficit, oil production, and industrial and economic development has become an area of interest for social thinkers, researchers, development policymakers, and the academic community. A substantial array of literature can be found that details the association amid trade deficit, oil productivity, industrial development, and economical expansion for different countries in different periods utilizing globally recognized statistical methodologies. For example, Bao [30] examined the oil price and trade balance linkages for Vietnam using the ARDL model and observed that, both in the longer and shorter term, an increase in oil prices adversely influences the balance of trade. Tiwari and Olayeni [31] examined the association between the balance of trade and oil prices in India using wavelet-based analysis and found that an upsurge in oil prices boosts the trade balance in the study area. Baek [32] highlighted the oil price and trade balance relationship between Korea and its 14 trading companions by utilizing a NARDL model, and concluded that the increase and decrease in oil price have an asymmetrical influence on Korea’s trade, both in the longer and shorter term, for most of the countries.

Similarly, Faheem, et al. [33] studied the asymmetrical association between oil prices and trade balance for three oil exporting countries: Kuwait, the United Arab Emirates, and Saudi Arabia. The findings revealed that positive and negative asymmetries exist between the prices of oil and the balance of trade in all three countries in the long and short term. Baek, et al. [34] also discussed the asymmetrical relationship between the prices of oil and the balance of trade in four OPEC countries (Iran, Nigeria, Saudi Arabia, and Venezuela). They found that, across all four countries, substantial positive and negative asymmetries exist between oil prices and trade balance in the long run, although not in the short run. Arouri, et al. [35] described the nexus between the prices of oil and the balance of trade in India using VAR (vector autoregression), Granger causality, and frequency dominance tests. The findings revealed that one standard deviation shock to oil price positively influences the trade balance. However, the Granger causality and frequency dominance tests revealed the bi-directional causal association between the two variables.

Similarly, Umoh and Effiong [36] and Adamu and Doğan [37] studied the long- and short-run linkages between trade openness and industrial growth in Nigeria. Utilizing the ARDL model, they concluded that, in both periods, trade openness and industrial growth are positively associated with each other, which ultimately means that industrial growth is the strongest pillar of an economy to reduce the trade deficit. Onakoya, et al. [38] also examined the long- and short-run association between trade openness and industrial sector growth for the Nigerian economy using the Johansen co-integration method. They concluded that trade openness and industrial sector growth are directly and strongly associated in the long and short run. Chandran [39] empirically inspected the long-run relationship between manufacturing growth and trade openness in Malaysia and showed that both indicators are positively linked in the study area. Ding, et al. [40] empirically highlighted the relationship between green total factor productivity and trade openness at a provincial level in China utilizing a dynamic panel model and concluded that green total factor productivity and trade openness have significant positive linkages. Ellahi, et al. [41] analyzed the numerical association between industrial value added and trade openness in Pakistan using the ordinary least squares (OLS) model and the Granger causality test. The findings highlighted that industrial value added and trade openness are directly linked in Pakistan. Ahad and Anwer [42] delineated the asymmetrical relationship between the balance of trade and industrial growth in Pakistan in both long and short run context and concluded that asymmetry exists between the trade deficit and growth of the industry in both periods, which means that an upsurge (decline) in the productivity of industry declines (upsurges) the trade deficit for Pakistan over longer and shorter periods.

Furthermore, Blavasciunaite, et al. [43] described the nexus between trade balance and economic growth for European Union countries using a multivariate fixed effect model and found that trade balance and economic growth are negatively associated [44]. Hobbs, et al. [45] tested the linkages among FDI, economic growth, and trade in Albania utilizing the Johansen co-integration method and the Granger causality test. The estimated measurements suggested strong co-integration and uni-directional causality among Albania’s FDI, trade, and economic growth. The unit analysis further elaborated that increased economic growth boosts FDI and trade in Albania in the short run, although not in the long run. Hosan, et al. [46] investigated the economic growth in thirty developing nations from 1995 to 2018; results suggest that sustainable economic development negatively affects energy intensity, while urbanization capital formation positively affects economic development.

Belloumi and Alshehry [6] empirically explored the linkage between trade openness, environmental quality, and economic expansion in SA (Saudi Arabia) utilizing the ARDL model. They concluded that, in the long run, all three variables are strongly co-integrated with a negative impact on each other, while in the short run, the relationship among them is insignificant. Kong, et al. [47] studied the likely linkages between trade openness and economic growth in China using the ARDL model and found that trade openness and economic growth are positively associated in both (longer and shorter) periods. Jebran, et al. [48] analyzed the influence of trade on economic growth in Pakistan using the ARDL model and revealed that trade terms have a substantial negative influence on economic growth in both periods (long and short run). Hassan, et al. [49] traced the key factors that influence the deficit of trade in both periods (long and short run) in three neighboring countries (Pakistan, India, and Bangladesh) using the ARDL bounds testing approach. The findings for all three countries clearly displayed that depreciation in the real effective exchange rate and expansion in economic growth reduce the trade deficit. However, increasing the money supply also significantly increases the trade deficit.

3. Methodology

3.1. Data Description and Model

The under-consideration research problem concerns the long- and short-run asymmetrical effect of industrial productivity, oil price, consumer price index, and economic growth on the trade deficit in China utilizing quarterly data from 1995Q1 to 2021Q4. The numerical data of all the variables taken for the current study were obtained from various globally recognized sources, including the CEIC (Census and Economic Information Center), IMF (International Monetary Fund), and TE (Trading Economics). The general presentation of the model is as follows:

TD_t = ƒ (IP_t, OP_t, CPI_t, GDP_gr)(1)

In a current study, the trade deficit (TD_t) is taken as the dependent variable and estimated as export unit value divided by import unit value in USD, following Faheem, et al. [33] and Ahmad, et al. [50]. Similarly, based on former literature, industrial production (IP_t), oil price (OP_t) per barrel in USD, consumer price index (CPI_t), and economic growth rate (GDP_gr) are taken as key explanatory variables for the problem under discussion in China [51,52,53].

