Climate change and its impact on rice acreage in high-latitude regions of China: an estimation by machine learning

Abstract

Purpose

Fewer researchers have investigated the climatic and economic drivers of land-use change simultaneously and the interplay between drivers. This paper aims to investigate the nonlinear and interaction effects of price and climate variables on the rice acreage in high-latitude regions of China.

Design/methodology/approach

This study applies a multivariate adaptive regression spline to characterize the effects of price and climate expectations on rice acreage in high-latitude regions of China from 1992 to 2017. Then, yield expectation is added into the model to investigate the mechanism of climate effects on rice area allocation.

Findings

The results of importance assessment suggest that rice price, climate and total agricultural area play an important role in rice area allocation, and the importance of temperature is always higher than that of precipitation, especially for minimum temperature. Based on the estimated hinge functions and coefficients, it is found that total agricultural area has strong nonlinear and interaction effects with climate and price as forms of third-order interaction. However, the order of interaction terms reduces to second order after absorbing the expected yield. Additionally, the marginal effects of driven factors are calculated at different quantiles. The total area shows a positive and increasing marginal effect with the increase of total area. But the positive impact of price on the rice area can only be observed when price reached 50% or higher quantiles. Climate variables also show strong nonlinear marginal effects, and most climatic effects would disappear or be weakened once absorbing the expected rice yield. Expected yield is an efficient mechanism to explain the correlation between crop area and climate variables, but the impact of minimum temperature cannot be completely modeled by the yield expectation.

Originality/value

To the best of the authors’ knowledge, this is the first study to examine the nonlinear response of land-use change to climate and economic in high-latitude regions of China using the machine learning method.

Citation

Yu, Y., Tian, Q. and Yan, F. (2022), "Climate change and its impact on rice acreage in high-latitude regions of China: an estimation by machine learning", International Journal of Climate Change Strategies and Management, Vol. 14 No. 4, pp. 313-331. https://doi.org/10.1108/IJCCSM-11-2020-0124

1. Introduction

There is a growing concern about the impact of climate change on sustainable agriculture production, especially in developing countries with high-density populations. It is reported by the Intergovernmental Panel on Climate Change (2019) that globally averaged land surface air temperature has risen faster than the global mean surface temperature from the preindustrial period (1850–1900) to the present day (1999–2018). And there has been a lively discussion about the potential negative impact of climate change on crop production (Battisti and Naylor, 2009; Schlenker and Roberts, 2009). Prabnakorn et al. (2018) argued that the loss of rice production will become more serious in the future if increasing trends of temperatures persist.

Climate change could also induce changes in crop area allocation. Cohn et al. (2016) found that the area of cropland shows strong sensitivity to climate change. Moreover, adjusting cropping acreage allocation is considered as one of the most important adaptation strategies under climate change, as higher temperature and precipitation could also make crop production possible in previously uncultivated regions (Du et al., 2017). Yang et al. (2007) found that global warming has led to a significant increase in accumulated temperature and a decline of cold stress in high-latitude regions. These factors have contributed to improving crop growth conditions and caused the agroclimatic zone to move northward, especially for thermophilic crops. Liu et al. (2013) found that the centroid of rice production in China moved more than 200 km to the northeast in the past three decades. Thus, the high-latitude regions of China, where rice might benefit from climate change, have become the important rice production regions. It will be beneficial to understand how farmers could adapt to climate and develop climate-smart agriculture if the effects of climate change on farmers’ area allocation in these regions could be estimated.

Rice is the most important staple food in the world, and almost half of global people take rice as the main source of calorie intake (Maclean et al., 2002). Also, rice is vital for Chinese as more than 840 million people depend on it for 40% of total calorie intake and rice planting contributed nearly 36% of the grain production income (CHNS, 2015). China is the largest rice-producing country in the world that accounts for 22% of the world’s rice production in 2017 (FAOSTAT, 2017). And consumption and import of rice in China exceed those in any other country (FAOSTAT, 2017). It is not surprising that even small changes in China's rice production will have a significant impact on the domestic and global rice market. Therefore, it is essential to investigate climatic drivers that affect China’s rice production, whether it is for food security or farmers’ income.

The literature on estimating supply response function have a long history in agricultural economics. Much of the early literature focused attention on the price factors and price expectations in the specification of area response (Nerlove, 1956; Chavas et al., 1983; Clark and Klein, 1996). The explanation from Miao et al. (2016) is that an increase in the output price of the crop can be expected to increase the acreage devoted to the crop by creating incentives to switch land from other uses to this crop. However, the speed of switching crops induced by price was found to be usually slower in the short term because of partial adjustment costs (Nerlove, 1956; Chavas et al., 1983). On the set of price variables, Nerlove (1956) pointed out that farmers react to the price they expected, and some later studies tried to use different types of proxies for expected prices, such as lagged-year received prices and current-year future prices (Lin and Dismukes, 2007; Xu et al., 2019). Chavas et al. (1983) and Shideed and White (1989) found that the price elasticities estimated by lagged received price or future price in the analysis of crop area responses are similar. And Miao et al. (2016) also suggested that lagged received price and future price can be used interchangeably in describing farmers’ price expectations.

