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Impacts of rising temperatures and farm management practices on global yields of 18 crops


Understanding the impact of changes in temperature and precipitation on crop yields is a vital step in developing policy and management options to feed the world. As most existing studies are limited to a few staple crops, we implemented global statistical models to examine the influence of weather and management practices on the yields of 18 crops, accounting for 70% of crop production by area and 65% by calorific intake. Focusing on the impact of temperature, we found considerable heterogeneity in the responses of yields across crops and countries. Irrigation was found to alleviate negative implications from temperature increases. Countries where increasing temperature causes the most negative impacts are typically the most food insecure, with the lowest calorific food supply and average crop yield. International action must be coordinated to raise yields in these countries through improvement and modernization of agricultural practices to counteract future adverse impacts of climate change.


As part of the 17 United Nations Sustainable Development Goals (SDGs), governments have agreed on a target to end hunger and ensure access to sufficient, nutritious food by 2030 for 850 million people classified as undernourished globally1. Given the SDGs’ interlinked nature2, failure to reach this target risks undermining many others. Achieving food security represents an important challenge, bearing in mind increases in global population, rising levels of affluence, a shift towards diets consumed in Organisation for Economic Co-operation and Development countries and climate change3,4,5. Indeed, the global food production system is particularly vulnerable to climate change, directly through the impact of temperature and precipitation6,7, and indirectly through competition for land with negative emissions technologies and afforestation8.

As the effect of climate change on crop yield is an established concern for global food security9, the impact of historical variation in weather has provided valuable insights7,10,11,12, with both process-based and statistical models reaching similar conclusions about the impact of future climate9,13,14. Since the current literature has so far focused on a few staple crops, there is an identified need to broaden our understanding across a wider range of crop types15.

By implementing statistical modelling, we assess the impact of weather variation on crop yield for 18 crops. Specifically, empirical literature has primarily focused on the impact of weather on six major crops, namely wheat, maize and soybeans10,11,16, rice10,16, barley11,12,17 and sugar beet12,17. Our analysis also includes cassava, cotton, groundnuts, millet, oats, potatoes, pulses, rapeseed, rye, sorghum, sunflower and sweet potatoes. Together, these crops represent 70% of the global crop area18 and around 65% of global calorific intake. Besides modelling a wider set of crops, we extend previous approaches10 by accounting for additional factors affecting crop yield—including pesticides, fertilizers and irrigation—to provide insights into the role of agronomy in ameliorating the impacts of changing climate. We focus our discussion on the effect of temperature given that the empirical relationship of crop yield with temperature is much better understood than with other weather factors19 (and, in some cases, temperature was found to be the predominant factor in explaining crop yield variability20).


Marginal impact and optimal growing conditions

We estimated an inverted-U-shaped relationship between temperature and crop yield for all 18 crops, with the values for the optimal temperature reflecting credible conditions of crop production (Supplementary Table 1). Statistically significant estimates for precipitation are harder to achieve, also reflecting previous results21. In 10 of the 18 crops assessed in this study, an increase of 10 mm in precipitation induces a decrease in the yields, evaluated at the global mean, while in the remaining crops the impact is positive. Analysis of the impact of a 1 °C rise in temperature on the set of 12 crops rarely assessed in the literature highlights a negative impact across the majority of countries growing cassava, cotton, groundnuts, millet, oats, pulses and rye, and a positive impact for those crops with the highest levels of global consumption (that is, potatoes, sweet potatoes, rapeseed and sorghum). From a food-security perspective, three crops widely consumed in developing countries tend to be either positively affected (sorghum and sweet potatoes) or suffer a small reduction in the yield (cassava) in response to a 1 °C increase. By definition, the marginal effect described assumes no changes in other factors, when in reality changes in temperature are likely to occur in the presence of changes in other factors, such as precipitation. In some cases, the changes in temperature considered here could imply lack of analogue historical climatic conditions22. Such ‘novel climates’ greatly increase the uncertainty of the estimated impacts of our models, as extrapolation occurs outside the sample used in the estimation.

