Climate change and winter wheat yields: the roles of freezing days and long-run adaptations

Abstract

1. Introduction

Climate change has been found to have broad implications across the economy (Stern, 2007; Dell, Jones and Olken, 2014; Burke, Hsiang and Miguel, 2015), and the agricultural sector is expected to experience challenges (McCarl, Villavicencio and Wu, 2008; Schlenker and Roberts, 2009; Deschênes, Greenstone and Shapiro, 2017). Ortiz-Bobea et al. (2021) indicate that anthropogenic climate change has reduced global agricultural total factor productivity by about 21 per cent since 1961. A good understanding of climatic effects on agricultural productivity is important in determining the extent of needed adaptive actions as climate change proceeds (Liu et al., 2016).

From the perspective of food security, wheat supplies nearly 20 per cent of human calories with 70 per cent of that coming from winter wheat (FAOSTAT, 2021). Many studies have investigated the aspects of climate change impacts on wheat yields (as well as the agriculture sector as a whole). Two approaches have been widely used: process-based simulation models (also known as biophysical or crop simulation models, etc.) and statistical models (mainly cross-sectional models and panel data with fixed effect models). These approaches have different strengths and weaknesses. While the process-based models portray physiological mechanisms governing crop growth and yield, they are concerned about uncertainties associated with a large number of model parameters (Lobell and Asseng, 2017; Moore, Baldos and Hertel, 2017; Dokoohaki et al., 2021). As for statistical models, the strength is that they adopt flexible functional forms taking advantage of extensive observational data (Roberts et al., 2017). Besides, statistical models allow for endogenous management practices (though implicitly), whereas process-based models treat them exogenously (Roberts et al., 2017). However, statistical models’ reliability partially relies on the assumption that biological processes are reflected in the observational data (Gammans, Mérel and Ortiz-Bobea, 2017).

In the past decade, the literature has witnessed a growing popularity of statistical models, partially due to the extended availability of climate and agricultural data. In the case of winter wheat, many statistical analyses rely on climatic variables calculated over the entire growing period (Lobell, Schlenker and Costa-Roberts, 2011; Zhang and Huang, 2013; Xiong et al., 2014; Asseng et al., 2015; Yi et al., 2016). However, a number of studies highlight the significance of considering seasonal variations in estimating climate change effects on crop yields and beyond (Mendelsohn, Nordhaus and Shaw, 1994; Van Passel, Massetti and Mendelsohn, 2017). For instance, Massetti, Mendelsohn and Chonabayashi (2016) show that the coefficients of temperature, degree-days and precipitation are significantly different across seasons in a Ricardian analysis of climate effect on farm values. Similarly, Schlenker, Hanemann and Fisher (2006) stress that plant growth depends on exposure to moisture and heat throughout the growing season, albeit in different ways at different periods in the plant’s life cycle. This issue is more relevant for winter wheat, because it is generally planted in September/October then harvested in the following May/June, and exhibits three growing stages corresponding to three seasons (Fall, Winter and Spring).¹ Thus, as pointed out by Tack, Barkley and Nalley (2015), simple total growing season aggregates of climatic variables may overlook seasonal influences on growing stages and resultant yields.

On the other hand, there has also been a long-lasting debate in the statistical domain concerning whether the panel data model estimations can properly account for long-run adaptations, compared with the estimates from cross-sectional counterparts. Regardless of which statistical method is chosen, how to empirically identify these adaptation effects has gained more and more attention in recent literature (Butler and Huybers, 2013; Burke and Emerick, 2016; Blanc and Schlenker, 2017; Mendelsohn and Massetti, 2017; Kolstad and Moore, 2020; Mérel and Gammans, 2021; Carleton et al., 2022; Bareille and Chakir, 2023; Cui et al., 2023).

With the above issues in mind, this paper performs a statistical analysis of the impacts of climate change on winter wheat yields in China. China is the world’s largest wheat producer accounting for 17  per cent of total global production (FAOSTAT, 2021), and over 90  per cent of Chinese production comes from winter wheat (National Bureau of Statistics, 2019). We address the seasonality issue by constructing season-specific climatic variables using county-level data spanning from 1981 to 2015. To do our analysis, we first divide the growing period into three seasons (Fall, Winter and Spring), and run regressions to identify important lower and upper temperature thresholds for each season and construct degree-day variables accordingly. Second, we employ the climate penalty model, recently proposed by Mérel and Gammans (2021), to address the concern that fixed effects panel data models tend to reflect short-run estimates (i.e. the impacts of annual weather fluctuations rather than long-run effects induced by climate change). More importantly, this climate penalty framework allows us to differentiate the short- and long-run estimates and reveal adaptation effects. Finally, we project future yields under a variety of climate change scenarios and compare our results with prior studies.

Our results lead to several important findings. First, we find that heat in Fall and freezing days in early Spring are the most significant contributors to yield reduction. In particular, long-run estimates from the climate penalty model indicate that a 10 degree-day increase in Fall temperatures over 24°C decreases yields by 7.0 per cent, while a 10 degree-day decrease in Spring freezing conditions increases yields by 8.8  per cent. Such results highlight the importance of accounting for changes in seasonal conditions especially early Spring freezing days when studying climate effects on winter wheat yields because global warming tends to influence yields in opposite ways. When freezing effects were omitted, our yield projections with Shared Socioeconomic Pathway scenarios (SSPs) portend large yield reductions (12.5  per cent to 48.2  per cent) as opposed to small yield gains (1.9  per cent to 2.5  per cent) when the reduction of the number of freezing days is considered. Finally, by comparing short-run and long-run estimates, we find substantial adaptation effects that could even reverse the sign of climate change impacts. Moreover, our results also demonstrate that conventional fixed effects panel models tend to reveal climatic effects that lie between short-run and long-run estimates identified from the climate penalty model, although this finding is more evident in scenarios with higher temperature increases.

