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Does Environmental Pollution hurt Agricultural Productive Efficiency? A New Evidence using ARDL and Wavelet Coherence Approaches


 Environmental change daunts the aptitude to ensure global food security. The greatest significant threat to world fronting is how to mitigate environmental pollution without sacrificing agricultural productivity. The sharp rise in carbon dioxide emissions and global warming is altering the agriculture productivity's patterns as its vulnerability can be sensed by farmers. The spillover impact of climatic changes predicted to be great but differs by area and crop. This research fulfills the unprecedented need of adopting robustness methods to quantify the impact of CO2 emissions, agriculture labor, land, feeds, and fertilizers on agriculture productivity over five decades-long data structured in time-series. The fully modified ordinary least square (FMOLS), dynamic ordinary least square (DOLS), wavelet transform coherence (WTC) method, and gradual shift causality, tools have been espoused to observe the dynamic linkage in the long-term and short-run. The ARDL bound test confirms long-term co-integrated relation among the indicators. Furthermore, there is evidence of positive association between agriculture productivity and regressors which is also supported by the wavelet coherence outcomes. The Gradual shift causality test present a uni-directional causal link from all determinants to agriculture productivity which illustrates that all the regressors can significantly predict agriculture productivity. So, policies need to be formulated to explore a practical expansion approach with efficient use of fertilizers and feeds at an optimum level, in addition to environmental protection by encouraging public and private investment in agricultural research.


Introduction
The current generation is facing enormous challenges by climate change that has very adverse socioeconomics and environmental impact. The whole world is witnessing unprecedented heat waves, cruel droughts, an increase in air pollution and CO2 emissions. The relentless surge in greenhouse gases like fluorinated gases, methane (CH4), nitrous oxide (N2O), and carbon dioxide (CO2) are affecting the pattern of rain and temperature and negatively influencing land resources and water (Alexandratos, Nikos ;Bruinsma, 2012;Ali et al., 2017;Kurukulasuriya et al., 2006;Mendelsohn, 2014). All poses of these dangers are a severe threat to food security. No country has strong enough to counter these challenges in a quicker way. However, more widen impacts are touched in developing countries due to high vulnerabilities and incapacity to mitigate the threats (Parker et al., 2019). Currently, an immense challenge comes from the loss of natural environments to make room for farming. Rainfall trends around the countries have started to alter, and these shifts are expected to escalate over the next years. It means more prolonged cycles, often within the same areas, with heavy rain and more extended dry periods.
Similarly, scientific evaluation about the air quality, including pollution forecasts and future greenhouse gas sequestration, is an imperative new environmental science field that presents foremost challenges to regulatory authorities. It is becoming notoriously hard to normalize CO2 emissions of gases and specific substances from agriculture as this segment concerns the most fundamental human needs, i.e., foods. The current proposal blends preliminary research with social and political overlays, spanning a vast spectrum of practices in a dynamic sector.
Pakistan being an agriculture-based economy is affected the most because of straight contact with nature, ranked 8 th in the world's primarily vulnerable country through climate change with the substantial difference in rainfall due to 2-3° expected rise of temperature by 2050 (Ahmad and Afzal, 2020). For instance, tropospheric ozone (O3) is particularly harmful to crop yields among different air pollutants. Ozone-induced crop fatalities, supposed to cost around US$ 11.18 billion in the year 2000 (Ainsworth et al., 2012). Temperature change with negative intensity to be unfavorable for various crops (Proskurowski et al., 2008). These uncertain events prompt us with a critical resilience thought message that unpredictable climate changes cause a rapid impact on agriculture productivity. Changes in crop management can alleviate climate change's negative influence, primarily due to temperature increases on crop phenology. But the introduction of new cultivars and a longer growth cycle could significantly affect yield phenology and potentially increase under a warming trend (Abbas et al., 2017).
Experts have given more alternative methods to ease the procedures to obtain technological advancement and foreign direct investment . It is hard for mainly developing nations to adopt unconventional methods with financial and high-tech constraints. However, emerging countries are the ones that have a high economic dependency on agriculture production, such as Pakistan, India, and Bangladesh in South Asia. Although Pakistan is still selfsufficient presently in major staplesranked 8 th in wheat production, 5 th in sugarcane, 10 th in rice, and 4 th in milk (UNICEF, 2018). In contrast, moving towards urbanization is a vast threat to a rise in population, an enormous number of cutting trees, and overcrowded places that negatively impact Pakistan's ecosystem. All these led to rising floods, soil erosion, air pollution, and greenhouse gases in the environment (Kousar and Shabbir, 2021).
The possible impacts are less pronounced; however, food and hunger insecurity in different areas are caused by climate change (Wheeler and Braun, 2013). Previous studies have established that this sector permits the development of various non-agriculture industries and may have a hostile effect on crop yields with climate change (Lobell et al., 2015). The link between environmental change and agricultural productivity is a meaningful area for researchers to assess for developing countries (Anjum, Zada, and Tareen, 2016). Though the requirement to determine this topic is exceptional as in the worst case, if the agricultural productivity does not equal the food demand, it might lead to costly buying and raise the rate of poverty and hunger worldwide (Ahmad et al., 2016;Godfray et al., 2010;Foley et al., 2013;Lashkari et al., 2012). Therefore, this research examines the impact of CO2 emissions, agriculture labor, land, feeds, and fertilizers on Pakistan's agriculture productivity using data from 1961 to 2016. The robustness of methods portrays the high efficiency of results while examining the lag phase and coherence between time series function of frequency and time. The current study is different from the prior research by employing the novel wavelet coherence test. Some essential properties of the wavelet transform coherence: like capable of analyzing signals with functionality that differ over time, offers illustration on a diverse scale, and conveniently obtainable via filter bank. The literaturebased knowledge indicates that not a single researcher had applied the wavelet coherence approach to analyze environmental data to enumerate agriculture productivity. The advantage of the wavelet coherence tests is that it can capture both correlation and causal linkage between series at different frequencies and time periods. Thus, the present study fills the gap in the ongoing literature. The practice of finding an intense relationship between climate change, CO2 emission, and productivity in agriculture development presents new evidence both in tabular and visual forms.
Besides the introductory part, the below portion of this research consists and organized as follows: a review of relevant studies section provides the particular literature and systematic review in tabular form. Data & methods section contains a new approach series of methodology while finding & discussion parts present the outcomes in detail.
Finally, the conclusion & policy implications fall in the last section.