Our results support the role of adaptation in global agriculture, as we demonstrate that agricultural management practices such as irrigation can ameliorate the negative impacts on crop productivity. Pesticides and fertilizers are generally found to enhance crop productivity. The use of pesticides has a positive impact on the yield of about half of the crops in our sample, specifically potatoes, pulses, rice, sugar beet, sunflower, sweet potatoes and wheat. Fertilizer use contributes to increasing yields of sugar beet, sunflower and sweet potatoes. The impact of pesticides and fertilizer is modelled through a linear approximation without allowing for interaction with other factor such as temperature.

Figure 1 illustrates the functional relationship between crop yield and temperature in countries with low irrigation (black curve) and high irrigation (red curve), using cassava as an example. The curves are obtained by assigning the value zero to all of the non-temperature variables in Supplementary Table 1 (except irrigation), since using a different value for those variables would affect the level of the yield but not the shape of the yield–temperature relationship. In Fig. 1, the gently sloping curves indicate a relatively small variation in the marginal effect of temperature as temperature changes (that is, the first derivative of the red and black curves). In fact, for cassava, the impact of a 1 °C increase in temperature across the globe varies between −3% and 1% in both countries with low levels of irrigation and those with high levels. Irrigation allows for a higher optimal temperature (that is, the vertex of the parabolas in the figure). These are about 26 °C in countries with high levels of irrigation compared to about 20.5 °C in the remaining countries.

Fig. 1: Functional relationship between temperature and crop yield of cassava.

The red dots indicate the global mean (middle point) and the points that are 4 °C colder and warmer than the global mean. The marginal effect of temperature increasing 1 °C is indicated at these three points in Fig. 2a. The functional relationship is indicated by the red curve when irrigation is low, and the black curve when irrigation is high.

Estimated optimal temperatures tend to occur near the global mean for a number of crops (Fig. 2a). This implies that warming temperatures will deliver yield increases, at least initially, in some of the growing countries. The number of countries benefiting from temperature rises however decreases with the magnitude of the rise, as more and more countries are pushed beyond the optimal temperature. More detailed results from the statistical crop yield models can be found in Supplementary Table 1.

Fig. 2: Impacts of rising temperatures on crop yield and food safety globally for barley, cassava, cotton and groundnuts.

a, The functional relationship between temperature and crop yield. The global temperature mean computed over 1986–2012 in the countries cultivating a specific crop is indicated by the central dot and vertical dashed line. The other two dots indicate temperatures 4 °C warmer and 4 °C colder than the global mean. The percentage next to the dots indicates the marginal effect, as explained in Fig. 1. b, The geographical distribution of the marginal effect related to a 1 °C temperature rise. The colours indicate the percentage change in the crop yield for a country expected as a consequence of an increase of 1 °C. The range of the colour scale reflects the marginal sensitivity to temperature estimated in our study. c, The frequency distribution of crop yield (kilograms per hectare) by country with the marginal effect of a 1 °C temperature increase. For each point in the bars of the histogram, the colours indicate the value of the marginal effect according to the colour scale in b. d, The frequency distribution of crop yield (kilograms per hectare) by average calorie intake (kilocalories per capita per day), using the same colour scheme as the one described for the histograms in c.

Heterogeneous marginal impact of temperature across the globe

Major crops tend to be negatively affected by a 1 °C increase, as a 2.8%, 2.6% and 2.4% decrease in the yield is estimated for rice, maize and wheat, when evaluated at the global mean temperature of each crop. This contrasts with yields of potatoes and soybeans that increase by 1.5% and 2.2% respectively. Comparison of the marginal effect at the global mean is reductive as the effect of temperature varies across countries. Winners and losers from rising temperatures can be identified by evaluating the marginal effect of a 1 °C increase from the mean observed in each country over the 1986–2012 sample (Methods). The maps in Figs. 2b, 3b, 4b, 5b and 6b clarify that most countries are negatively (red countries) instead of positively (blue countries) affected. Maize, oats, pulses and wheat are widely impacted by rising temperatures, as the yield decreases in almost all countries while potatoes, sorghum, soybeans and sugar beet overall benefit from rising temperatures. The plots in Figs. 2b, 3b, 4b, 5b and 6b show the sensitivity of different crops to increases in the temperature. Ranges as wide as 30 percentage points can be observed in the case of millet, pulses, rapeseed, rice and rye. Conversely, cassava, oats and potatoes are among the crops least affected by a 1 °C increase, with the range of marginal impact being under 10 percentage points in all cases (Figs. 3 and 4). However, crops with a highly diverse marginal impact of temperature tend have a much smaller range for the great majority of countries where they are grown. As an example, the range of the marginal impact in 80% of the countries where rice is grown is only half the width shown in Fig. 4.