This paper contributes to the literature in three ways. First, our analysis adds statistically based evidence on key factors influencing wheat yield climate change sensitivity. Relevant studies are not uncommon in the literature, which provide insightful results (Albers, Gornott and Hüttel, 2017; Chavas et al., 2019; Bucheli, Dalhaus and Finger, 2022; Schmitt et al., 2022; Bareille and Chakir, 2023; Malpede and Percoco, 2023; Syme, An and Torshizi, 2023). However, few of them consider the seasonal variation of climatic effects, which is critical for winter wheat. The exception is Bucheli, Dalhaus and Finger (2022), who constructed climatic variables based on specific growing stages. In the present research, we cover the entirety of the growing cycle and establish season-specific climatic variables using a data-driven method. Our work is also closely related to Tack, Barkley and Nalley (2015) which investigates season-specific climate impacts on winter wheat in Kansas, United States. We extend the framework further by estimating the effects of long-run adaptations.

Second, our work adds a detailed wheat statistical analysis to the broad climate change—agricultural productivity literature (Deschênes and Greenstone, 2007; Schlenker and Roberts, 2009; Lobell, Schlenker and Costa-Roberts, 2011; Chen, Chen and Xu, 2016). As one of the most important food crops, our analysis of winter wheat provides insightful guidelines for agricultural activities in response to climate change, which seems to be inevitable (IPCC, 2018). Lastly, our work also contributes to a growing body of literature that discusses panel data models’ ability (inability) to account for long-run adaptation effects in the estimation (see a detailed discussion in the model part). In this paper, we adopt the climate penalty model proposed by Mérel and Gammans (2021), which allows us to explicitly identify short-run and long-run estimates and more importantly uncover long-run adaptation effects. Our winter wheat practice with the climate penalty model adds to the strand of empirical literature that attempts to identify long-run climate effects in panel data settings.

The remainder of this paper is organised as follows. Section 2 describes data collection procedures. Section 3 covers the estimation of seasonal temperature thresholds. Section 4 covers the model specification. Section 5 reports the main results and yield projections. Lastly, Section 6 presents conclusions.

2. Data collection

We assembled a data set unifying Chinese county-level winter wheat yield data in an important winter wheat producing region and associated climate data for the years 1981–2015. The choice of the study region and data sources are discussed below.

2.1. Study region

Herein we focus on a sub-region within the North China Plain (NCP),² which produces over 70  per cent of the winter wheat in China (Zhao, 2010). The region covers the southern part of Hebei, most of Henan, the entirety of Shandong and the northern part of Anhui and Jiangsu. We choose this region for particularly two reasons. First, it has an arguably uniform growing period (October to May for winter wheat) and cropping pattern (winter wheat plus summer corn). Second, rainfall in this region is greater than in the northern part of the NCP with the winter wheat being largely rain-fed or less irrigated (Zhao, 2010; Zhang and Huang, 2013), avoiding issues with irrigation to a certain extent. Nevertheless, irrigation remains a significant concern, and thus we performed extensive statistical tests in the Section 5.2 to examine its role in our estimates.

2.2. Yield data

County-level winter wheat yields in tons/hectare were obtained from the Institute of Agricultural Information in the Chinese Academy of Agricultural Science (Yi et al., 2016) for the years 1981–2015. In preparing the data for estimation, we dropped counties that had less than 10 years of yield observations (five counties were dropped). This left us with observations for 352 counties and 8,867 annual data points in total.

2.3. Climate data

Temperature and precipitation data were assembled from two sources: the China Meteorological Data Service Center (CMDC) and the China Meteorological Forcing Dataset.

Daily minimum and maximum temperatures were drawn from CMDC (Chen and Gong, 2021). The raw data were available on a 0.5°× 0.5° grid. A county-level data set was formed by constructing a weighted average over grid cells within each county with the area of the grid cell in that county acting as weights, following Auffhammer et al. (2013) and Burke et al. (2018).

We moved further by constructing hourly temperatures from daily county-level data (Luedeling, 2020)³ and then used the hourly temperatures to construct degree-day variables. For instance, when using a threshold of 25°C, then 1 h of 30°C temperature contributes to 5 degree-hours, which we convert to degree-days by dividing it by 24, following Tack, Barkley and Nalley (2015). We will illustrate the identification of season-specific temperature thresholds in detail in the next section.

It should be noted that in processing the temperature data, we did the spatial aggregation first (i.e. from grid level to county level) and then interpolated the daily county data to hourly. Some studies have suggested the opposite ordering (Schlenker and Roberts, 2009); that is doing interpolation at the grid level in the first place, followed by the spatial aggregation at the county level. This ordering issue would matter more in applications where the gridded data are coarse either in spatial or temporal resolutions (Auffhammer et al., 2013), which is not in our case. Nevertheless, we ran regressions with data constructed the other way around and the results proved to be almost identical (see Supplementary Table A6 in the Appendix).