These variables are further converted into natural logarithm form to improve their accuracy and to facilitate comparison and understandability as follows:

(2)$LnT{D}_t={\rho }_0+{\rho }_{1}LnIP{I}_t+{\rho }_{2}LnO{P}_t+{\rho }_{3}LnCP{I}_t+{\rho }_{4}LnGD{P}_{gr}+{\xi }_t$

A detailed explanation of each variable, its source of collection, and possible signs are presented in Table 1. The study variables are detailed further by presenting a graphical view that not only straightens the path toward the stationary situation measurement of each variable but also confirms whether these variables have increased, are constant, or show a declining trend over time (Figure 1).

3.2. General Arrangement of the Asymmetrical Model

The problem under consideration has been formulated as a linear equation to inspect the asymmetrical association among trade deficit, industrial productivity, prices of oil, consumer price index, and economic growth in China for long and short-run periods. Statistically, the equation is written as:

(3)$LnT{D}_t={\alpha }^{+}{z}_t^{+}+{\alpha }^{-}{z}_t^{-}+{\upsilon }_t$

In Equation (3), Ln TD_t represents the trade deficit in logarithm form, which is the dependent variable, while α positive and negative are the parameters of positive and negative partial sums. Here z_t is the function of $z_t^{+}$ and $z_t^{-}$ while both these positive and negative coefficients are partial sums that describe the positive and negative changes in z_t. Finally, ʋ_t is the residual term that captures the impact of those variables that are not discussed in the study but affect it from outside. The above generally describes explanatory variables are further decomposed into long- and short-run positive and negative partial sums as follows:

(4)$z_t=z_0+z_t^{+}+z_t^{-}$

where:

(5)$z_t^{+}={\displaystyle \sum }_{i-1}^t\mathsf{\Delta }{z}_i^{+}={\displaystyle \sum }_{i=1}^t\mathit{max}\left(\mathsf{\Delta }{z}_i,0\right)\&z_t^{-}={\displaystyle \sum }_{i-1}^t\mathsf{\Delta }{z}_i^{-}={\displaystyle \sum }_{i=1}^t\mathit{min}\left(\mathsf{\Delta }{z}_i,0\right)$

In Equation (4), z₀ represents intercept, $z_t^{+}$ is illustrative of long-run positive asymmetries, and $z_t^{-}$ is demonstrative of long-run negative asymmetries for all the explanatory variables. Similarly, in Equation (5), $\mathsf{\Delta }{z}_i^{+}$ represents all short-run explanatory variables while $\mathsf{\Delta }{z}_i^{+}$ and $\mathsf{\Delta }{z}_i^{-}$ represent short-run positive and negative asymmetries of all explanatory variables taken for the current study.

3.3. Testing for Serial Dependence

Before estimating the asymmetrical association among the variables under consideration, it is necessary to test the serial dependence of each variable separately. In time series data, BDS (Brock–Dechert–Scheinkman) statistics developed by Brock, et al. [54] are usually used to test for serial dependence. The BDS test uses the idea of spatial correlation from chaos theory [55], having the null hypothesis that data series are independently distributed and the alternative hypothesis that data series are not independently distributed. All three basic significance levels (1%, 5%, and 10%) are used to accept or reject the null hypothesis. Empirically, the BDS test is defined as:

(6)$BD{S}_{\upsilon ,m}=\frac{\sqrt{N}}{V_{\upsilon ,m}}\left[C_{\upsilon ,m}-{\left(C_{\upsilon ,1}\right)}^m\right]$

In Equation (6), root N represents the sample size of the time series data under discussion. Subscript m is the number of implanting dimensions, ranging between 2 and 5 (2 ≤ m ≤ 5) if the sample size consists of up to 500 observations. Finally, [C_v,m − (C_v,1)^m] is the asymptotic normal distribution with constant variance (V_ʋ,m) and zero mean.

3.4. Unit Root Test

Following the BDS test of serial dependence, two globally recognized unit root tests, ADF (augmented Dickey-Fuller) [55] and PP (Phillips–Perron) [56], are widely used to predict the stationary situation (mean zero and variance constant) of each variable. These statistics have a null and alternative hypothesis: H_o: $\mathsf{\Pi }$₂ = 0; and H₁: $\mathsf{\Pi }$₂ < 0. However, ADF significantly differs from PP by involving n lags, especially at the first difference estimation [57]. Statistically, it is represented as:

(7)$\mathsf{\Delta }{X}_t={\mathsf{\Pi }}_0+{\mathsf{\Pi }}_{1}t+{\mathsf{\Pi }}_2{X}_{t-i}+{\displaystyle \sum }_{i=1}^q{\phi }_i\mathsf{\Delta }{X}_{t-i}+{\zeta }_t$

In Equation (7), ΔX_t is the representative of all the variables which are taken for unit root calculation. Π₀ is the coefficient of intercept. Π₁ is the coefficient of the time-variant trend, and ‘t’ is the time. Π₂ is the slope coefficient, and X_t−i is the lag of the variable taken for the unit root testing. However, if we drop the lag term, i.e., ${\displaystyle \sum _{i-1}^q{\varphi }_i}\Delta X_{t-i}$ from Equation (7), the outcomes are purely representative of the PP test. In recent research, the assessment of the stationary situation of variables has been discussed further by calculating structural breaks of the data. When the data under discussion contain structural breaks, then basic neither test (ADF and PP) estimates are particularly reliable [55]. Thus, to overcome this issue, the current study also uses the Zivot–Andrews unit root test [58] to predict the stationarity of the data with a structural break. Moreover, in structural break stationary calculations, numerous dummies are involved for every probable break, and the ADF method is employed to pick apt breakpoints [23]. Generally, the structural break stationarity test is expressed as follows:

(8)$Z_t={\epsilon }_t+\alpha D{U}_t+\delta t+\pi Dt+\beta Z_{t-1}+{\displaystyle \sum }_{j=1}^p{\phi }_j\mathsf{\Delta }{Z}_{t-j}+{\mu }_t$

In Equation (8), the trend and mean shift are represented by Dt and DU dummies, respectively.