Review of Relevant Studies
In terms of labor contribution, agriculture remains Pakistan's most important sector of the economy, and as such, the mainstream of the population relies directly or indirectly on it. The main crops like rice, wheat, maize, cotton, and sugarcane account for 21.73% in the agriculture sector and contributing 4.20% in GDP, while 11.53% accounts for other crops with a 2.23% share in GDP (Pakistan, 2020). Stages of crops guided by the prevailing weather conditions and reflected in the accumulation of rising degree days influence the field management methods, including selecting crops and improvements in sowing dates (Ahmad et al., 2017;Wajiha and Qadir, 2016).
Higher temperatures in the growing season may have a major effect on agricultural production and food security (DS and RL., 2009). Pakistan's climate is ideal for cultivating different crops, such as cotton, wheat, rice, corn, and sugar cane. Above all, the wheat crop is the primary due to high domestic demand and consumption (Dharmasiri, 2012).
The synergies between environmental concerns and agriculture productivity are highlighted by various authors (Aragón et al., 2019;Di Gregorio et al., 2017;Liang et al., 2017;Ukhurebor et al., 2021). The impact of business activities involves industrial production that pollutes the air, water, and various crops. The examination of the impact of air pollution of industries on farming crops includes recognizing the roles of the dose-response between the accumulation of contaminants and the loss of agriculture. Multiple studies have quantified the dose-response, and some applied the method of field experiments.
Consequently, some authors stated the relationship between total factor productivity of agriculture and air pollution (Zhou et al., 2018). Air pollution diminishes labor productivity from the economic side, leading to disrupting some certain degree of productivity of yield's physiological and biochemical, instigating the nutrient attention in acid rain and soil degradation (Heck et al., 1988;Zivin and Neidell, 2018). Parker (2015) claimed that financial considerations are beneficial in mitigating national environmental issues. Rafindadi (2014) evaluated the relations in Asia-Pacific countries between CO2 pollution, water supplies, and natural resources and concluded; those variables influence the country-wide environmental sustainability plan. Another author used the ARDL bounds test to determine the climate change impact on food crops from 1968 to 2014. The finding revealed CO2 emission and land area negatively effecting cereal yield while average rainfall, energy consumption, and labor force have a positive impact on Turkey's production . Schmidhuber (2007) proposed that climate change would directly affect economic growth, food supply, and prices after finding a strong relationship between CO2 emission and crop yield. Likewise, several studies have been carried out on climate change and agriculture productivity for developing nations, particularly in agriculture-based economy, from the exhaustive evaluation on the implementation of econometrics in agriculture and environmental economics (Fan and Carroll, 2012;Ozturk, 2015;Rehman et al., 2019). For the audience's ease, an indepth systematic review of additional literature has comprised in tabular form as follows.  Janjua et al., 2014). As with the world's growing population, it is vital to accelerate agricultural production to match the essentials nutrition to feed the world (Weeks, 2015). However, many climatic and environmental issues, including air pollution, rapid climate change, and ecological degradation, affect agricultural productivity. It is indispensable to identify the in-depth dynamics relationship of these factors with agricultural productivity to provide food security and meet Pakistan's future food demand. To the best of comprehension, earlier studies have provided only simple relational evidence among certain factors and used numeric techniques to capture relations differently with frequencies and periods such as simple regression, ARDL, FMOL, and more. However, there has been no sign from existing literature demonstrating a dynamic linkage between climate change, CO2 emissions, and agricultural productivity using the wavelet coherence technique. The wavelet method of analysis gives an in-depth association of determinants within the timescale and frequency bands (Pla et al., 2020). The wavelet efficiency becomes an upsurge when it comes to interacting lead-lag relationship on time series used in non-linear; it simultaneously allows to measure the dynamic linkages and causality (Adebayo and Akinsola, 2020). Thus, the wavelet coherence technique takes into account break-in time series, and it could otherwise disrupt measurement parameters without considering it (Kirikkaleli and Gokmenoglu, 2020).