The association between climatic variation with cropping area was also gradually documented. Weersink et al. (2010) found that the climatic variables have significant impacts on crop area, because the expected yield that is related to the historical climate is essential to the decisions of crop area. Cui (2020) mentioned that climate change will change comparative advantage in agriculture and induce a land-use change between different crops. In addition to historical climate, Sacks et al. (2010) and Miao et al. (2016) found that crop choices and acreage planted are also constrained by the precipitation in the seeding season. Some other studies conducted a micro field study to investigate the farmers’ response to climate and found that farmers are concerned about the change of temperature when they made crop seeding choices (Seo and Mendelsohn, 2008; Tessema et al., 2019). In addition, geographers are also interested in the influence of historical climate changes on crop shifts. Liu et al. (2013) and Fan et al. (2018) focused on movements of the geographical centroids for different crops under climate change, which neglected to investigate the complex relationship between climate change and crop acreage.

Studies on the impacts of climate on agricultural production have adopted massive climatic variables and approaches. Mehdi et al. (2018) highlighted that the climatic drivers of land-use change need to be well identified, and the interplay of these factors should be considered. The most influential climate variables on a global scale are monthly average/minimum/maximum temperature and precipitation in the growing season (Cabas et al., 2010; Cui, 2020). Generally, temperature has a slightly larger impact on crop area than precipitation (Weersink et al., 2010). Some other studies used growing degree days to calculate the accumulated heat supply (McMaster and Wilhelm, 1997; Robertson et al., 2013). On empirical model, these studies mainly constructed panel data methods for area, price and climate variables, including seeming unrelated regression (Weersink et al., 2010), general moment method (Haile et al., 2016), spatial error model (Miao et al., 2016) and fixed effect model (Cui, 2020). A limitation is that these models cannot automatically recognize the influence patterns of climate variables, therefore the form of climatic variables is mainly constructed by researchers. And the simulation effect of the obtained nonlinear effect has limited smoothness and less flexibility in high dimensional settings.

Building upon previous studies regarding the impact of climate change on agricultural output, the purpose of this study is threefold. First, this study seeks to examine nonlinear and dynamic interaction associations between rice area, climate and economic variables in high-latitude regions by extending the classical area response model. And the expected rice price is also put into the model to simultaneously estimate farmer’s response to economic factors. Second, this study further induces the expected rice yield into the model to explore the mechanism of farmer’s expected climate conditions on area allocation decision, which is ignored by many studies. Third, a multivariate adaptive regression spline (MARS) algorithm is applied to automatically select important explanatory variables and model the higher-order polynomials in crop acreage response function by minimizing root mean squared error of generalized cross-validation (GCV).

2. Model specification and study area

2.1 Empirical model

2.1.1 Area response function.

The general form of area response function is to regress the crop acreage A_i,t against the climate and economic variables X_i,t in region i for year t:

(1) Ai,t=f(Xi,t,β)+ui,t

Coyle (1993) argued that the increase in crop output price will increase the seeded area of the crop by creating incentives to convert the land from other uses to this crop, and total area as land endowment is positively correlated with rice area. Irwin and Thraen (1994) and Weersink et al. (2010) further pointed out that the decision on planting area has to be based on expectations of farmers because of biological lag in agricultural production. Therefore, this study considers the expectations of price and climate to investigate the farmers’ area allocation decision. In addition, nonlinear effects were significantly found in the yield function, which is the key to area allocation decision of farmers. And Mehdi et al. (2018) suggested that the driving factors of land-use change are caused by the interplay of myriad factors. To capture complex relationship, a more refined regression model could be written as follows:

(2) Ai,t=β0+C(Totalareai,t)+C(Pricei,t*)+C(Precipi,t*)+C(Tempi,t*)+Z(Totalareai,t,Pricei,t*,Precipi,t*,Tempi,t*)+ui,t

where C(…) and Z (…) represent nonlinear relationship and interaction relationship, respectively. ∗ represents the farmers’ expectations, which can be modeled by historical data. A_i,t is the amount of land devoted to rice in region i for year t. Totalarea_i,t is the total land area used to plant the crop, and Pricei,t* is a vector of expected rice price. The price effect of competing cop is not absorbed, as profit of rice production is much higher than that of corn and soybean production (see Figure A1 in Appendix). Precipi,t* and Tempi,t* are the expectation of monthly total precipitation and the expectation of monthly temperature during rice growing season, respectively, where the rice growing season is defined as May 1 to September 30, as Chandrasekaran et al. (2010) suggested. u_i,t is an error term.