3.5. Long- and Short-Run Description of the Non-Linear Co-Integration Model

Previous literature has comprehensively revealed that traditionally long-run relationships among variables can be measured through the methods proposed by Baillie and Selover [59], Engle and Granger [60], and Johansen and Juselius [61] due to the same stationary situation of the data series either at the level I(0) or at the first difference I(1). However, in subsequent more advanced research, the diverse nature of the order of integration has been widely found in most data series. A few variables are stationary at level I(0), and a few are stationary at the first difference I(1), but none of the variables are stationary at the second difference I(2). To resolve this assorted order of integration I(0)/I(1) problem, Pesaran, et al. [62] developed an ARDL bounds testing method that has been widely adopted to investigate co-integration among the variables under study. The selection of the ARDL model has certain key advantages. First, it is easily applicable and provides robust results with a small sample size. Second, it also follows the premise of the distinctive order of integration. Third, it is a suitable test to describe uni-directional linkages among variables, given the varied nature of integration [63].

Furthermore, Arize, et al. [64] asserted that if variables with an assorted order of integration do not show a long-run relationship in the traditional sense, then there must be a long-run relationship between their negative and positive components, termed concealed co-integration. A concealed co-integration or non-linear long-run association among variables cannot be assessed through the conventional ARDL approach. Therefore, Shin, et al. [65] introduced the NARDL model, a helpful tool for dealing with the ARDL shortcoming by exploring non-linear long-run associations between variables. Generally, the long-run equation for NARDL is formulated as follows:

(9)$\begin{array}{c}{\mathit{LnTD}}_t={\tau }_o+{\tau }_1{\mathit{LnTD}}_{t-1}+{\displaystyle \sum _{i=1}^q}{\tau }_{IPI}^{+}IP{I}_t^{+}+{\displaystyle \sum _{i=1}^q}{\tau }_{IPI}^{-}IP{I}_t^{-}+{\displaystyle \sum _{i=1}^q}{\tau }_{OP}^{+}O{P}_t^{+}+{\displaystyle \sum _{i=1}^q}{\tau }_{OP}^{-}O{P}_t^{-}+{\displaystyle \sum _{i=1}^q}{\tau }_{CPI}^{+}CP{I}_t^{+}\\ +{\displaystyle \sum _{i=1}^q}{\tau }_{CPI}^{-}CP{I}_t^{-}+{\displaystyle \sum _{i=1}^q}{\tau }_{GD{P}_{gr}}^{+}GD{P}_{grt}^{+}+{\displaystyle \sum _{i=1}^q}{\tau }_{GDPgr}^{-}GD{P}_{gr}^{-}+v_t\end{array}$

Equation (9) represents the long-run non-linear parameters linked with positive and negative changes in industrial production, respectively. Here, ${\tau }_{O{P}_t}^{+} \mathrm{and} {\tau }_{O{P}_t}^{-}$ the long-run asymmetric parameters are allied with a positive and negative change in oil price per barrel in USD. Similarly, ${\tau }_{CPI}^{+},{\tau }_{CPI}^{-},{\tau }_{GD{P}_{gr}}^{+} \mathrm{and} {\tau }_{GD{P}_{gr}}^{-}$ are the long-run asymmetric parameters akin to a positive and negative change in the consumer price index and GDP growth rate, respectively. Finally, ʋ_t is the long-run residual term that considers those variables’ impacts that influence the model from outside. Additionally, like ARDL, here also in NARDL, the long-run relationship among variables is broadly estimated through two globally acknowledged measures (the F-statistic [62] and the t-test under the null hypothesis $H_0:\left(\vartheta ={\varphi }^{+}={\varphi }^{-}={\phi }^{+}={\phi }^{-}={\delta }^{+}={\delta }^{-}={\gamma }^{+}={\gamma }^{-}=0\right)$ with symmetric (linear) long-run coefficients exist, and the alternative hypothesis $H_1:\left(\vartheta \ne {\varphi }^{+}\ne {\varphi }^{-}\ne {\phi }^{+}\ne {\phi }^{-}\ne {\delta }^{+}\ne {\delta }^{-}\ne {\gamma }^{+}\ne {\gamma }^{-}\ne 0\ne 0\right)$ asymmetric (non-linear) long-run coefficients exist. Based on the F-statistic and t-test calculations, the rejection of the null hypothesis reveals strong evidence that the variables of interest have a long-run relationship with each other, which means that the F-statistic and t-test calculations have a higher value than the upper and lower critical bounds. Finally, to estimate the short-run asymmetrical association among the variables, the NARDL equation is written as:

(10)$\begin{array}{cc}\hfill \Delta LnT{D}_t={\pi }_0+& \vartheta LnT{D}_{t-1}+{\varphi }^{+}IP{I}_{t-1}^{+}+{\varphi }^{-}IP{I}_{t-1}^{-}+{\phi }^{+}O{P}_{t-1}^{+}+{\phi }^{-}O{P}_{t-1}^{-}+{\delta }^{+}CP{I}_{t-1}^{+}+{\delta }^{-}CP{I}_{t-1}^{-}\hfill \\ & +{\gamma }^{+}GD{P}_{grt-1}^{+}+{\gamma }^{-}GD{P}_{grt-1}^{-}+\sum _{j=1}^{p-1}{\tau }_i\Delta LnT{D}_{t-i}+\sum _{j=0}^q{\alpha }_{i^{+}}^{+}\Delta LnIP{I}_{t-i}^{+}+{\alpha }_i^{-}\Delta LnIP{I}_{t-i}^{-}\hfill \\ & +\sum _{j=0}^q{\beta }_{i^{+}}^{+}\Delta LnO{P}_{t-i}^{+}+{\beta }_i^{-}\Delta LnO{P}_{t-i}^{-}+\sum _{j=0}^q{\chi }_{i^{+}}^{+}\Delta LnCP{I}_{t-i}^{+}+{\chi }_i^{-}\Delta LnCP{I}_{t-i}^{-}\hfill \\ & +\sum _{j=0}^q{\lambda }_{i^{+}}^{+}\Delta LnGD{P}_{grt-i}^{+}+{\lambda }_i^{-}\Delta LnGD{P}_{grt-i}^{-}+{\mu }_t\hfill \end{array}$

Similar to the previous long-run relationships, positive (+) and negative (−) describe the partial sum of each variable, while p and q represent the lag order of dependent and explanatory variables, respectively.

4. Results

This section presents a complete description and analysis of the empirical outcomes, including comprehensive justifications, utilizing the globally acknowledged methodology detailed in Section 3. Table 2 presents the outcomes of descriptive statistics for the People’s Republic of China from 1995Q1 to 2021Q4. The descriptive statistics calculation comprises a series of measures, including mean, median, maximum, minimum, standard deviation, skewness, and kurtosis. The numerical measures of the descriptive statistics for all the variables were primarily rational and presented normal distribution with zero mean and constant variance. These calculated statistics are also further verified through skewness (closer to 0) and kurtosis (closer to 3) values for every variable under consideration.

Pair-wise correlation is also calculated in Table 2, after the descriptive statistics, to analyze the relationship and actual association among the variables. Empirical calculations highlight that all the variables are substantially associated with each other; however, the precise association is not particularly strong to cause a multicollinearity problem because every explanatory variable (IPI_t, OP_t, CPI_t, and GDP_gr) relationship to each other is less than 0.90 [65,66,67]. Further, Gujarati [66] stated that for any regression analysis, the association among all explanatory variables is necessary, but such association is not stronger than the threshold measure of 0.90 under correlation analysis because 0.90 and above measures reveal the presence of a significant multicollinearity issue. These estimates have no multicollinearity and are also validated with VIF and Tolerance measures, which confirm that the data does not contain an issue of multicollinearity because all the explanatory variables’ estimates of VIF and Tolerance are less than 10 and greater than 0.10 [67] (Table A1, Appendix A). Furthermore, the actual association among dependent and explanatory variables demonstrates that all other variables (oil price, consumer price index, and economic growth rate) are positively associated with the trade deficit, except for industrial production.

Table 3 portrays the stationary situation of the variables based on the ADF and PP tests. The results show that the variables under study present mixed stationary conditions. All the explanatory variables, industrial production, oil price, consumer price index, and GDP growth rate, are stationary at the first difference I(1), while the dependent variable of trade deficit is stationary at a level I(0). Moreover, these estimates further show that none of the variables are integrated or stationary at the I(2) difference. The mixed order of integration at I(1)/I(0) but not at I(2) flattens the route toward the assessment of long- and short-run relationships through a bound testing approach [62].

In a current study, an assessment of the order of integration is extended further by calculating the structural breaks of the data under study. Bayar and Karamelikli [68] stated that conventional methods, ADF and PP, are unreliable enough to provide the correct order of integration when the data contain structural breaks [69]. Therefore, to deal with this problem, the current study calculates the structural break order for data integration using the Zivot–Andrews unit root test [58]. Such as the above calculations for the ADF and PP tests, the empirical outcomes of the structural break unit root test in Table 4 also present an incongruent stationary situation of the data. The initial two variables, trade deficit and industrial production, are integrated at the I(0) level with a structural break at 1996Q1 and 2012Q1; in contrast, the remaining three variables (oil price, consumer price index, and GDP growth rate) are integrated at the first difference I(1) with a structural break 2012Q4, 1996Q2, and 2021Q3. Furthermore, the Toda–Yamamoto causality measurements are presented in Table 5, showing that Ln TD_t causes Ln IPI_t, Ln OP_t, Ln CPI_t, and Ln GDPgr in a single directional spectrum at a 5% level of significance, and there is no evidence of bi-directional causality.

After estimating the stationary condition and direction of causality of the data, further asymmetry was checked in the data series through the BDS test. The reported outcomes in Table 6 clearly show that, for the trade deficit, industrial production, oil price, consumer price index, and GDP growth rate, the null hypothesis of linearity is rejected at a 1% level of significance, denoting that the overall described series is non-linear and not identically distributed, which reflects the existence of severe asymmetries. Further, Ahad and Anwer [16] and Liu, et al. [70] highlighted that when data series contain a mixed order of integration, uni-directional causality, and dynamic asymmetries, then the basic ARDL bounds testing approach is invalid for exploring long- and short-run association among variables. Therefore, to resolve this issue, the NARDL model [71] is employed to measure the long- and short-run relationship among the variables.

Given the mixed order of integration and non-linearity in the data, the NARDL model was adopted to explore the asymmetrical association among trade deficit, oil price, industrial production, consumer price index, and GDP growth rate in the People’s Republic of China. To calculate the NARDL asymmetrical model, a “general to specific” approach was adopted to select the appropriate lag length under AIC (Akaike information criteria).

Based on AIC, a calculation was made with maximum lags and drops (highly insignificant ones). A drop of insignificant value denotes a mis-specified model, causing various statistical issues, such as auto-correlation and multicollinearity. However, to avoid statistical issues and make the model quite simple under Occam’s razor philosophy, a “3” lag length was selected under AIC and two other information criteria, namely LR (sequentially modified likelihood ratio test statistics) and FPE (final prediction error) (Table 7).