Various temperature specifications have been used to examine the impacts on crop yields including (i) temperature bins (Schlenker and Roberts, 2009; Gammans, Mérel and Ortiz-Bobea, 2017; Zhang, Zhang and Chen, 2017; Chen and Gong, 2021), (ii) degree-days (Deschênes and Greenstone, 2007; Tack, Barkley and Nalley, 2015; Chen, Chen and Xu, 2016; Miller, Tack and Bergtold, 2021), (iii) average temperatures (Lobell, Schlenker and Costa-Roberts, 2011) and (iv) spline models (Bucheli, Dalhaus and Finger, 2022). We acknowledge that recent studies have favoured temperature bins and spline models over degree-days; however, these complicated specifications may not be perfectly suitable for our analysis. Conceptually, our purpose in this research is more about highlighting the seasonal climate impacts on winter wheat yields and identifying the long-run adaptation effects than obtaining a model that delivers the highest predictability. Besides, our limited sample size keeps us from utilising a highly flexible model approach as the results are likely very sensitive (Cui and Xie, 2022). Lastly, although Mérel and Gammans (2021) stated that the climate penalty model can accommodate a variety of empirical settings (i.e. average temperatures, degree-days, flexible time controls, etc.), whether the model works with temperature bin and spline specifications is not immediately clear. Even if it did, the derivation of short-run and long-run estimates would be difficult. Nevertheless, we performed out-of-sample cross-validations with four widely used degree-day specifications and a suite of robustness checks to comprehensively verify the credibility of our estimates.

For precipitation, we downloaded monthly data from the China Meteorological Forcing Dataset, developed by He et al. (2020). The initial data were gridded at 0.5°× 0.5°, and we converted them to county-level measures following the same procedure as described above. In turn, the county-level monthly precipitation data were aggregated by seasons (i.e. Fall, Winter and Spring).

Figure 1 shows trends in seasonal temperature and precipitation from 1981 to 2015. There we see upward trends in all seasonal temperatures, particularly in Winter and Spring. Precipitation exhibits more year-to-year variability and does not show significant trends.

Fig. 1.

Historical trends in temperature and precipitation data.

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Note: Temperatures are averaged across respective seasons in the study region. Precipitation is the total rainfall during the entire growing period. The straight lines indicate simple time-dependent regressions of temperature/precipitation on the year with county fixed effects added to the model. β denotes the yearly trend and the associated standard errors are shown in parentheses.

3. Empirically estimating temperature thresholds for deriving degree-day variables: what is too cold/hot?

To calculate degree-days, one needs a temperature threshold and a time interval. A number of papers use a 0°C threshold for winter wheat (Yang et al., 2015; Yi et al., 2016; Dreccer et al., 2018). For the time interval, degree-day variables are usually calculated over the entirety of the growing period (October to May) (Yang et al., 2015; Yi et al., 2016; Dreccer et al., 2018). However, here we will derive seasonal measures based on season-specific temperature thresholds. Additionally, a number of existing studies omit the impacts of freezing days (temperatures below 0°C), which agronomic studies have shown to have important yield effects (Porter and Gawith, 1999; Xiao et al., 2018) and we will use freezing degree-days.

We follow Tan et al. (2018), Xiao et al. (2018) and Zhou et al. (2018) and divide the growing period (October to May) into three intervals—Fall (October to November), Winter (December to February) and Spring (March to May). Next, we follow the piecewise linear approach in Schlenker and Roberts (2009) and Tack, Barkley and Nalley (2015) using alternative temperature threshold combinations, and then pick the one that exhibits the best fit (the highest R²).

Specifically, we construct four degree-day variables respectively for the Fall and Spring seasons. The first one is a freezing degree-day variable (Frez) that measures the number of days where temperatures are below 0°C. The other three are formed using season-specific thresholds. In particular, the second variable covers days when temperatures are observed between zero and a positive lower threshold (DDlow), while the third is the count of days with temperatures between the lower threshold and an upper threshold (DDmed), and the fourth counts days above the upper threshold (DDhigh). Alternative threshold values are tried ranging from 1°C to the highest temperature observed in that season, following Tack, Barkley and Nalley (2015).⁴ We then loop over all possible threshold combinations (i.e. 1–2°C, 1–3°C, 1–4°C, etc.) doing a yield estimation with variables for each season separately and pick the one which has the best fit (the highest R²).

The set-up for the Winter season is different. Specifically, we set the lower threshold so it falls below zero and the upper threshold above zero. Because winter wheat is dormant during the season, this temperature range reflects conditions where the wheat remains dormant but is not damaged (i.e. not too cold to harm wheat or too hot to interrupt wheat from dormancy—Porter and Gawith, 1999). In this case, we have three degree-day variables (i.e. below the lower, between thresholds and above the upper). We again loop over all possible threshold combinations and pick the lower-upper pair which produces the best fit.

The estimated temperature thresholds are shown in Table 1.⁵ Our results are generally consistent with the thresholds identified from field experiments (Cao and Moss, 1989; Slafer and Rawson, 1995; Porter and Gawith, 1999); however, they are somehow different from that estimated by Tack, Barkley and Nalley (2015), which reports thresholds of 10–17°C for Fall, 5–10°C for Winter and 18–34°C for Spring. The differences are probably attributable to several reasons. First, the growing season in our case starts in October, in contrast to September in Tack, Barkley and Nalley (2015). Second, while Tack, Barkley and Nalley (2015) focus specifically on Kansas, we cover a larger but further north geographic area with milder Spring temperatures. Third, we adopt a different setting for the Winter season, i.e. requiring the lower threshold below zero and the upper threshold above zero. We expect this set-up to be more (agronomically) suitable for winter wheat.

Supplementary Table A1 in the appendix also displays summary statistics on the constructed degree-day and precipitation variables. In that table, we also compared these hourly based degree-day variables with those constructed directly from daily average temperature. It turns out that degree-day variables constructed from daily temperatures tend to be smaller. For instance, the maximum and mean of DDhigh_fall calculated from hourly temperatures are 2.5 and 0.5 (in the unit of 10 degree-days), respectively, whereas they are as low as 0.9 and 0.01, respectively, if calculated from daily temperatures. Furthermore, the variation of variables calculated from hourly temperatures is also greater than those from daily temperatures.