Temp variable includes monthly maximum and minimum temperature. As the main decision-makers for the crop area, farmers may not be able to feel the change in average temperature, but they have the impression of the maximum and minimum temperature (Makuvaro et al., 2018). And the yield literature have widely investigated that the maximum/minimum temperature could better capture yield variability than average temperature (Miao et al., 2016). Additionally, it is found that the change of average temperature comes from the maximum temperature or the minimum temperature when analyzing the trend of climate shown in Section 3.1. Next, because the yield can be predicted by historical precipitation and temperature (Miao et al., 2016; Lu et al., 2018), the yield expectation is added into equation (2) to investigate the potential mechanism of climate effects on rice area and rewrite it as:

(3) Ai,t=β0+C(Totalareai,t)+C(Pricei,t*)+C(Precipi,t*)+C(Tempi,t*)+C(Yieldi,t*)+Z(Totalareai,t,Pricei,t*,Precipi,t*,Tempi,t*,Yieldi,t*)+ui,t

where Yieldi,t* is the expectation of rice yield.

In equations (2) and (3), the expectations of price and rice yield are measured as one-year lagging received rice price and rice yield (Xu et al., 2019), respectively. And expectation for each climatic variable is a weighted average of the last three years. According to Weersink et al. (2010), the weight coefficients are set equal to 0.50, 0.33 and 0.17, respectively.

2.1.2 Multivariate adaptive regression splines.

Machine learning algorithms, such as MARS, random forests and support vector machine, have gradually been used in multidisciplinary research, which can achieve high prediction accuracy. But most of these methods have a disadvantage, that is, they assumed data mechanism as a “black box” (Rudin, 2019), which makes the learned relations hidden and the results obtained hard to interpret (Martens et al., 2007). This leads to researchers and policymakers not being able to clearly find out the relationship between climate factors and rice acreage. However, MARS can capture the complex relationships between multidimensional variables and generate a simple model (Zhang et al., 2019), especially when the focus is on exploring the complex relationship between climate and rice acreage.

MARS is a flexible method to capture nonlinearity and interaction relationships between a set of input variables and a target dependent variable (Friedman, 1991). It is an extension of linear models and is used in a multivariate setting with a nonparametric technique. And MARS technique makes no special assumptions about the underlying relationships on the basis functions which are similar to step functions connecting the explanatory and explained variables smoothly. The determinations of the form and the number of the basis functions are automatically completed by the data without manual selection. This can help us to obtain a more accurate complex relationship between variables. Area response function described in the last section by building a MARS is as follows:

(4) Ai,t=β0+∑n=1mCn(x)+∑n=1jZn(x)=β0+∑n=1kαnhn(x)

where C_n (…) and Z_n (…) represent nonlinear and interaction relationship functions, respectively, x is a matrix of input variables described in area response function section and α₁–α_k are estimated coefficients. h_n (…) takes the form of a hinge function or multiplication of two or more hinge functions. If two or more single hinge equations are generated for the same variable, it represents a nonlinear effect, and if there is multiplication of two or more hinge functions, interaction effects can be described. A hinge function is defined by Friedman (1991) as:

(5) hn(x)= (x−θ)+

where (x − θ)₊ is an indicator function equaling to (x − θ) if it is positive and zero otherwise. θ is a constant and called knot, which can express the change of relationship between independent and dependent variables.

MARS is implemented by a two-stage process involving the forward and the backward stepwise stage (Friedman, 1991; Hastie et al., 2001). In the forward stepwise stage, it uses the adaptive regression algorithm to automatically search the overall possible univariate candidate knot location to split input samples and each divided point is a knot. A new basis function is obtained by fitting a spline function to each divided interval. But the forward process will generate many basis functions, resulting in an overfitting model. So, the backward phase is the process of using GCV to remove the redundant basis functions generated in the forward process to establish an optimally estimated model.

In addition to determining the number of knots, MARS model also has a strong power to assess potential interactions between different hinge functions. It could perform a grid search using tenfold cross-validation to identify the optimal combination of the order of interactions and the number of terms by minimizing the prediction error. This is in line with the process of rice area allocation decision, as farmers usually comprehensively consider the climate, economic and total land constraints.

2.2 Study area and data

As reported above, the high-latitude crop regions of China (Heilongjiang and Jilin) are selected as research area based on the data availability and importance of field crops. The latitudes of two provinces are located at 43°26′–53°33′ and 40°50′–46°19′, respectively. Because of the lower temperature in high-latitude regions, single-season rice is mainly grown in Northeast China, and the growing season is from May to September (Chandrasekaran et al., 2010; Ding et al., 2020). The average monthly rainfall ranges from 51.3 to 150.4 mm and average monthly temperature ranges from 15.8°C to 23.5°C during the rice growing season. And over the past 26 years from 1992 to 2017, the annual average efficient accumulated temperature for rice (accumulative growing degree days within 10°C–35°C) in high-latitude provinces of China showed an obvious upward trend, from 1,078.53°C in 1992 to 1,273.76°C in 2017. During this period, rice gradually becomes the dominant crop. The total seeded rice area in Heilongjiang and Jilin in 1992 was 1,220.80 thousand hectares, which accounted for 3.80% of China’s rice seeded area, but by 2017, it had increased to 4,769.72 thousand hectares, which is 15.50% of the total national rice acreage (see Figure 1). And the number of cities with more than 100 thousand hectares of rice acreage has increased by nine.