Table 8 presents long- and short-run asymmetries under Wald test statistics. The empirical results show that the Wald test strongly rejects the null hypothesis of no asymmetries for the log of industrial productivity, prices of oil, CPI (consumer price index), and GDP growth rate at the 1% significance level.

The results for the short-run asymmetries are similar to those for the long-run asymmetries, and the Wald test rejects the null hypothesis of no asymmetries at the 5% and 10% significance levels for most variables. Furthermore, it can be seen that substantial asymmetries exist in the data under study. Therefore, a linear model for the estimation of long- and short-run estimates would perhaps be mis-specified in the case of the People’s Republic of China for the current study.

After confirming the presence of long- and short-run asymmetries, two tests (the F-statistic [62] and the t-test) were used to explore asymmetric co-integration among the variables in Table 9. The numerical measures of F_PSS (7.22) and t_BDM (−7.60) are greater than the lower and upper bounds, reflecting the rejection of the null hypothesis of no co-integration or long-run asymmetrical association among variables in favor of the alternative hypothesis that there exists a co-integration or long-run asymmetrical association among variables at the 5% level of significance. The study’s findings highlight that a long-run non-linear or asymmetrical association exists among trade deficit, industrial production, oil price, consumer price index, and GDP growth rate in the People’s Republic of China from 1995Q1 to 2021Q4.

5. Detail Discussion of Calculated Outcomes

After verifying the presence of long- and short-run relationships, the NARDL test was performed to explore each explanatory variable’s positive and negative impact (Ln IPI_t, Ln OP_t, Ln CPI_t, and Ln GDP_gr) on the dependent variable (TD_t). The results in Table 10 show that a 1% increase in industrial production (Ln IPI⁺_t) reduces the trade deficit by 0.347%, while a 1% decline in industrial production (Ln IPI⁻_t) increases the trade deficit by 0.145%. These estimations are consistent with [72,73,74]. The main reason behind China’s increasing investment in the local industrial sector over the past few decades is to boost its production, especially in manufacturing. On the other hand, a decline in imports because people mostly used locally manufactured inexpensive goods, while on the other hand, due to new investments under the accelerator rule, excess production (more than the demand of local people) occurred, leading to a boost in exports. Thus, due to an upsurge in industrial production, an increase in exports and a decline in imports have caused more receipts inflow than payments outflow, leading to a decrease in the trade deficit in China. However, a decline in industrial production fails to fulfill the demand of the local population and compels them to buy imported goods. Such an increase in imports boosts the import payments and leads to an increased trade deficit [10,29].

According to Baek and Choi [75], Faheem, et al. [33], Baek ad Kwon [76] and Tang, et al. [77], oil price and trade deficit have an asymmetrical association, which means an increase (decrease) in oil prices increases (decreases) the trade deficit. The numerical results of the current study are largely consistent with previous views, showing that a 1% increase in the oil price (Ln OP⁺_t) increases the trade deficit by 2.78%; contrarily, a 1% decrease in the oil price (Ln OP⁻_t) reduces the deficit of trade by 1.045%. The increase (decrease) in trade deficit with increasing (declining) oil prices in China mainly happens due to higher oil imports and smaller oil exports. The logical conclusion is that China’s current oil demand is extremely high. To reduce this oil demand, China must focus on converting as many oil-using energy sources as possible into advanced green technology (solar and wind farm energy) and make every effort to fulfill the remaining oil demand from locally produced oil. These measures will reduce China’s oil import payments and lead to a substantial decline in the trade deficit [25]. Moreover, Ogbonna and Ichoku [52], Beak [32], and Arouri, et al. [35] contradict the above views indirectly and demonstrate that an upsurge (decline) in prices of oil increases (declines) the trade balance, which ultimately upsurges oil price and declines the trade deficit and when oil price declines, trade deficit increases.

Similarly, the calculated long-run coefficients of the consumer price index (Ln CPI⁺_t and Ln CPI⁻_t) reveal that a 1% increase and decline in the consumer price index, or inflation, increase the trade deficit by 1.253% and 3.119%, respectively, which reveals that the consumer price index does not have an asymmetrical impact on the trade deficit. These results support Ahad [16] and Islam [78]. The logical reason is that a rise in the consumer price index, or inflation, decreases people’s purchasing power in China. Because of this, the domestic population feels that locally-produced goods are more expensive than internationally imported products. Hence, the domestic population is more attracted to buying inexpensive international products than local ones, which causes an increase in imports and an enlarged trade deficit. Contrarily, a decline in inflation boosts ordinary people’s purchasing power, improving their livelihood and giving more preference to imported goods made with advanced technology than local ones. Accordingly, there is a significant increase in imports, ultimately increasing the trade deficit. However, the outcomes further show that the influence of increasing inflation on the trade deficit is smaller than that of decreasing inflation: increasing inflation (weakening purchasing power) leads to imports of low-priced necessities, while decreasing inflation (strengthening purchasing power) leads to imports of high-priced luxury products. This indicates that the impact of decreasing inflation on the trade deficit is more severe than increasing inflation. Sarac and Karagooz [79] explain that trade deficit and consumer price index are inversely associated with indirect impact. A higher rate of inflation leads to a higher rate of interest that ultimately depreciates the exchange rate and causes a reduction in the trade deficit.

