Autoregressive distributed lag (ARDL) approach to study the impact of climate change and other factors on rice production in South Korea

This study aims to explore the impact of climate change, technology, and agricultural policy on rice production in South Korea. In the presence of a long-run relationship among variables, the results show that an increase in CO 2 emissions increases rice production by 0.15%. The mean temperature raises rice production by 1.16%. The rainfall has an adverse impact on rice production which shows improper irrigation systems and weather forecasting reports. Similarly, for technical factors, the area under rice and fertilizer used in the study has a direct effect on rice production. The study suggests that the Korean government needs to implement new policies and acquire advanced technology for weather forecasting. The concerned authorities need to inform rice growers about future weather and climate changes. We recommend that Korea needs to provide virgin arable undivided land to deserving rice growers based on ownership and/or lease for future food security. Finally, the study recommends that legislators should recommend policies for sustainable food security with the introduction of new agricultural technologies and subsidies, along with the provision of new varieties of seeds that can absorb the adverse shock of climate change and ensure a suitable amount of food.

1.9%, and the contribution of rice in agriculture to GDP was 13.1% (KOSTAT ). The most grown crops in Korea are rice, barley, millet, corn, sorghum, buckwheat, etc. The production of rice in Korea decreased by 2.6% from the last year's production reported by KOSTAT (). Korea mostly depends on imports of agricultural products but these can be affected by various factors (Nasrullah et al. ). The most important Korean crop is rice, and is 90% of the country's total grain. Korean farmers cannot be competitive rice producers in the international market, but produce enough rice to fulfill domestic demand. The Korean agricultural policy in 1990 hugely disturbed farming communities due to removal of subsidies from agricultural inputs (fertilizer, pesticides, farm equipment, machinery, etc.). This policy not only caused a declines in agricultural production but also increased the demand for international agri-products (OECD ). Researchers are trying to find the uncertainties in parameter values because of a lack of understanding during model projection, which misleads the required predicted results (Lobell & Burke ). For field experiments, enough time and funds are required to get more sample results (Guo  )) because of its difference in the ability to identify long-/short-run relationships among variables compared to the previous approach. The ARDL is applied respectively to find the integrations of variables, which is also a good fit for small sample data. Therefore, this study was organized to find the short-and long-run impact of climatic factors, technical factors, and agricultural policy (1990) on rice production of Korea by using the ARDL model. Based on the results, the study will also provide some possible suggestions.

Data collection
The study uses important factors that are responsible for affecting rice production in South Korea (Republic of Korea). Previous studies of Yang (), Zhou (), and Guo () stated that natural factors and agricultural technology significantly affect agricultural production. Hence, the study jointly uses agricultural technology (e.g., area and fertilizer) and natural factors (e.g., carbon dioxide (CO 2 ) emission, mean temperature, and rainfall) along with an additional variable of agricultural policy as an explanatory variable and rice production is used as an explained variable. The annual data covering the period from 1973 to 2018 for rice production, CO 2 , mean temperature, rainfall, area under rice, and fertilizers were gathered from the Korean Statistical Information System (KOSIS ), as shown in Table 1. The study highlights the 1990 agricultural policy of Korea in the model which hugely affects domestic rice production. The data are converted into log form before applying the ARDL bound test.

Methodology
The study applied a well-known approach by Pesaran et al.
() called the autoregressive distributed lag (ARDL) approach. The ARDL model is considered as the best econometric method compared to others in a case when the variables are stationary at I(0) or integrated of order I(1). Based on the study objectives, it is a better model than others to catch the short-run and long-run impact of independent variables on rice production.
The ARDL approach is appropriate for generating shortrun and long-run elasticities for a small sample size at the same time and follow the ordinary least square (OLS) approach for cointegration between variables (Duasa ).
ARDL affords flexibility about the order of integration of the variables. ARDL is suitable for the independent variable in the model which is I(0), I(1), or mutually cointegrated (Frimpong & Oteng ), but it fails in the presence I(2) in any variables. To find the relation between dependent and independent, the following model was constructed as: By converting all variables of Equation (1) into the natural log, the model is designed below: where RPro represents rice production, while t represents the time period from 1973 to 2018. α 0 represents the constant while α 1 to α 6 are the coefficients of variables and CO 2 , MT, MRF, Area, Fert and D are the CO 2 emission, mean temperature, mean rainfall, area under rice, fertilizer use, and the dummy (dummy ¼ 0 before 1990, above 1990 ¼ 1) used for agricultural policy, while ∈ t represents the error term. Equation (2) can be written in ARDL form as follows: where α 0 represents drift component while Δ shows the first difference, ϵ t shows the white noise. The study uses the Akaike information criterion (AIC) for choosing the lag length. After finding the long-run association existing between variables, the study uses the error correction model (ECM) to find the short-run dynamics. The ECM general form of Equation (3) is formulated below in Equation (4): where Δ represents the first difference while ∅ is the coefficients of ECM for short-run dynamics. ECM shows the speed of adjustment in long-run equilibrium after a shock in the short run.

Descriptive statistics
The empirical study uses the time series data to find the effects of climate variation, technology variation, and agricultural policy on rice production in South Korea. The descriptive statistics of the important variables stated in Table 2 specified that the Jarque-Bera test for entire variables used in the study is insignificant, which implies that all the selected variables are normally distributed. The trend in rice production shows that the rice production was high in 1988 but after 1990 it shows a continuous reduction untill 2018, as shown in Figure Table 2.
The trend line in Figure 2 shows that the CO 2 emission continuously increases at a rate of 0.05% each year. Similarly, the mean temperature observed during the study period Note: The results are taken before using Logarithm. RPro, CO 2 , MT, MRF, Area, Fert, D represent rice production, CO 2 emission, mean temperature, mean rainfall, area under rice, fertilizer used for rice, and agricultural policy in 1990.