The 21 city-level acreage and yield data for rice over 1992–2017 were collected from Provincial Statistical Yearbook, which could meet the requirement of MARS for sample size (Friedman, 1991). Greater Khingan Range virgin forest was not included as the acreage of rice was zero in most years. Received rice prices and consumer price index were obtained from Agricultural Costs and Profits Yearbook and China Statistical Yearbook, respectively. Then received prices were deflated by consumer price index. Climate data, including daily minimum, maximum and average temperature, as well as daily precipitation from May 1961 to September 2017, were collected from China Surface Climate Database. To match city-level area data, the temperature and precipitation data were selected from representative weather stations located within the crop districts, and the corresponding monthly climate variables were calculated based on the daily climate data. Table 1 contains the summary statistics for crop acreage, rice price and climate variables.

3. Results

This section first presents the trend of climate in the growing season and then discusses the estimation results of acreage response function by MARS model, including assessing model performance and variable importance and estimating coefficients and marginal effects.

3.1 Trend of climate during the growing season

The climate normal is defined as averages of climatological variables from 1961 to 1991 according to the National Oceanic and Atmospheric Administration, and then the deviation of climate is calculated during study period. The deviation of the temperature in each region from the climate normal every year can reflect the gradual update of the local climate (Cui, 2020).

Figure 2 features the variation both across space and time in the growing season. The starting point of all temperature planes is greater than zero, indicating a higher average temperature compared with temperature normal. And the slope of the plane reflects a gradual upward trend. Specifically, over the past 26 years, the monthly average temperature from May to September increased by 0.85°C, 0.94°C, 076°C, 0.60°C and 1.14°C, respectively. In addition, minimum temperature in May and June shows a faster upward trend, whereas maximum temperature in August and September increases faster. Precipitation does not show a similar upward trend during this period (see Figure A2 in Appendix).

3.2 Assessment of model performances

The performances of MARS model are calculated and compared with that of multiple linear regression (MLR) model. Evaluation criteria used in the application are root mean square errors (RMSE) and mean absolute errors (MAE), which are widely used to assess the forecasting capability of the data-driven models (Chai and Draxler, 2014). And their statistics are given as:

(6) RMSE=1N∑i=1N(actual areait−predicted areait)2

(7) MAE=1N∑i=1N|actual areait−predicted areait|

where N is the number of samples, and the predicted area is estimated by MARS model and MLR model for equation (3). Tenfold cross-validation is conducted to evaluate the performance of MARS model. During each cross-validation, one subsample is reserved as the verification data for testing the model and the other nine subsamples are used as the training data. The cross-validation process is repeated ten times so that each of the ten subsamples is used exactly once as verification data, and the relevant RMSE and MAE for each validation could be calculated. The average RMSE and MAE in MARS model are 45.76 and 32.19, whereas RMSE and MAE in MLR model are 66.13 and 43.79, respectively. This means that MARS model could better capture the association between rice area and independent variables with a smaller error. Moreover, the result in Figure 3 also shows that predicted area by MARS could obtain a smaller deviation of predicted area and better fit the actual rice area.

3.3 Assessment of variable importance

Based on the great performance of MARS, this study next assesses the variable importance to recognize the important variables and exclude the inefficient factors. The importance for each set of variables is measured by setting a tenfold GCV method and use residual sums of squares as a robust check. The area response model [equation (2)] which does not consider yield expectation (model without yield expectation) is first assessed, and then the expected yield is added into the model [equation (3)] to investigate whether climate effect is affected by expected yield (model with yield expectation).

As shown in Figure 4, total agricultural area shows the strongest importance in rice area function in two models. This means that the variability and change of rice area highly depend on the owned total area. The expected rice price is another important variable for farmers’ decision-making on area allocation in two models. However, the importance of expected rice price might be less than that of climates on the decision-making, as climate change might induce higher profit variability and force farmers to adopt area-adaptive behaviors.

The importance of temperature, especially for minimum temperature, is much higher than that of precipitation in the overall sense. When not considering the expected rice yield, monthly minimum temperature from May to September play an important role, but the maximum temperature from June to August present lower importance in these high-latitude regions because of a low probability of heat stress. However, the importance of temperature variables is weakened after absorbing the expected yield into model. For example, minimum temperature in May and August is no longer important in the model with yield expectation, and minimum temperature in June and September becomes less important. One main explanation is that the importance of temperature in area response might be modeled by the expected rice yield. In other words, farmers attach importance to climate is mainly out of the consideration of expected yield, and warmer minimum temperature is beneficial for rice growth and yield increasing. However, the importance of temperature variables cannot be completely modeled by expected yield, because minimum temperature in July still plays an important role in determining the area allocation.