4. The estimation model

The literature reveals two basic statistical approaches for estimating climate impacts: the use of cross-sectional models and the use of fixed effects panel data models. The cross-sectional models (also known as the Ricardian models) implicitly take account of long-run climate change adaptations because they directly compare outcomes across different regions in which farm practices have been optimised for long-run local climate (Mendelsohn, Nordhaus and Shaw, 1994; Schlenker, Hanemann and Fisher, 2006; Fezzi and Bateman, 2015; Mendelsohn and Massetti, 2017; Van Passel, Massetti and Mendelsohn, 2017; Bozzola et al., 2018). However, their estimates may be plagued by endogeneity issues such as omitted variable bias (i.e. ignoring differences in soil quality and other location-specific characteristics—Blanc and Schlenker, 2017). Nevertheless, this concern has been well addressed in the literature by including a wide variety of control variables. See detailed reviews in Mendelsohn and Dinar (2010) and Mendelsohn and Massetti (2017), and recent developments in Bareille and Chakir (2023) and DePaula (2020).

Compared with the cross-sectional models, fixed effects panel models are able to alleviate the omitted variable bias to some extent by introducing location-specific effects (Schlenker and Roberts, 2009; Dell, Jones and Olken, 2014, 2012; Burke, Hsiang and Miguel, 2015; Carleton and Hsiang, 2016; Hsiang, 2016; Ortiz-Bobea, Knippenberg and Chambers, 2018; Chen and Gong, 2021). Those effects control for locational time-invariant characteristics that would confound the estimates if omitted. However, panel regressions rely on time-series variations, i.e. comparing yield changes and weather conditions across each year for each location. In this respect, fixed effect panel models tend to reflect the effects of short-run weather shocks (year-to-year weather fluctuations) on the outcomes. As a result, they do not fully take into account long-run adaptations as is done in cross-sectional models (see detailed reviews in Hsiang, 2016; Blanc and Schlenker, 2017; Kolstad and Moore, 2020).

Lastly, we also want to elaborate on the interpretation of the results obtained from these statistical models. Indeed, cross-sectional analysis usually focuses on climate change impacts on the entire agricultural system (farmland values), where the discounted stream of future rents is capitalised with the consideration of adaptation strategies in place. However, we also notice a growing number of cross-sectional studies perform additional analysis based on subsamples (i.e. specific farm types, crops, production activities, etc.) to understand how different parts of the farming sector respond to climate. For instance, Van Passel, Massetti and Mendelsohn (2017) conducted separate investigations on rain-fed and irrigated farms and crop-land and livestock farms across Western European. The results are informative; however, the underlying assumption inherent in these subsample analyses is that the farm-type or economic activity remains the same amid climate change, which seems counterintuitive from the perspective of adaptation. Nevertheless, subsample analysis could still be an important supplement to the estimates of the overall climate change effects.

In what follows, we first build the research framework based on the conventional fixed effects panel data model, and then address long-run adaptations by introducing the climate penalty model, following Mérel and Gammans (2021). It should be noted that we try not to mask the advantages of conventional panel models, which have been extensively used in the literature. Instead, our goal is to empirically estimate long-run adaptation effects utilising the state-of-the-art development from these models.

4.1. The conventional fixed effects panel data model

The conventional panel data model takes the form below.

where

_i denotes the county.

t denotes the year.

s denotes Fall, Winter and Spring seasons.

y_it is the logarithm of winter wheat yield in county i for year t.

δ_i indicates the fixed effects by county that absorb time-invariant factors that differ between counties, such as soil quality and other geographic features.

t and t² are linear and quadratic time trend terms, respectively, and are a proxy for technological development, following Schlenker and Roberts (2009), Miller, Tack and Bergtold (2021) and Tack, Barkley and Nalley (2015).

ε_it is the error term, and in Section 5, we construct standard errors following Conley (1999) to address possible spatial correlations.⁶

The term |$\sum\limits_s {{f_s}} (W_{it}^s;{{\beta}^s})$| in equation (1) includes climatic variables which vary in composition by season. Specifically, for the Fall season (s = fall)

While for the Winter season (s = winter):

And for the Spring season (s = spring):

where for Fall and Spring in county i at year t we have

Degree-day variables for Winter are slightly different and are

Lastly,

|$Pre{c_{it}}$| and |${(Pre{c_{it}})^2}$| denote linear and quadratic terms, respectively, for seasonal precipitation.

4.2. The climate penalty model

As discussed previously, the conventional panel data model has been criticised for its inability to reflect long-run adaptation impacts. Several hybrid approaches have been developed to address this, such as the long differences model (Burke and Emerick, 2016) and the multistage model (Butler and Huybers, 2013; Kolstad and Moore, 2020). These approaches exploit cross-sectional variation and thus require a large number of counties to obtain reliable estimates.⁷

Recently, Mérel and Gammans (2021) proposed a method to estimate short- and long-run impacts by adding a ‘climate penalty’ term in the form of |${({x_{it}} - {u_i})^2}$| to the conventional panel model. To better illustrate, suppose that one intends to estimate the impacts of climate change on yields |${y_{it}}$| and constructs a simple climate penalty model as follows.