Unit root test
It is important to check the unit root of each variable before applying the ARDL bound test. For finding the bound     and Phillips-Perron (PP) unit root test as used by the previous study of Rizwanullah et al. (). The result of ADF and PP reflects that there is no unit root in the series. Table 3 shows that rice production, CO 2 emission, mean temperature, and mean rainfall is stationary at order I(0), while the area under rice, fertilizer used, and agricultural policy is stationary at order I(1).  Table 4.

Lag selection criteria
Before applying the ARDL bound test for checking cointegration exists or not among rice production, carbon dioxide emission, mean temperature, rainfall, area under rice, fertilizer used, and agricultural policy, it is important to select an appropriate lag order of the variable. The study employed the optimal lag order of the vector autoregression (VAR) model for the selection of appropriate lag order. The observed results in Table 5 show the entire lag selection criteria for employing the ARDL bound test which implies that the model gives better results at lag 1 as compared to lag 2 and 3.
Additionally, the polynomial graph is also used for the confirmation of appropriate lag length under the VAR method, as shown in Figure 7. The graph shows that the dots inside the circle confirm the validation of good results at lag 1.   Table 7, provide the evidence of robustness and effective long-run association among the variables.

Short-and long-run estimation of parameters
After verifying the existence of a long-and short-run association between variables from the ARDL bound test, the study finds the short-and long-run parameters of the variables. Rice is a major staple food crop in South Korea     the mean rainfall has a substantial negative long-run association with rice at a 5% significant level. This outcome implies that a rise of 1% in mean temperature can increase rice production by 1.16% while an increase in 1% of rainfall In the short run, the coefficient of climatic factors such as CO 2 , mean temperature, and rainfall significantly influence rice productivity. The results shown in Table 9 indicate that in the short run an increase of 1% carbon dioxide emission and mean temperature in the Republic of Korea can increase rice production by 0.15% and 1.11%.
The study also finds that a 0.12% reduction in rice production occurs due to an increase of 1% in rainfall in the  ARDL (1, 0, 0, 0, 0, 1) based Akaike information criteria.
short run. In technical factors, rice cultivated area is significant at a 1% level which shows that in the short run the rice productivity increases by 0.69% with a 1% increase in a cultivated area. The study also finds that fertilizer used in the short run has no impact on rice production. This result is opposite to a previous study by Saddozai et Table 9.

Diagnostic tests
Numerous diagnostic tests are used to find the errors in the model and are shown in Table 10.   and mean temperature. It is concluded that elevated atmospheric CO 2 in the respondent area during the study period increases rice production. The increase in CO 2 emission in Korea increases the photosynthesis process, which is    highly valuable for the production of rice. Likewise, the climatic factor, mean temperature also increases rice production. It is concluded that the mean temperature has a valuable effect on the vegetation and production process.
On the other hand, the climatic factor rainfall is not stable during the study period, and has an adverse shock on the production. The technical factors (area under rice and fertilizer) have a direct positive effect on rice production, which implies that an increase in area and fertilizer can boost rice production. The agricultural policy against subsidies on agricultural inputs is also responsible for the reduction in rice production. Similarly, the various stability and diagnostic tests verify that the model is a good fit, functional form is correct, the model is normal, and there are no problems of heteroscedasticity and serial correlation in the model.
The trend line in Figure 1 shows a significant decline in rice production after the withdrawal of agricultural subsidies. Similarly, the trend line of fertilizer used also shows a continuous decline. Therefore, to avoid food shortage in the near future the government needs to avoid this kind of policy which discourages the farmers. The estimated elasticity of rainfall significantly decreases rice production; therefore, it is suggested that the Korean government needs to implement new policies and acquire advanced technology for weather forecasting. The government also needs to reinforce and develop a better irrigation system.
The concerned authority needs to inform rice growers about future weather and climate changes. The study also specifies that the area under rice has a significant effect on rice production, but the trend line shows that the agricultural area continuously decreases. Therefore, it is recommended that the Korean government needs to provide virgin arable undivided land to deserving rice growers based on ownership/lease for future food security. In short, the study specifies that the concerned authorities and policymakers should spot the aggressive effect of climate change on the main food crops. Therefore, the legislators should recommend some strong policies regarding sustainable food security by introducing new agricultural technologies, subsidies on agricultural inputs, and a new variety of seeds that absorb the adverse shock of climate and ensure a suitable amount of food for the massive population of Korea.
The study also suggests that further research is needed to discover the impact of climate change and other factors that are responsible for the decrease in agricultural production in Korea and worldwide.

Scope and limitation of the study
The study provides evidence to the research community of how much climate change and other factors are responsible for the decrease in rice production in South Korea. This study provides a significant pathway to understanding the climatic changes and their various impacts on rice production. This study begins and helps to develop a strong understanding of current and potential impacts that will affect the agriculture of today and in coming decades worldwide. This understanding is crucial because it allows decision-makers to place climate change in the context of other large challenges facing the nation and the world.
The study is limited to finding out the impact climatic factors (CO 2 , mean temperature, and rainfall), technical factors (area under rice and fertilizer used for rice), and agricultural policy (anti-subsidy policy for agricultural inputs in 1990) have on rice production from 1973 to 2018 in South Korea.