The importance of precipitation tends to be small, especially in June and July. The weak importance in these two months reflects that farmers would pay less attention to the change of precipitation in the early growing season as rice production has a better irrigation system. The results show that the total precipitation in May and September is important when not considering expected yield, but the importance of precipitation in the decision-making of the area allocation is greatly weakened after taking into account yield expectation, which reindicates the mediating effects of expected yield variable.

3.4 Response of rice acreage to climate and economic factors

Table 2 shows the estimated parameters for rice area response to total agricultural area, climate and economic variables. The optimal order of interactions selected by tenfold cross-validation is three in the model without yield expectation, but it becomes two after absorbing yield expectation. Among all factors, total agricultural area has a nonlinear effect on the rice area allocation. Specifically, when total agricultural area is less than 844.7 thousand hectares, the estimated coefficient is 0.1982. However, when total agricultural area exceeds 844.7 thousand hectares, the estimated coefficient becomes 0.3993. This is slightly different from some studies that found a linear effect of total sown area on crop area (Coyle, 1993) but neglected the change of coefficient slope of total crop area. In addition, total area also has strong interaction effects with climate and price with second- or third-order interaction form, especially when total area is higher than 844.7 thousand hectares. In other words, when total agricultural area of farmers is relatively small, the effect of climate would be considered less by farmers who tend to diversify crop types in each growing season for dispersing risk or self-use.

Climatic and price factors also show a strong interplay in rice area. First, the covariability of temperature in different growing stages might affect the variability of planted area, like the interaction effects between the minimum temperature in June and August. Second, the interaction effects between temperature and precipitation significantly exist as a dynamic form. An explanation is that the temperature or precipitation in the previous month may affect the change of temperature and precipitation in the next month, which could help farmers form expectations of crop yield. Third, interaction effects between climate and price reflect two sources of crop production income. Farmers need to simultaneously consider the price and yield, where yield is extremely dependent on climatic conditions, and ultimately form the expectation on income (Weersink et al., 2010). The results support the study by Mehdi et al. (2018) who argued that there is an interactive relationship between the drivers of land-use change.

However, the interaction effects become weaker after adding the expected yield variable into the model, with third-order interaction effects between climate, price and total area disappearing. Additionally, the interactions between total crop area and precipitation have dropped sharply, leaving only the interaction with precipitation in September. This means that the effects of previous climate interaction are mainly used by farmers to predict crop yield.

The marginal effects of each variable are further calculated at five different quantiles, and the results are shown in Table 3. In the model without yield expectation, both the total area and the rice price show positive effects. The estimated coefficient of the total area is 0.11 in the low and middle quantiles (5%, 25% and 50%), and higher effects are observed at the higher quantiles, where the estimated coefficients are 0.12 and 0.19 at 75% and 95% quantiles, respectively. This indicates that the larger the total area, the higher the share of rice planting area. Therefore, the total area might play a certain restrictive effect on the extension of rice area.

For rice prices, when the rice price is low, its impact on the rice area allocation decision is zero, but the impact at 50% or higher quantiles (75%, 95%) is 0.04. It means that only when the price of rice exceeds a certain level will it have an impact on the area allocation decision of farmers. This is different from some previous studies which mainly found the linear effect of price and its positive effect on crop area (Weersink et al., 2010). The explanation is that rice production in new land needs large adjustment costs, like specific machinery input and irrigated land (Nerlove, 1956; Haile et al., 2016). Farmers need to determine whether the revenue brought by the increase of predicted price could cover the adjustment cost and a threshold point might appear.

Among the climate variables, the monthly minimum temperature in the growing season plays a relatively more important role, followed by precipitation and maximum temperature. When the minimum temperature in May, June and July are in the low or middle quantiles, it will have a positive effect on the increase of rice area, but it shows no effect or even a negative effect when the minimum temperature continues to rise. The minimum temperature in August shows a different result that higher minimum temperatures in August are preferred when farmers make rice area decisions. Both minimum temperature in September and maximum temperature in May show a relatively negative impact, whereas maximum temperature in September at all quantiles play a favorable role in the decision to increase rice area. This indicates that effects of the minimum temperature and maximum temperature in growing season might be different.

The impact of total precipitation will be slightly weakened or disappear after the yield expectation entering into the model. For example, the impact of precipitation weakened in September and disappeared in May. This is consistent with the finding by Weersink et al. (2010) who mentioned that factors affecting crop area allocation are the crop returns that can be decomposed into price and yield, and the relative importance of climatic variables on area allocation could be measured through their impact on yield. In other words, the expected yield has a mediating effect on the association between climatic conditions and rice area. However, the minimum temperature in June, July and September still show a strong effect on the rice area, indicating that the impact of climate cannot be completely modeled by expected yield. This is because the minimum temperature as an extremely cold temperature might be given higher weight when determining the rice area.