Finally, asymmetrical outcomes of GDP growth highlight that a 1% increase (decrease) in the GDP growth rate (Ln GDP⁺_gr and Ln GDP⁻_gr) increases (decreases) the deficit of trade by 0.227% and 0.777% in China. These outcomes align with Jebran, et al. [48] and Shahid, et al. [23]. The reason behind these results is that China’s increasing GDP growth rate leads to an upsurge in the domestic population’s income, which ultimately raises their standard of living. An increase in the living standard creates a desire among people to purchase luxurious imported products and advanced technology, this increase in imports increases the outflow of payments and causes a severe trade deficit [9], Zhang, et al. [80] and Christensen [81]. Contrarily, a decline in the GDP growth rate reduces the trade deficit because the domestic population’s GDP growth rate per capita income leads to a low-quality standard of living, which compels the population to consume domestically produced products rather than imported goods. This leads to a reduction in the outflow of payments and causes a decline in the trade deficit [82,83]. Furthermore, Awan and Mukhtar [84] and Ahmad [50] had contradictory views regarding trade deficit and economic growth association. Both these studies explored that increasing economic growth declined the trade deficit in the long run, while in short, these studies also revealed an insignificant relationship between both variables of interest.

The long- and short-run asymmetrical outcomes also reveal a similar trend in the case of all other variables is increasing the trade deficit, except for industrial production. Contrarily, in case of a negative impact, industrial production and the CPI increase the trade deficit, whereas oil price and GDP growth rate decrease the trade deficit. However, the impact of almost all variables in the short run is insignificant, which means that linkages between trade deficit, industrial production, oil price, consumer price index and GDP growth rate are a long-run phenomenon and cannot be judged in the short run, especially when considering the asymmetrical perspective. The ECM_t−1 (coefficient of the error correction mechanism) embodies the speed of adjustment from short to long periods. The estimated value for ECM_t−1 is quite high, 1.03, and is significant at the 1% level, which proposes that any shock to the TD_t of China in the short run will have a high (quarterly) speed of adjustment or conversion rate, which is 103%. These measures are consistent with [85] that also have ECM_t−1 values greater than 100%. Further, dynamic multiplier graphs were also used to check the robustness of the estimated long-run outcomes (Figure 2). These graphs also reveal that, except for the consumer price index, all variables exhibit long-run asymmetries because the zero line (blue color) is significant and lies between positive and negative change.

The model’s strength, overall significance, and accuracy were also assessed using measures such as R-square, F-statistics, and the various diagnostic estimates described in Table 10. An initial estimate of R-square reveals that 77% of the variance in the calculated model is explained by the explanatory variables, while the remaining 23% is explained by other factors that are not part of the model but influence it from outside. A high R-square value reveals that the overall model is well-fitted. Similarly, the F-statistic value (6.57) shows the model’s strength, rejecting the null hypothesis while favoring the alternative hypothesis of the overall model at a high significance level (1%). Finally, reliability analysis shows that the calculated model is not affected by any statistical issues such as heteroscedasticity, auto-correlation, normality of the residuals, and functional misspecification. Figure 3 and Figure 4 depict the stability outcomes through the CUSUM (cumulative sum) and CUSUM square tests, respectively. Both figures reveal that the stability lines lie between critical bounds, which rejects China’s null hypothesis of non-stability in the long run [70,86].

6. Conclusions

The present study has examined the direction of causality, as well as the long- and short-run asymmetrical association among trade deficit, prices of oil, industrial productivity, consumer price index, and GDP growth rate in the People’s Republic of China using time series quarterly data from 1995Q1 to 2021Q4 and two statistical methods (Toda–Yamamoto test and NARDL model). Based on the objectives, initial results for the causality test reveal a single direction of causality from the explanatory variables (industrial production, oil price, CPI, and GDP growth rate) to the dependent variable (trade deficit). However, long-run asymmetrical estimates under NARDL demonstrate that long-run asymmetries exist from industrial production, oil price, and GDP growth rate (but not consumer price index) to trade deficit. An assessment of industrial production highlights that an increase (decrease) in industrial production in China decreases (increases) the trade deficit. Increasing industrial sector investment boosts productivity to a greater extent by reducing imports and increasing exports, which ultimately reduces the trade deficit because import outflows decline and export inflows increase.

Further, oil price and GDP growth results show an upsurge (decrease) in oil prices and a rate of GDP growth (decrease) in the trade deficit. Increasing oil prices puts adverse pressure on import payments, which increases the trade deficit, while replacing oil-usage energy sources with green technology decreases oil imports, thus reducing the adverse pressure on import payments and causing a decline in the trade deficit. The GDP growth shows a similar impact to oil imports on the trade deficit, meaning that an increase in GDP growth rate increases the living standards of the domestic population because their income grows significantly. They are more attracted to modern imported products than local ones, which increases imports and the trade deficit. Contrarily, a decline in GDP growth rate reduces the trade deficit because the domestic population’s GDP growth rate per capita income leads to decreased living standards, which compels the population to consume domestically produced products rather than imported goods, which reduces the outflow of payments and causes a decline in the trade deficit.

Finally, the consumer price index results do not show any asymmetry and reveal a positive impact on the trade deficit, both in increasing and declining contexts. However, the impact of increasing inflation on the trade deficit is smaller than that of decreasing inflation. Increasing inflation reduces the domestic population’s purchasing power so that they import only life’s necessities, which puts smaller adverse pressure on import payments. In contrast, declining inflation increases the local population’s purchasing power and drives the import of luxuries, which puts heavy adverse pressure on import payments. Ultimately, the short-run asymmetrical results show a similar trend to the long-run asymmetrical results, having an insignificant impact, which means that the influence on the trade deficit of almost all explanatory variables is a long-run phenomenon and cannot be judged in the short run, especially in the context of an asymmetrical continuum. Moreover, the error correction mechanism estimate is relatively high, which recommends that any shock to the trade deficit in China in a shorter period has a high speed of adjustment quarterly toward equilibrium.

6.1. Policy Recommendations

Regarding policy recommendations, China’s government must boost the industrial sector by undertaking some rapid reforms, such as upgrading the industrial sector with heavy investment and using advanced technology in production processes. Both these measures can enable China’s industrial sector to produce locally and internationally accepted products that not only decrease China’s imports but also increase China’s exports, thus ultimately lessening the trade deficit.