The conceptual underpinnings
This portion emphasizes the connotation and the climatic impact on agriculture productivity. According to think-tank German watch on global climate index report, Pakistan ranked 5 th most vulnerable globally, vanished 9989 lives, $3.8 billion economic suffering, and perceived 152 extreme weather events between 1999 to 2018 (Eckstein et al., 2020).
However, these large scale effects have been remained and continue under great debate.

Data and Assessment Scheme
This article uses a time series yearly data of TFP and CO2 emission, Agri-Land, Agri-Labor, Fertilizers, and Feeds spanning from 1961 to 2016 of Pakistan. The TFP is the dependent variable in the model, and the independent variables are CO2 emission, Agri-Land, Agri-Labor, Fertilizers, and Feeds. The natural logarithm of the series has been taken to ensure the normality conforms. Table 2 depicts the source, unit, and description of the determinants. The study analysis flow is depicted in Figure 1. The economic function and econometric model are highlights in equations 1 and 2 as follows; [1] In Equation 2, TFP denotes total factor productivity of agriculture that reflects agricultural efficiency; ALB, ALD, FD, FT, and CO2 signifies agricultural labor, land, feed, fertilizer, and carbon dioxide emissions, respectively.

Unit root tests
It is imperative to investigate series stationarity features before conducting further analysis. Thus the present research utilized conventional unit root tests (ADF and PP). The sensitivity to serial correlation in error terms and heteroscedasticity is the main distinction between ADF and PP tests. The Equations of ADF and PP explain as below; ADF test: Whereby depicts the deterministic term vector while the error term is represented by .

ARDL Approach
Auto-Regressive Distribution Lag Model (ARDL) developed by Pesaran and Shin (1998) and Pesaran et. al (2001) was used to capture the long-run co-integration association between the dependent and independent variables.
Benefits of the ARDL bounds test over the other conventional or traditional co-integration techniques areas: (i) it can be used when there is a mixed order of integration; (ii) it incorporates both the short and long-run coefficients simultaneously; (iii) it is perfectly fit for small sample size; (iv) accommodating different lag length; (v) autocorrelation problem is removed. The calculated F-statistics are being compared to the lower and upper bound critical values. When the calculated F-statistics is below, the null hypothesis is not rejected; when the calculated F-statistics is greater, the null hypothesis is rejected, which shows evidence of a long-run relationship among the variable. Equation (7) below explains the ARDL bounds model; The null hypothesis and the alternative hypotheses are no co-integration and evidence of co-integration, respectively. We fail to accept the null hypothesis if the F-statistics is more than the lower and upper bond critical values. The alternative and null hypothesis are illustrated by Equations 8 and 9 correspondingly; Where 0 denotes the null hypothesis and illustrates the alternative hypothesis.
After the long-run relationship is established, the ARDL model derives the error correction model (ECM Where: i=5 denote coefficients in the short run, εt represents the error term, βi=5 mean coefficients, in the long run, t denotes the lags lengths, ECTt-i denotes error correction term. It is showing the speed of adjustment from a shortrun shock to the long-run equilibrium. represents ECM coefficients, which will be negative and significant.