As expected, yield expectation shows a zero effect at 5% and 25% quantile, and an inverted V-shaped relationship with the increase of quantiles. First, when the rice yield is very low, the increase of yield would not induce a higher rice area because of potential negative profit, which is similar to the effect of rice price. Then, the effect of rice yield becomes positive with a coefficient of 30.10 at 50% quantile driven by the positive profit. However, the effect of rice yield would become negative (−3.02, −3.01) at higher quantiles. An explanation is that farmers would give up low-quality land which is not suitable for rice production and requires higher nutrition inputs when they have a higher expected yield (Miao et al., 2016; Feng and Babcock, 2010).

4. Discussion and policy implication

Compared with the previous studies, the first major contribution is that this study further extends the classical area response model by investigating nonlinear and dynamic interactions between rice area and climate variables. The literature on estimating supply response to price and climate factors have a long history in agricultural economics (Nerlove, 1956; Chavas et al., 1983; Clark and Klein, 1996; Weersink et al., 2010; Miao et al., 2016; Von and Weersink, 1993). However, these studies adopted regression model and assumed a linear relationship between expected price and area. Even though numerous studies have focused on nonlinear relationships, but it is mainly in the yield model (Schlenker and Roberts, 2009; Lu et al., 2018). And they ignored the interaction effects in the area model and yield model. This study finds the strongly nonlinear effects of total area, expected price and climate variables. And price has a completely different effect on the rice area allocation at low and high price quantiles. This is consistent with expectation and economic theory, as the higher price would easily induce incentive to farmers’ tendency toward rice cultivation, especially the expected revenue change induced by price is higher than adjustment cost. Therefore, policymakers should adopt some supporting measures to help farmers construct irrigation systems and implement agricultural machinery subsidies.

Moreover, this study also finds significant interaction effects between total cropland and climate variables. In other words, the total cropland constraints might change farmers’ adaptation to climate change. Because of the higher requirement of rice production on capital investment and irrigation system (Haile et al., 2016), partial adjustment principle might lead to a slow speed adjustment of cropland area. And limited total agricultural area would lead to a lower willingness to extend the rice area so as to keep crop diversity and avoid adjustment cost. Therefore, the interaction effect of climate can be only observed under larger cropland. Compared with previous studies (Weersink et al., 2010), it is also found that effect of rice price would be also affected by climate as farmers need to simultaneously consider the price and yield and form the expectation on revenue.

Next, this study explores the mechanism of climate effects by adding the yield expectation into the area response model. Generally, the previous studies have widely investigated the impact of climate variables on crop yield, and they found that growing degree days are beneficial for crop yield, but overheating or extremely low temperature could cause damage to crop yield (Miao et al., 2016; Lu et al., 2018). This supports that the climate would show a nonlinear effect on the crop output. This is consistent with the association between crop yield and climate variables. When adding the yield expectation into the model, the interaction effects of climate variables are weakened to second order, and the marginal effects of some climate variables disappear. This means that climate variables could affect farmers’ area allocation decision partly through affecting farmers’ yield expectation (Weersink et al., 2010). Based on the positive effect of expected yield, the policy implication is that the relevant agricultural department should further carry out agricultural technical education to help farmers build confidence in rice production. However, the impacts of some climate factors persist after the expected yield variable is incorporated. This indicates that the impacts of climate factors could not be completely modeled by the expected yield, as minimum temperature as an extremely cold temperature might be given higher weight when determining the rice area. This is relevant for policymakers that constructing a climate risk crop insurance could help farmers reduce the concern on output uncertainty and expand rice production.

In terms of the empirical model, most studies adopted the traditional panel model in area response function, like fixed-effect model and spatial panel model (Miao et al., 2016; Cui, 2020). In these models, the variables and the forms need to be set in advance. MARS technique does not make any special assumptions about the function, like variables of interest or the form of function (Friedman, 1991). In this approach, the function would be determined automatically, instead of selecting them in advance. And MARS model could also consider the potential nonlinear and interactional association. It is found that predicted area by MARS could obtain a smaller deviation of predicted area and better fit the actual rice area. This study also assesses the importance of variables and determines the form of variables (from first to third order) by comparing tenfold GCV’s root mean squared error. Then, coefficients could be estimated for the selected variables. Therefore, the model could be beneficial for future studies on climate change. However, this paper is not without its limitations. Further work could include adding more crops (maize, wheat) to the multiproduct area response model and considering the impact of price risk (price volatility).