Here, x_it denote weather variables (i.e. average temperature, degree-days, etc.) for year t at location i. μ_i indicates the long-term climate in location i calculated by averaging the weather variable across the study period. |$(x_{it}-\mu_{i})^{2}$| is the climate penalty variable, which is the squared distance between weather realisation and local climate. In the long-run, agents adapt to climate rather than to weather fluctuations, and thus one would expect that conditional on the contemporaneous weather realisation, locations with an underlying climate closer to that realisation will have higher yields than locations for which the deviation happens to be larger. In other words, coefficient |${\beta _2}$| is expected to be negative and the term |${\beta _2}{({x_{it}} - {u_i})^2}$| indicates the agents’ capability to adapt. In the long-run scenario when actions can be gradually adapted to changes in climate, the penalty term will be gone. Consequently, |${\beta _1}$| will be the long-run marginal response to climate, whereas the short-run response is the combination of the long-run response and the climate penalty term. In Appendix A1, we mathematically show how long-run adaptations are captured in the climate penalty model.

To introduce the climate penalty variable in our case, taking DDhigh_fall_it as an example, |$\beta _4^{\,fall}DDhigh\_\,fal{l_{it}}$| in equation (1) becomes

where |$\overline {DDhigh\_\,fal{l_i}}$| is the average |$DDhigh\_fal{l_{it}}$| across the study period (1981–2015) in county i. |$\beta _4^{\,fall,1}$| indicates the long-run responses to changes in degree-days, whereas the short-run impacts are determined by the long-run impacts plus the climate penalty (⁠|$\beta _4^{\,fall,2}{(DDhigh\_\,fal{l_{it}}\_\overline {DDhigh\_\,fal{l_i}} )^2}$|⁠).

As demonstrated previously, while |$\beta _4^{\,fall,1}$| in equation (3) can be interpreted as the marginal long-run climate impacts, such ‘marginal’ interpretation for short-run impacts is contingent on the actual weather realisation and the local climate. The adaptation effects are then revealed by comparing the yield projections with long-run impacts and short-run impacts.

It should be noted that certain conditions need to be satisfied before implementing the climate penalty framework. One such is the stationarity of historical climate (this does not imply that future climate will be the same as current climate). In the case of a trending historical climate, the climate penalty model can still be used; however, the estimates tend to perform poorly in empirical applications. Nonetheless, there are exceptions. As argued by Mérel and Gammans (2021), when climatic trends are responsible for a very small share of locational weather variation, which is dominated by year-to-year fluctuations and cross-sectional variation, the climate penalty model will work approximately to the conditions of stationary climate. In our case, as can be seen from Figure 1, trends in temperatures are observed. We thus carefully justified the stationary climate assumption by examining the share of climatic trends in locational weather variation (see Appendix A2 for a more detailed discussion). The results indicate that trends in historical climate only account for 1  per cent to 5  per cent variation in locational weather variation.

5. Empirical results

Here we first report estimation results for the conventional fixed effects panel model to obtain a general picture of seasonal climate effects on winter wheat yields. We then compare our model with four alternative model forms to examine whether this paper’s setting featuring seasonal effects performs better than previous ones. A suite of robustness checks is also conducted. Following that, we discuss short- and long-run climate impacts by introducing climate penalty terms to the conventional panel model. Finally, we project future yield consequences of climate change scenarios and examine the effect of adaptation actions.

5.1. Regression results from the conventional panel model

Figure 2 portrays estimated degree-day variable effects and is based on the numerical results in column 1, Table 2. Before estimation, we hypothesised that the medium degree-day variable (DDmed) would be the key determinant of winter wheat growth, whereas the other degree-day variables Frez, DDlow and DDhigh would reduce yields. We find our estimation results are largely in line with those expectations. We consistently observe positive effects within the identified DDmed temperature range. Also, we observe negative effects outside of that interval, both under hotter and cooler conditions.

Fig. 2.

Winter wheat yield responses to temperatures across different seasons.

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Note: The x-axis indicates the temperature ranges defining degree-day variables. Bars show the estimated coefficients from the conventional panel data model in equation (1). The whiskers represent the 95 per cent confidence intervals using Conley-type standard errors that account for spatial correlations.

We also find significant seasonal-specific effects. Heat in Fall and freezing in Spring are the most significant determinants of yield reductions. In the Fall season, an additional 10 degree-days over 24°C is associated with a yield reduction of 11.4  per cent. Similarly, an additional 10 Spring freezing degree-days reduces yields by 11.3  per cent. Finally, for the Winter season, cold temperatures below −5°C and hot temperatures above 8°C both have negative effects on yields, although the former is statistically insignificant. It is worth noting that recent literature highlights the importance of snow cover variables in determining yields because snowpacks can insulate winter wheat from extremely low temperatures and mitigate the damages (Schmitt et al., 2022; Zhu et al., 2022). In Section 5.2, we constructed alternative freezing variables and introduced snow depth variables to the model to examine whether our estimates are sensitive to different settings.

We do not observe significant damages from Spring extremely hot days contrary to the results of Tack, Barkley and Nalley (2015) who find that associated with the largest yield reduction. This result may be due to a number of factors, such as differences in geographic characteristics, wheat varieties, growing seasons, farm management, etc. For instance, temperatures above 34°C occur in over 75  per cent of Tack, Barkley and Nalley’s (2015) observations while this only occurs in 39  per cent of our observations. Another possible explanation is that the Spring heat estimate is biased by irrigation. Unfortunately, we do not have detailed irrigation data. Nevertheless, to address this concern, we performed extensive empirical tests in Section 5.2 and consistently observed statistically insignificant heat effects.

Precipitation exhibits an inverted U-shape effect on yield (see Table 2) with turning points at 134.6 mm for the Fall season and 188.3 mm for Spring above which increasing precipitation leads to yield reductions. Note that mean rainfall in these two seasons is, respectively, 62.0 mm and 159.1 mm, indicating a significant shortage of rainfall in Fall but less so in Spring. Winter precipitation, on the other hand, shows a weakly negative impact on yields.