Second, China’s current oil demand is extremely high, which causes a severe trade deficit. To reduce oil demand, China must focus on converting as many oil-using energy sources as possible to advanced green technology (solar and wind farm energy) and make every effort to fulfill oil demand from locally produced sources. Further, China should invest heavily in exploring new oil resources to meet increasing local energy needs. These measures can help reduce China’s oil import payments and lead to a substantial decline in the trade deficit.

Third, a higher GDP growth rate will upsurge the living standards of the local population, which also increases the trade deficit. To address this issue, China must develop a taxation system so that the increasing income of the domestic population utilizes more local products than imported ones. This approach will also be a helpful tool to reduce import outflows and reduce the trade deficit.

Both increasing and declining inflation increase the trade deficit; therefore, China’s government must control inflation at an economically acceptable threshold, limiting increases or decreases in inflation as much as possible. The rapid implementation of the above recommendations will significantly reduce the trade deficit in the People’s Republic of China.

6.2. Limitations and Future Research Directions

The existing research has measured the asymmetrical impact of industrial production, oil price, GDP growth, and CPI on the trade deficit of China. In the future, this study can be expanded by increasing the time length, on the one hand, and the number of indicators, such as the money supply and exchange rate, on the other hand. Further, the present study is limited to the time series perspective; however, future studies can expand on this perspective by using, for example, panel data. Such studies could also involve more than one country’s data for cross-country comparisons.

Author Contributions

Data curation, L.P. and A.A.; funding acquisition, L.P.; supervision, A.A.C.; writing—original draft, L.P., A.A. and A.H.S.; writing—review and editing, L.P., A.A., N.Z. and E.Y.N. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Figures and Tables

Figure 1. Data plots show the data trends over time.

Figure 1. Data plots show the data trends over time.

Figure 2. Dynamic multiplier graphs from explanatory variables to the dependent variable.

Figure 3. CUSUM test.

Figure 4. CUSUM square test.

Table 1

Portrayal variables along data source and anticipated signs for China.

Variables	Definition	Source	Possible Signs
Dependent variable
Ln TDt	Log of trade deficit is estimated as export unit value divided by import unit value in USD.	IMF	-
Explanatory variables
Ln IPIt	Log of industrial production index. It is measured through real output in dissimilar production segments, such as mining, gas, electricity, and manufacturing, relative to the base year, 2010 = 100.	CEIC	Negative/positive
Ln OPt	Log of oil price barrel/day in China in USD.	TE	Positive/negative
Ln CPIt	Log of a consumer price index. It is measured as the average change in rudimentary price that a consumer pays for a specific basket of food and non-food items or services relative to the base year, 2010 = 100.	IMF	Positive/negative
Ln GDPgr	Log of GDP growth rate. It is typically measured by the relative change in country GDP from one year to the selected base year, i.e., 2010 = 100. Usually, GDP is the value of final goods and services produced within the country’s border within one year.	CEIC	Positive/negative

Notes: IMF, CEIC and TE are data sources well described above. Source: Authors, based on references [30,43,44,45,46,47,48].

Table 2

Descriptive statistics of variables.

	Ln TDt	Ln IPIt	Ln OPt	Ln CPIt	Ln GDPgr
Mean	0.17	3.42	9.30	4.60	2.14
Median	0.16	3.46	9.31	4.57	2.12
Std. dev.	0.08	0.37	0.101	0.17	0.22
Maximum	0.33	4.01	9.44	4.88	2.68
Minimum	–0.08	2.54	9.07	4.29	1.73
Skewness	–0.14	–0.34	–0.26	0.22	0.36
Kurtosis	2.50	2.25	2.37	2.59	2.20
Observations	108	108	108	108	108
Ln TDt	1.000
Ln IPIt	–0.424 *	1.000
Ln OPt	0.196 **	–0.315 *	1.000
Ln CPIt	0.284 *	–0.658 *	0.732 *	1.000
Ln GDPgr	0.286 *	0.774 *	–0.289 *	–0.608 *	1.000

Notes: *, and **, show the significance level, i.e., 1%, 5%, and 10%, respectively.

Table 3

Unit root analysis to predict the stationary situation of the variables.

Variables	Exogenous	ADF Test	PP Test	Decision
				ADF	PP
Ln TDt	Intercept	−3.42 **	−5.69 *	I(0)	I(0)
Ln IPIt	Trend and intercept	−12.00 *	−12.84 *	I(1)	I(1)
Ln OPt	Trend and intercept	−10.25 *	−10.26 *	I(1)	I(1)
Ln CPIt	Trend and intercept	−3.96 **	−8.62 *	I(1)	I(1)
Ln GDPgr	Intercept	−10.35 *	−10.84 *	I(1)	I(1)

Notes: *, and **, show the significance level, i.e., 1%, 5%, and 10%, respectively.

Table 4

Empirical results for the structural break unit root test.

Variable	Exogenous	I(0)		I(1)		Decision
		t-Value	Time Break	t-Value	Time Break
Ln TDt	Intercept	−5.45 *	1996Q1	−15.05 *	1996Q3	I(0)
Ln IPIt	Trend and intercept	−4.85 **	2012Q1	−12.86 *	2009Q4	I(0)
Ln OPt	Trend and intercept	−2.97	2004Q2	−10.79 *	2012Q4	I(1)
Ln CPIt	Trend and intercept	−4.20	1998Q1	−9.50 *	1996Q2	I(1)
Ln GDPgr	Trend and intercept	−2.42	2021Q3	−10.31 *	2021Q3	I(1)

Notes: *, and **, show the significance level, i.e., 1%, 5%, and 10%, respectively.

Table 5

Toda–Yamamoto Granger causality results.