Wavelet Approach
The wavelet approach is utilized in the current research to gather information about the time-frequency dependency between TFP and CO2 emission, agri-land, agri-labor, fertilizers, and feeds in Pakistan using yearly data spanning from 1961 to 2016. Goupillaud et al. (1984) initiated the Morlet family. It is accepted that when time series variables are estimated and not stationary, the result will yield bias estimates if the conventional time-domain method is not employed. Additionally, in economics and finance, time-series data are prone to break (s); hence the traditional test of causality outcomes with parameters fixed are susceptible to surface (Adebayo and Odugbesan, 2020). Contrary to time-domain causality, the standalone frequency domain method major concern, also known as Fourier transform.
Therefore, to abolish these issues in the estimations, the wavelet coherence technique is utilized in this research. Morlet wavelet equation is presented below; where:, is utilised on time series frequency that is limited; p( ), = 0,1, 2, 3……N-1; i is √−1. The time series is transmuted into the time-frequency domain and transmits to the change of wavelets. Is converted and developing into , . This formula can be seen below: Where: k describes the time and place of whereas f denotes the frequency. Odugbesan and Adebayo (2020) stated that k and f are the main parameters in the wavelet approach. The CWT Equation is depicted as follows: The revitalization of the time series variable p(t) is depicted by the next equation and the coefficient .
The 2 ( , ) reveals the intensity of the interaction without including the nature of this connection being recommended. Torrence and Compo (1998) initiated a suggestion of associated direction by wavering the two-time series by signifying deferrals. Equation 8 depicts the Phase difference: Where, O is the real component operator, while L is the imaginary operator.

Gradual Shift Causality
Toda and Yamamoto (1995) established a framework, which is anchored on vector autoregressive (VAR) built by Sims (1980). In calculating the optimal lag length, p + dmax is added to the lag of dmax, which is ascertained by the series maximum order of integration in the VAR framework. However, ignoring the structural shifts can cause the VAR model to be unreliable and contradictory (Enders and Jones, 2016;Figueiredo et al., 2012). To examine the causal linkage between TPF and CO2 emission, agri-land, agri-labor, agri-machinery, fertilizers, and feeds, Nazlioglu (2016) developed the Gradual shift causality test, which captures the structural shifts in Granger causality analysis and including the gradual and smooth shift. It can also be called the "gradual-shift causality test." The Fourier Granger causality test was developed using single-frequency (SF) and cumulative frequencies (CF), respectively, known as Fourier approximation. The modified Wald test statistic (MWALT) is generated by adding the TY-VAR analysis and Fourier approximation. Table 3 provides an introductory summary of all the variables used in this study. In the context of skewness and kurtosis tests, all the listed variables are approving to normal distributed, which confirms the normality assumption of the classical regression model. The probability value of the Jarque-Bera test is the standard test to measure. It reveals that all included variables are normally distributed, excluding total factor productivity of agriculture. In the first step, we grasp integrating the time series variables for this study. For this purpose, two traditional stationarity tests, such as ADF (Elliott et al., 1996) and PP (Phillips and Perron, 1988) have been utilized. The results of these unit root tests imitate in Table 4. The ADF test results show no static variable at the level, and only one variable is named total factor of agricultural productivity stationary at the first difference, i.e., I (I). Likewise, the PP test reveals that only agricultural land is stationary at the level, and CO2 is found to be stationary at the first difference,