5.2. The examination of model performance and robustness checks

Our framework has a different climate variable specification from those commonly used in previous wheat statistical studies, and we expect it to perform better in yield predictions. To examine this, we conduct out-of-sample cross-validations versus four alternative specifications, following Schlenker and Roberts (2009). The process is that we randomly choose 28 years out of our 35  year observations to train the models.⁸ Then we use the trained models to predict yield outcomes within the remaining 7 years (15  per cent) of the sample. The root mean squared error (RMSE) is used as a measure of fit. We repeat this process 1,000 times for each specification and compare average RMSEs. The results in Figure 3 indicate that our preferred temperature specification exhibits the lowest RMSE, outperforming the other alternatives in predicting yields, although the margins are small for certain cases.

Fig. 3.

Out-of-sample prediction comparison for multiple specifications.

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Note: A lower RMSE indicates a higher model accuracy. ‘Simple tavg’ in the figure refers to the model with linear and squared terms for average temperature and total precipitation calculated over the entire growing season (October to May). ‘Seasonal tavg’ means the model with linear and squared terms for seasonal (Fall, Winter and Spring) average temperature and seasonal total precipitation. ‘Simple dd’ refers to the model that includes linear and squared terms for growing degree-days and a linear term for freezing days, respectively, computed above and below the threshold temperature of 0°C over the entire growing period along with the total precipitation variable. ‘Seasonal dd’ represents the model that includes linear and squared terms for degree-day variables defined for each season (Fall, Winter and Spring) based on the threshold temperature of 0°C along with seasonal freezing and precipitation variables.

Besides, we also performed a suite of robustness checks to further verify the sensitivity of our estimates (see a more detailed discussion in Appendix A3). First, we followed Chen, Chen and Xu (2016) and Zhang, Zhang and Chen (2017), and introduced an irrigation variable (defined as the ratio between effective irrigated areas and total planted areas) to our models. The inclusion of the variable barely changes the estimation of the climatic variables, and the Spring heat estimates remain insignificant (see Supplementary Table A2 in the appendix). Note that we did not include this irrigation variable in our main analysis, partially because it measures the overall irrigation areas and does not tell specific information for individual crops. We also reran the regressions excluding regions that are identified with intensive irrigation activities by the literature (Lin, Qin and Li, 2008), and the results are again qualitatively consistent (see Supplementary Table A2). Lastly, we turned to the literature to seek some indirect evidence on irrigation effects. While the overall findings are mixed, studies that do find positive irrigation effects suggest that the inclusion of irrigation barely changes their estimations of climatic variables, which is in line with our results (see Supplementary Table A3). Nevertheless, we acknowledge that even though the evidence suggests irrigation is unlikely to confound our estimations, we still cannot completely rule out the possibility that it does (in this case, we expect its impacts to be minimal). This remains one of our limitations.

Second, we also examined whether our results are robust to alternative frost variables and snow cover. Following Schmitt et al. (2022), we constructed a black frost variable which is the accumulations of degree-days during critical growing stages when their daily minimum temperatures were below the first percentile of the daily minimum temperatures in the sample and when snow depth is less than 5 cm. We constructed this variable respectively for the Winter and Spring seasons. Consequently, we replaced the original DDlow_winter and Frez_spring variables with the black frost variables and also included the monthly mean snow depth for these two seasons in the climate penalty model. The results can be found in Supplementary Table A4, and the estimations on degree-day and precipitation variables remain consistent. In the primary analysis, we chose DDlow_winter and Frez_spring over the black frost and snow depth variables, partially due to the fact that nearly 95 per cent and 98 per cent of our observations had a snow depth of 0 in winter and early spring, respectively. Another reason is reliable climate model projections on snow depth data are scarce.

Third, recent studies also highlight the importance of including additional climatic variables in the estimates (Zhang, Zhang and Chen, 2017). Thus, we tested whether our results were sensitive to the inclusion of wind speed, specific humidity, shortwave radiation and longwave radiation variables. Monthly gridded raw data with a spatial resolution of 0.1 * 0.1 were downloaded from the China meteorological forcing dataset (He et al. 2020) and were transferred to the county level following a similar procedure for temperature data. We then constructed season-specific measurements and ran regressions with these variables added to the model separately for each season and all at once. The results can be found in Supplementary Table A5. While wind speed and specific humidity tend to contribute to yield increases regardless of seasons, radiations show positive effects in Fall and Spring and negative effects in Winter. Importantly, the identified degree-day and precipitation effects on yields are not significantly affected.

Finally, in Appendix A3, we further show that our estimates are robust with respect to alternative temperature thresholds (Supplementary Figures A1 and A2), wider geographic coverage (Supplementary Table A6), different time effects (Supplementary Table A7), as well as alternative standard errors that nonparametrically account for spatial and serial correlations (Supplementary Table A8).

5.3. Short-run impacts, long-run impacts and adaptations

In Table 2, we present the results from the climate penalty model and compare them with the estimates of the conventional panel model. Specifically, column (1) shows the conventional model estimates without any penalty terms. In column (2), we add penalty terms for DDhigh_ fall and Frez_ spring, which are the most significant contributors to yield losses and we are interested in how farmers adapt in the long run. Column (3) further adds penalty terms for all climate variables including precipitation.