5. Conclusion

Adjusting cropping acreage allocation is considered to be one of the most important ways by which grain farmers could adapt to climate change, but fewer researchers have investigated the climatic and economic drivers simultaneously and the interplay of these drivers. Based on the analysis of climate change trends, this study investigates the response of rice area to total cropland and expectations of climate and economic variables in high-latitude regions of China with 21 districts over the period 1992–2017. Furthermore, the expected yield variable is added into the model to explore the effects and the mechanism of farmer’s expected yield on area allocation decision. It is found that monthly average temperature during rice growing season (from May to September) have increased by 0.85°C, 0.94°C, 076°C, 0.60°C and 1.14°C, respectively, compared with the temperature normal. And the trend shows that the increase of temperature in the early stage of the rice growing season (May and June) is mainly because of the increase in the minimum temperature, whereas in the later growing period (August and September) is mainly because of the increase in the maximum temperature.

This study uses a machine learning algorithm, MARS, to characterize the complex nonlinear and interaction effects of climate change on the rice acreage. It is found that the total agricultural area plays an important role in estimating the rice area function and its importance is higher than that of price and climate variables no matter whether considering expectation of yield. The expected rice price is another important variable for farmers’ decision-making on area allocation. The monthly minimum temperature from May to September both play an important role when not considering the expected rice yield. The importance of precipitation tends to be small, except in May and September. But the importance of climatic variables is weakened after absorbing the expected yield into the model.

The hinge functions and estimated coefficients show that the total agricultural area has positive and nonlinear effects on rice area, where the marginal effects are higher at the higher quantiles. The impact of price on the rice area is zero when rice price is low; until the price reached 50% quantile or higher quantiles, it will have a positive effect. The total area has strong interaction effects with climate and price as a third-order interaction form, especially when total area is higher than 844.7 thousand hectares. The order of interactions will be reduced to second order after adding the expected yield variable into the model, and marginal effects of climatic variables will be slightly weakened or disappear, both of which support the mediating effect of expected yield. However, the impact of minimum temperature cannot be completely modeled by the yield expectation.

Figures

Figure 1.

Seeded area of rice in northeast China

Figure 2.

Difference in climate normal during rice growing season

Figure 3.

Performance of MARS and MLR models (a) Prediction of rice area by MARS approach. (b) Prediction of rice area by MLR approach

Figure 4.

Importance of variables in different models (a) Assessment using generalized cross-validation. (b) Assessment using residual sums of squares

Figure A1.

Net profit of grains in high-latitude regions

Figure A2.

Difference in climate normal during rice growing season

Table 1.

Summary statistics of variables, 1992–2017

Variables	Mean	SD	Min	Max
Rice area (1,000 hectares)	94.78	108.93	0.84	638.10
Total area (1,000 hectares)	675.76	561.05	51.34	2,303.10
Rice price (US$/ton)	253.90	99.63	132.50	414.10
Rice yield (ton/hectare)	7.20	1.53	1.79	12.10
Minimum temp. in May (°C)	8.59	1.76	2.35	12.41
Minimum temp. in June (°C)	14.88	1.73	9.16	17.96
Minimum temp. in July (°C)	18.30	1.29	14.46	21.28
Minimum temp. in August (°C)	16.61	1.39	11.08	19.38
Minimum temp. in September (°C)	9.24	1.67	3.30	12.71
Maximum temp. in May (°C)	21.13	1.36	16.79	24.79
Maximum temp. in June (°C)	26.24	1.23	23.29	29.45
Maximum temp. in July (°C)	27.78	1.00	25.24	30.99
Maximum temp. in August (°C)	26.61	1.01	23.25	29.03
Maximum temp. in September (°C)	21.71	1.23	17.71	24.84
Precipitation in May (mm)	56.62	23.24	2.75	155.65
Precipitation in June (mm)	88.73	29.51	20.50	201.84
Precipitation in July (mm)	140.44	48.47	44.15	334.54
Precipitation in August (mm)	122.14	49.52	31.31	335.15
Precipitation in September (mm)	49.27	24.06	5.01	143.63

Notes:

All variables represent farmers’ expectations, except for rice area and total area. The expected price and rice yield are proxied by one-year lag of received rice price and rice yield, respectively. And expectation for each climatic variable is a weighted average of last three years, with a weight of 0.50, 0.33 and 0.17

Table 2.