Findings and Discussions
i.e., I (I).
Further, we examined the ZA unit root test by considering the structural break of time to prevent us from the misleading results of traditional unit root tests. The findings of the ZA unit root test listed in Table 5. The findings expose that only agricultural land stationary at level, i.e., I (0). However, all the named variables have proved to be stationary after taking the first difference, i.e., I (I). In the context of the unit root test, the literature has reported that when we found a mixture of variables' integration, it is crucial to test long-term and short-run associations using the ARDL approach (Rehman et al., 2019). Note: Significance level of 1% , 5% and 10% is depicted by *,** and *** Note: Significance level of 1%, 5%, and 10% are depicted by * and ** Table 6 lists the ARDL bounds test findings to co-integration at the 10%, 5%, and 1% significance levels. This model is used to measure the long-run equilibrium and the linkage between incorporated variables. The ARDL Bounds Test F-statistics has a value of 6.11 that reveals the long-run co-integration association between total agricultural factor productivity, CO2 emissions, farmland and labor, fertilizer, and feed at the significance level of 1%. The ARDL test obtains a long-term and short-run relationship between the variables, following the bounds test results to cointegration, which confirms linkage and co-integration among all selected variables. In addition, we performed several post-diagnostic tests, and the results are list in Table 6. The finding unveils our proposed model's smartness to tackle heteroscedasticity problems, misspecification, and residuals normality. So, the P-values of all these tests reflect 0.11, 0.11, 0.50, and 0.68, respectively. Sorely, there is also evidence of the structural break in Pakistan's agricultural productivity determinants during the research period. However, the post estimation graphs demonstrate the stability of the long-term coefficient with short-term movement in both equations using the cumulative sum (CUSUM) and the cumulative sum of square (CUSUMSQ) diagram, which is shown in Figures 2 and 3, respectively. Both figures reflect that the long-term coefficient framework is stable at the 5% level of significance.   4 1975 1980 1985 1990 1995 2000 2005 2010 2015 CUSUM of Squares 5% Significance After verifying the co-integration among agricultural productivity and its determinants, we discover short-and longterm dynamic linkage of these variables using the ARDL approach and illustrate the results in Table 7. The long-term ARDL estimates show that feeds positively and significantly connect with agricultural productivity, as the estimated coefficient value and its probability are 0.2132 and 0.005, respectively. In other words, a 1% increase in feed leads to an upturn in the agricultural productivity of Pakistan by 0.21%. Similarly, fertilizers' findings also positively impact agricultural productivity at the 5% significance level. These outcomes confirm that a 1% increase in fertilizer would augment agricultural productivity by 0.07%, exposing the maximum use of feed and fertilizer to increase Pakistan's agricultural production. As expected, rapid population growth will double the global demand for livestock and other agricultural products by 2050.
Meanwhile, the increasing use of fertilizers in crops and livestock feeds to meet growing demand is a significant reason for increased greenhouse gas (GHG) emissions. Only livestock has contributed 14.5% to global GHG emissions (Rojas-Downing et al., 2017). The drastic climate change is a significant threat to agricultural production, and mitigating this impact on agriculture has become a crucial challenge to save food for the coming generation. In this context, our feed and fertilizer coefficient values show better results for agricultural production in Pakistan; on the other hand, it would be alarming for environmental pollution. We need to develop serious policies to monitor and address feed and fertilizer use and limit it to acceptable food security levels and save the world from global warming.
However, many scholars have researched to solve this problem and bring the real picture before the economies' policymakers (Appiah et al., 2018;Edoja et al., 2016). Experts believe that sustainable crop production is the only way to save the world from pollution and food security for the present and future generations.
Moreover, sustainable agricultural production can be achieved by discouraging weak farming practices that affect the environment (Asumadu-Sarkodie and Owusu, 2017;Manandhar et al., 2018). The estimated cost of agricultural labor and land is 0.130 and 0.3227, respectively, indicating a positive and significant linkage of these two vital factors with long-term agricultural productivity. Furthermore, these results mean that a 1% increase in farm labor and land results in a 0.13% and 0.32% increase in Pakistan's agricultural productivity. Interestingly, agricultural land's productive effect is larger than the agricultural labor, feed, and fertilizer used in agricultural activities, suitable for sustainable agriculture. Likewise, CO2 estimated value is 0.1711, which reveals the positive and significant effect of environmental pollution on agricultural productivity. If we assume a 1% increase in Pakistan's CO2 emissions, it increased agricultural productivity by 0.17%. This finding is in line with the results of (Manzoor Ahmad et al., 2021;Munir Ahmad et al., 2021;Khattak et al., 2020;Rehman et al., 2020). Furthermore, the term error correction term (ECT)'s negative coefficient value indicates the validity of short-term linkages between variables. As presented in Table 7, there is also a short-run linkage of agricultural productivity with agricultural feeds, fertilizers, labor, and land.
Overall, the ARDL approach results show a long-term and short-run relationship between all variables of the study. Note: 1%, 5% and 10% level of significance is depicted by *, **, and *** respectively We further employed FMOLS and DOLS to measure the robustness of the outcome of long-term estimates of the ARDL approach. The results of these two tests clarify in table 8. As per the results, there is a positive and significant long-term relationship between agricultural productivity determinants, including feed, fertilizers, agricultural labor, and carbon emissions. However, agricultural land exerts a positive but insignificant effect on agricultural efficiency in Pakistan. Note: *, ** and *** depicts 1%, 5% and 10% respectively The current research utilizes the wavelet transform coherence (WTC) approach to catching the causality and correlation between TPF and the regressors. This method is crafted from the domain of physics to obtain formerly undetected information. Therefore, the research investigates the connection in the short, medium, and long-run between TPF and its regressors. The cone of influence (COI) is the white where discussion is carried out in the WTC.    Table 9, reveal a uni-directional causality from agricultural labor to agricultural productivity at the 10% significance level. Similarly, this test has found a one-way causality from factor productivity to agricultural land, from CO2 to agricultural productivity, and from fertilizers to productivity. This further means that labor, CO2, and fertilizers cause the agricultural productivity in Pakistan, while the factor productivity only causes Note: Significance level of 1% , 5% and 10% is depicted by * , ** and *** agricultural land. Besides, the findings of this causality test also support the graphical measures of the wavelet technique.