As can be seen from column (2), the coefficients associated with the climate penalty terms (DDhigh_ fall_penalty and Frez_spring_penalty) are negative which meets the expectations. Compared with the conventional estimates in column (1), long-run estimates indicate smaller marginal damages. For instance, yield reductions induced by 10 degree-days increase in DDhigh_ fall decrease from 11.4 per cent in the conventional panel data model to 7.0 per cent in the model with climate penalty terms, whereas freezing damages in early Spring reduce from 11.3 per cent to 8.8 per cent. However, we observed unexpected results in column (3). While most newly added penalty terms’ coefficients are statistically insignificant, two out of three precipitation penalty coefficients are positive, implying that if a location has a normal climate far from a given weather realisation, it systematically performs better under that weather, which seems counterintuitive. We suspect the problem might be caused by dimensionality issues with a lot of correlated regressors. There is a tendency for the quadratic precipitation terms to be collinear to the quadratic penalty term, particularly if there is less cross-sectional variation in precipitation in the sample. Thus, in doing yield projections, we mainly used the long-run estimates with penalty terms added only for DDhigh_fall and Frez_spring (i.e. the estimation in column 2), because they show the most significant negative impacts on yields. Projections with the full list of climate penalty terms will not be reliable.

Finally, as we have mentioned previously, the marginal short-run impacts are not directly revealed in Table 2 (i.e. no such coefficients or combination of coefficients can be interpreted as so). This is different from applications using the long differences model (Burke and Emerick, 2016; Chen and Gong, 2021), which directly considers estimates from the conventional panel model as the short-run impacts. We will discuss the long-run adaptation effects in detail in the following sections.

5.4. Projecting climate change impacts on winter wheat: the role of freezing days

Two interesting questions emerge while considering climate change impacts on winter wheat. First, Fall heat and Spring freezing days are the largest drivers of yield reduction. But climate change affects these in opposite ways (De Winne and Peersman, 2021). Thus, it is not immediately clear what the overall impact will be. Second, if climate change damages are expected, how much of the damages could be alleviated through adaptation?

To answer these questions, we performed yield projections with a set of scenarios derived from five climate models (i.e. ACCESS-CM2, BCC-CSM2-MR, CMCC-ESM2, HadGEM3-GC31-LL, IPSL-CM6A-LR) under two SSPs (SSP245 and SSP585) for two time period (2041–2060 and 2081–2100). To be detailed, we first obtained downscaled and bias-corrected future monthly temperature and precipitation data from WorldClim.⁹ Second, we calculated changes in these data relative to historical modeled data in 1970–2000, following Auffhammer et al. (2013), and then applied the changes to our hourly temperature and monthly precipitation data, based on which we re-calculated climatic variables. Note that in doing so, we assume the growing season of winter wheat remains unchanged (i.e. October to May). In practice, farmers can alleviate yield losses through the adjustment in planting and harvesting dates (Cui and Xie, 2022). Lastly, we combined changes in climatic variables and the long-run estimates in column 2 of Table 2 to project future yields, with and without factoring in changes in freezing days to illustrate their relative importance.

The results of yield changes are shown in Figure 4. In the figure, ‘All degree-day variables’ denotes the yield projections with all degree-day variables, whereas ‘Omit freezing’ indicates the yield projection without the consideration of terms capturing freezing effects (Frez_fall, DDlow_winter and Frez_spring). We primarily focus on projections with degree-day variables because there is less agreement about where and how precipitations will change, which makes rainfall projections less reliable (IPCC, 2021). Additionally, studies have shown that rainfall plays a less important role than temperature in climate change impact projections for crop yields (Schlenker and Roberts, 2009; Burke and Emerick, 2016; Mérel and Gammans, 2021; Da, Xu and McCarl, 2022). In Supplementary Figure A3 in the Appendix, we present projections with the consideration of precipitations as a robustness check, and in line with expectations, the inclusion of precipitation only marginally increases yields.

Fig. 4.

Projected yield consequences under a variety of scenarios.

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Note: This boxplot reflects the distribution of yield changes across counties. Each box is defined by the upper and lower quartile, and the horizontal line within the box depicts the median of yield impacts. The endpoints for the whiskers are the upper and lower adjacent values, which are defined as the relevant quartile ± three-halves of the interquartile range, and the dots refer to changes outside of the adjacent values.

In Figure 4, two basic findings emerge. First, the potential yield increases stemming from the reduction in freezing days largely offset the yield decreases from the added heat. Ignoring this leads to projections of a substantial yield reduction. For instance, under the SSP245 scenario, yield forecasts ignoring freezing effects show an average yield reduction of 12.5 per cent in 2041–2060, whereas projections accounting for the freezing effects show weak gains in yield (2.3  per cent). This phenomenon persists in all scenarios and tends to be more evident for SSP585 in 2081–2100.

To make the results more illustrative, we compared our yield projections with those in the existing studies. We find that when the ‘freezing’ terms are omitted, our projections are largely consistent with previous studies where freezing impacts were not explicitly considered. For instance, an ensemble projection made by 30 crop simulation models at 30 agricultural sites indicates a global yield reduction of 6 per cent under a 1°C uniform warming scenario (Asseng et al., 2015), compared with a yield reduction between 3.5  per cent and 7.1 per cent in our case.¹⁰ Only 7 out of those 30 simulation models seem to take advantage of the freezing information. On the statistical side, Chen, Chen and Xu (2016), using a temperature bin model with no freezing variables, concluded a winter wheat yield reduction of 11.9 per cent under a temperature increase of 3°C–4°C. The disparity between projections with and without freezing effects echoes the importance of such effects when evaluating climate change impacts on winter wheat yields. Finally, we acknowledge that there may exist other factors that contribute to the differences between our yield projections and previous ones, such as the spatial coverage of the study region, location-specific attributes, crop varieties, etc.

5.5. What is the effect of the adaptation term?

We have shown weak yield gains in the projections with long-run impacts. An important question arises is what effect is introduced by the long-run adaptations? To answer this question, we first conducted yield projections with the short-run estimates and compared that with the projections derived from the long-run estimates.