Basis functions and corresponding coefficients of MARS model

Model (without yield expectation)		Model (with yield expectation)
Basis function	Coeff.	Basis function	Coeff.
h(844.7-Total area)	−0.1982	h(844.7-Total area)	−0.2658
h(Total area-844.7)	0.3992	h(Total area-844.7)	0.1136
h(15.1-June mintemp)	−29.0707	h(18.0-July mintemp)	−74.1314
h(June mintemp-15.1)	−64.0442	h(July mintemp-18.0)	−59.3917
h(May maxtemp-20.6)	−10.9453	h(Sep maxtemp-20.4)	−45.4061
h(Rice price-206.0) * h(9.6-Sep mintemp) * h(Total area-844.7)	0.0007	h(Rice price-243.4) * h(Total area-844.7)	0.0009
h(8.7-May mintemp) * h(Sep precip-42.8) * h(Total area-844.7)	−0.0046	h(Rice yield-6.8) * h(Total area-844.7)	0.1827
h(June mintemp-15.1) * h(1232.3-Total area)	0.0665	h(Rice yield-7.7) * h(Total area-844.7)	−0.2004
h(June mintemp-15.1) * h(Aug mintemp-17.1) * h(Total area-1232.3)	0.0770	h(June mintemp-15.1) * h(Total area-844.7)	−0.0552
h(16.5-June mintemp) * h(844.7-Total area)	0.0305	h(15.1-June mintemp) * h(Total area-844.7)	−0.1740
h(June Mintemp-15.2) * h(Sep precip-42.8) * h(Total area-844.7)	−0.0036	h(July mintemp-18.0) * h(844.7-Total area)	0.0888
h(15.2-June mintemp) * h(Sep precip-42.8) * h(Total area-844.7)	−0.0063	h(18.0-July mintemp) * h(844.7-Total area)	0.0975
h(19.1-July mintemp) * h(42.8-Sep precip) * h(Total area-844.7)	−0.0096	h(July Mintemp-18.6) * h(Total area-844.7)	0.1022
h(Sep mintemp-8.2) * h(Sep precip-42.8) * h(Total area-844.7)	−0.0047	h(Sep mintemp-10.1) * h(Aug precip-65.2)	0.2420
h(8.2-Sep mintemp) * h(Sep precip-42.8) * h(Total area-844.7)	−0.0047	h(Sep mintemp-10.2) * h(65.2-Aug precip)	5.6194
h(Sep maxtemp-21.8) * h(42.8-Sep precip) * h(Total area-844.7)	0.0037	h(10.2-Sep mintemp) * h(Total area-844.7)	0.2089
h(21.8-Sep maxtemp) * h(42.8-Sep precip) * h(Total area-844.7)	0.0064	h(10.2-Sep mintemp) * h(Total area-1130.8)	−0.5888
h(22.1-Sep maxtemp) * h(Total area-844.7)	−0.2051	h(10.2-Sep mintemp) * h(Total area-1224.5)	0.4001
h(Aug precip-66.5) * h(Total area-844.7)	0.0007	h(21.9-Sep maxtemp) * h(Total area-844.7)	−0.1560
h(69.1-May precip) * h(Total area-844.7)	−0.0025	h(Sep maxtemp −20.4) * h(Total area-1428.8)	0.0934
h(Sep precip-42.8) * h(Total area-844.7)	0.0167	h(Sep maxtemp-20.4) * h(1428.8-Total area)	0.0325
h(42.8-Sep precip) * h(Total area-844.7)	−0.0101	h(39.7-Sep precip) * h(Total area-844.7)	−0.0045

Notes:

h (x) = (x − θ)₊ is an indicator function equaling to (x − θ) if it is positive and zero otherwise. mintemp refers to minimum temperature and maxtemp is maximum temperature

Table 3.

Marginal effects of variables at different quantiles by MARS model

	Model without yield expectation					Model with yield expectation
Variables	5%	25%	50%	75%	95%	5%	25%	50%	75%	95%
Total area	0.11	0.11	0.11	0.12	0.19	0.12	0.12	0.12	0.17	0.13
Rice price	0.00	0.00	0.04	0.04	0.04	0.00	0.00	0.00	0.15	0.15
Rice yield	–	–	–	–	–	0.00	0.00	31.10	−3.02	−3.01
May mintemp	7.29	7.29	3.28	0.00	0.00	–	–	–	–	–
June mintemp	28.85	28.85	25.87	−34.99	−24.65	29.61	29.61	29.61	−9.34	−9.40
Jul mintemp	12.05	12.05	12.05	0.00	0.00	41.07	41.07	−29.28	−11.88	−11.88
Aug mintemp	0.00	0.00	0.00	7.77	7.77	–	–	–	–	–
Sep mintemp	−3.98	−18.98	−11.45	−7.49	−7.49	−9.91	−9.91	−9.91	7.53	21.56
May maxtemp	0.00	0.00	−10.95	−10.95	−10.95	–	–	–	–	–
Sep maxtemp	26.90	26.90	31.32	4.60	4.60	26.55	11.95	11.95	−14.59	−14.59
May precip	0.43	0.43	0.43	0.00	0.00	–	–	–	–	–
Aug precip	0.00	0.12	0.12	0.12	0.12	−1.24	0.05	0.05	0.05	0.05
Sep precip	1.52	1.52	0.34	0.34	0.34	0.77	0.77	0.00	0.00	0.00

Note:

mintemp refers to minimum temperature and maxtemp is maximum temperature