Conclusion and Policy Implications
This study mainly explores the real picture of the linkages between agricultural productivity and its determinants such as CO2 emissions, agricultural lands, labor, feeds and fertilizers using the recent time-series data spanning from 1961 to 2016. In the first phase, the study examined the order of integration utilizing the ADF, PP, and ZA unit root tests and founds a mixture of level I (0) and the first difference I (I) data stationery. Since then, the ARDL bounds test has been employed, discovering the Cointegration relationship between the study variables at a 5% significance level.
Meanwhile, the subsequent approach is ARDL with the error correction term, which we applied to capture the longterm and short-term linkages among agricultural productivity and the regressors. These findings exposed that the CO2 emissions, agricultural land, labor, feed, and fertilizers have a positive and significant long-run impact on Pakistan's agricultural efficiency. Likewise, each regressors has a positive and considerable influence on productivity, excluding labor, as it has a positive but insignificant association with the outcome variable. Our findings' robustness has been verified utilizing the FMOLS and DOLS approach, which indicates our results almost robust and stable. The wavelet coherence technique has been employed as it has the advantage of capturing correlation and causality simultaneously at different levels of frequencies and periods. Subsequently, we applied the Toda-Yamamoto causality techniques to measure the long-term causality between agricultural productivity and all explanatory variables. This gradual shift causality test has the benefit of detecting causal linkage among factors even in the presence of structural breaks in series. In the context of the gradual shift causality test results, agricultural labor, CO2 emissions, and fertilizers have a one-way relationship with agricultural productivity. In contrast, productivity has a uni-directional causal link with agricultural land.
Overall, this study has contributed to the current literature by proving that the determinants included have been validated because they have explained 99% agricultural productivity changes. It is proven that CO2 emissions, land, labor, fertilizer, and feed have a positive and significant impact on agricultural performance in the long and short term.
We make the following policy recommendations based on the experimental results of the study: (a) Considerably, Pakistan's most agriculture is semi-arid; in fact, it is vulnerable to climate change shocks. It needs the hours to strengthen Pakistan's agricultural sector to resilience against extreme weather such as heat, drought, cold, and floods to meet sustainable yield in agriculture, as it is observed that the summer season has been intensifying for the past decade. Furthermore, substantial investments and policies are needed to protect and strengthen production against pests and diseases. It has also increased, and farmers use more and more pesticides and bio-control. As a result, the environment deteriorated. Therefore, this is possible only when we encourage public, private investment, and public