Null Hypothesis	Decision	F-Statistics	Prob.
Ln IPIt → Ln TDt	Yes	6.10 **	0.047
Ln IPIt ← Ln TDt	No	0.76	0.682
Ln OPt → Ln TDt	Yes	8.33 **	0.015
Ln OPt ← Ln TDt	No	0.40	0.817
Ln CPIt → Ln TDt	Yes	6.22 **	0.044
Ln CPIt ← Ln TDt	No	1.51	0.469
Ln GDPgr → Ln TDt	Yes	8.25 **	0.016
Ln GDPgr ← Ln TDt	No	3.06	0.216

Notes: * and, **, show the significance level, i.e., 1%, 5%, and 10%, respectively.

Table 6

Estimates of non-linearity under the BDS test.

Dimension	Ln TDt	Ln IPIt	Ln OPt	Ln CPIt	Ln GDPgr
2	0.047 *	0.135 *	0.185 *	0.195 *	0.136 *
3	0.075 *	0.224 *	0.320 *	0.329 *	0.220 *
4	0.078 *	0.275 *	0.414 *	0.423 *	0.267 *
5	0.088 *	0.298 *	0.481 *	0.490 *	0.293 *
6	0.085 *	0.305 *	0.526 *	0.536 *	0.305 *

Notes: *, and **, show the significance level, i.e., 1%, 5%, and 10%, respectively.

Table 7

Apposite lag selection for the NARDL model.

Lag	LogL	LR	FPE	AIC	SC	HQ
0	395.71	NA	3.24 × 10−10	−7.66	−7.53	−7.60
1	921.28	989.30	1.77 × 10−14	−17.47	−16.70 *	−17.16 *
2	944.60	41.60	1.84 × 10−14	−17.44	−16.02	−16.86
3	975.22	51.62 *	1.66 × 10−14 *	−17.55 *	−15.49	−16.71
4	995.47	32.17	1.85 × 10−14	−17.46	−14.75	−16.36

Notes: LR = sequential modified likelihood ratio test statistics; FPE = final prediction error; AIC = Akaike information criteria; SIC = Schwarz information criteria; HQ = Hannan−Quinn information criteria.* represents the maximum lag length which is adopted are ARDL model.

Table 8

Long- and short-run asymmetries under Wald test statistics.

Period	Variable	Wald Test	Period	Variable	Wald Test
Long-run asymmetries	W Ln IPI	12.21 *	Short-run asymmetries	W Ln IPI	6.45 **
	W Ln OP	7.74 *		W Ln OP	0.25
	W Ln CPI	11.92 *		W Ln CPI	3.36 ***
	W Ln GDPgr	29.45 *		W Ln GDPgr	1.037

Notes: *, **, and *** show the significance level, i.e., 1%, 5%, and 10%, respectively.

Table 9

NARDL asymmetric co-integration outcomes.

Critical Bound	Significance Level
	5%	10%
H0: No long-run asymmetrical association among variables
FPSS (7.22)
LB I(0)	2.22	1.95
UB I(1)	3.39	3.06
tBDM (−7.60)
LB I(0)	−2.86	−2.57
UB I(1)	−4.76	−4.40

Notes: LB = lower bound; UB = upper bound.

Table 10

NARDL long- and short-run results.

Variables	NARDL Model
Design of the model for empirical calculations	(1,1,2,2,3,3,2,1,3)
Long-run NARDL results
LnTDt−1	−0.039(0.0982)
Ln IPI+	−0.347 * (0.050)
Ln IPI−	0.145 ** (0.061)
Ln OP+	2.786 * (0.478)
Ln OP−	−1.045 * (0.253)
Ln CPI+	1.253 * (0.498)
Ln CPI−	3.119 * (0.826)
Ln GDPgr+	0.227 * (0.100)
Ln GDPgr−	−0.777 * (0.074)
Short-run NARDL results
Δ Ln IPI+	−0.092 (0.072)
Δ Ln IPI+t−1	0.179 ** (0.089)
Δ Ln IPI−	0.125 (0.075)
Δ Ln IPI−t−1	−0.085 (0.082)
Δ Ln IPI−t−2	−0.1466 ** (0.066)
Δ Ln OP+	0.836 (0.72)
Δ Ln OP−	−0.08 (0.85)
Δ Ln OP−t−1	−1.31 (0.799)
Δ Ln CPI+	3.34 * (0.926)
Δ Ln CPI+t−1	−3.57 * (0.987)
Δ Ln CPI+t−2	−2.007 ** (0.993)
Δ Ln CPI−	−0.584 (1.78)
Δ Ln CPI−t−1	1.50 (1.72)
Δ Ln GDP+gr	−0.010 (0.125)
Δ Ln GDP−gr	0.213 (0.134)
Δ Ln GDP−gr t−1	−0.615 * (0.137)
Δ Ln GDP−gr t−2	−0.233 (0.150)
ECMt −1	−1.03 * (0.098)
Constant	0.117 ** (0.055)
R 2	0.77
F-statistic	6.57 *
Diagnostic measures for the NARDL model
Auto-correlation LM chi2 test	31.93 (0.8147)
Breusch–Pagan heteroskedasticity chi2 test	0.1838 (0.6682)
Ramsey reset model specification F-test	1.76 (0.1636)
Residual normality Jarque–Bera test	1.20 (0.5487)

Notes: Statistics in parenthesis are estimated standard errors for long- and short-run measurements; however, for F-statistics and diagnostic measures, statistics in parenthesis are estimated probabilities. Further, the overall NARDL calculations utilize AIC (Akaike information criteria). *, and **, show the significance level 1%, 5%, and 10%, respectively.

Appendix A

Table A1

VIF and Tolerance Estimates for Multicollinearity.

Variables	VIF	Tolerance
Ln IPIt	4.29	0.233
Ln OPt	1.11	0.889
Ln GDPgr	4.23	0.236
Mean VIF	3.21

VIF (Variance Inflation Factor). Source: Autor’s Calculations following Miles (2014).

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