The results are shown in Figure 5. In the figure, ‘short-run’ and ‘long-run’ refer to the yield projections with short-run and long-run impacts, respectively. ‘conventional’ refers to the yield consequences using the conventional panel model estimates with no penalties. The adaptation effects are essentially the difference between long-run projections and short-run projections. Here we see that adaptation effects are substantial and can even reverse the sign. Specifically, projections with long-run impacts indicate small yield gains ranging from 1.9 per cent to 2.5 per cent for most of the scenarios, whereas those with short-run impacts result in yield reductions from 7.1 per cent to 44.8 per cent.

Fig. 5.

Yield projections with different estimates.

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Note: This boxplot reflects the distribution of yield changes across counties. Each box is defined by the upper and lower quartile, and the horizontal line within the box depicts the median of yield impacts. The endpoints for the whiskers are the upper and lower adjacent values, which are defined as the relevant quartile ± three-halves of the interquartile range, and the dots refer to changes outside of the adjacent values.

Having such large effects from adaptation is not unexpected (at least in the Chinese context). Studies based on process models have found that the combined effects of changing cultivars, improving farm management practices and reaping the benefits of technological advancement have offset the negative impacts of climatic change on wheat yields in China (Liu et al., 2010; Wang et al., 2012, 2021; Xiao and Tao, 2014). For instance, Tao et al. (2014) conclude that cultivars with longer reproductive growth periods led to an overall yield increase of 0.9–12.9 per cent in northern China from 1981 to 2009. In addition, both process-based studies and statistical analyses indicate that adjustments in growing seasons could mitigate climate change damages (Ding et al., 2016; Zhang et al., 2015). For corn, Cui and Xie (2022) find that the adaptive behaviour in growing season adjustments can avoid up to 9  per cent of the crop damages caused by climate change. By comparing the conventional panel estimates with the long differences estimates, Chen and Gong (2021) also state that long-run adaptations appear to have mitigated 37.9  per cent and 46.8  per cent of the short-run effects of extreme heat on agricultural total factor productivity and land output value, respectively, partially through adjustments in agricultural inputs (such as labour, fertiliser and machinery).

Another interesting finding is that the projections with the conventional panel model roughly lie between projections from the short- and long-run impacts. The evidence becomes more obvious in scenarios with higher temperature increases. This finding seems to echo Mérel and Gammans’s (2021) argument that climatic effects identified by conventional panel models represent a weighted average of underlying short- and long-run responses. With that being said, applications that recover long-run adaptations by comparing long differences estimates with that of a conventional panel model (see examples in Burke and Emerick, 2016; Chen and Gong, 2021) might underestimate the adaptation effects to a certain extent.

Lastly, regardless of how the long-run adaptation effects are revealed (i.e. either through climate penalty terms as in this paper or the long difference model as in Burke and Emerick, 2016; Chen and Gong, 2021), they are always estimated from historical data and thus entail historical adaptive actions. But adaptations in the future could be substantially different from what we have observed nowadays.

6. Conclusion

The agriculture sector is quite vulnerable to climate change as temperature and precipitation are key determinants of crop yields. As one of the major stable crops, a better understanding of climate change effects on wheat is critical for addressing food security challenges, especially in developing nations.

In this paper, we statistically analyse climate change impacts on Chinese winter wheat, highlighting the importance of freezing days and long-run adaptations. Differing from the existing studies that adopt temperature thresholds directly from the literature to construct degree-day variables, we established ours respectively for each growing stage (season), using a data-driven method. On the methodology side, we employed the climate penalty model, recently proposed by Mérel and Gammans (2021), which allows us to explicitly estimate the long-run and short-run yield responses to climate change and thus reveal long-run adaptation effects. We find heat in Fall and freezing days in early Spring are the most important influencers of yields. In particular, from a long-run perspective, a 10 degree-day increase in Fall temperatures over 24°C decreases yields by 7.0 per cent, while a 10 degree-day decrease in Spring freezing conditions increases yields by 8.8 per cent. Such results highlight the importance of accounting for changes in seasonal conditions especially early Spring freezing days when studying climate effects on winter wheat yields. When such effects were omitted, the yield projections under climate change scenarios portend large yield reductions (12.5 per cent to 48.2 per cent) as opposed to small yield gains (1.9 per cent to 2.5 per cent) when freezing is part of the model. Finally, we also find the inclusion of terms that reflect adaptation effects cause substantial changes in projected yields in cases reversing the sign of the climate change impacts.

Undoubtedly, there are limitations. First and foremost, our data restrict us from performing more detailed analyses on irrigation, which could play a critical role in governing yields. Although the robustness checks show that the effect of irrigation seems to be minimal, we cannot completely rule out the possibility it confounds the estimates. Second, the climate penalty framework can only uncover the overall adaptation effects, whereas the effects of specific adaptation strategies cannot be estimated. Third, a number of studies feature more sophisticated models for estimating climate change impacts on yields, such as restricted splines line models in Bucheli, Dalhaus and Finger (2022). How to address long-run adaptation effects in these models remains an open question. We look forward to new developments in this arena.

Acknowledgements

Yabin Da wishes to thank the financial support from the Intergovernmental Panel on Climate Change (IPCC) and the Cuomo Foundation. Fujin Yi acknowledges the financial support from the Joint Agricultural Research Project between National Natural Science Foundation of China (NSFC) and the Bill & Melinda Gates Foundation (BMGF) (72261147758), National Social Science Foundation of China (22VRC178) and Leading Talents Project of Philosophy and Social Science Foundation in Zhejiang Province (24YJRC01ZD). The authors also want to thank valuable comments from Editor Salvatore Di Falco and three anonymous reviewers.

Supplementary data

Supplementary data are available at ERAE online.

Footnotes

References