Fig. 3: Impacts of rising temperatures on crop yields and food safety globally for maize, millet, oats and potatoes.

More details can be found in the caption of Fig. 2.

Fig. 4: Impacts of rising temperatures on crop yields and food safety globally for pulses, rapeseed, rice and rye.

More details can be found in the caption of Fig. 2.

Fig. 5: Impacts of rising temperatures on crop yields and food safety globally for sorghum, soybeans, sugar beet and sunflowers.

More details can be found in the caption of Fig. 2.

Fig. 6: Impacts of rising temperatures on crop yields and food safety globally for sweet potatoes and wheat.

More details can be found in the caption of Fig. 2.

Impact on food security and productivity

The wide productivity differences across countries will be exacerbated by rising temperatures, unless corrective action is taken. We explore this by assessing the relationship between the prevailing yield and the marginal effect of temperature, as shown in Figs. 2c, 3c, 4c, 5c and 6c. The highest positive marginal effects are scattered throughout the geographical distribution of crop yield, while the most negative impacts tend to be in countries, such as those in sub-Saharan Africa, that have not benefited from the green revolution23. This is particularly strong in the case of barley, maize, millet, pulses, rice and wheat. A similar pattern can be observed in the case of the relationship between the daily intake of calories and the marginal impact of temperature (Figs. 2d, 3d, 4d, 5d and 6d), as most of the countries that are worst affected by warming temperatures have a very low daily calorific intake. This is a concerning finding, as the countries with the worst level of food security (as measured by the daily intake of calories) are also worst affected by rising temperature.


Crop dependence on temperature and agronomic practice

Weather variables significantly contribute to the yield variability of the 18 crops studied here. Our analysis confirms results from existing global studies focusing on maize, rice, soybeans and wheat10,21 and shows at the global scale that potato, the most widely produced non-grain crop in the world, and sorghum and soybeans are resilient to moderate increases in temperature—confirming previous results in the case of soybeans24.

In five of the modelled crops, irrigation implies higher optimal temperatures and a more positive impact of rising temperatures. This confirms, at the global scale, the results from previous studies focused on the United States11,25,26. Irrigation has been argued to limit evapotranspiration demand related to heat10 and have cooling effects on the canopy temperature, reducing the impact of heat and drought stress on crop yield27. Similarly, the role of irrigation intervals in maximizing the functioning of the stomata and enhancing photosynthetic and yield efficiency has been examined in the literature28. Some producers facing negative impacts of temperature (for example, Israel and Greece) have invested in irrigation (the effects of rising temperatures would have been worse without such schemes). Expansion of irrigation may be possible in some cases, but in many countries, notably in Africa, expansion of land under irrigation is impractical or impossible29. Alternative options for the management of rainfall (for example, through collection and soil management) exist and should be integrated into agricultural policy where appropriate29.

Countries with very low yields use a low amount of pesticides and fertilizers, while highly productive countries tend to have a higher-than-average consumption of pesticides and fertilizers. For example, wheat yields in the 10 countries with the highest level of pesticides (4,177 kg ha−1) were more than double the level observed in the 10 countries with the lowest consumption (1,857 kg ha−1). As pesticides and fertilizers have a strong effect on a number of crops, some of the yield difference across countries could be overcome by increasing their use, although this may be associated with other environmental challenges. We observe that high use of fertilizers and pesticides may serve to even out the effect of management intensity across countries and so compensate for decreases in the yield brought about by rising temperatures. Although not explored in this study, the interaction between marginal impacts of temperature and the use of fertilizers and pesticides should be urgently addressed by empirical studies. As an example, evidence of the marginal effect of temperature being lower in African countries with low use of fertilizers has been discussed before30. Similarly, as rising temperatures facilitate the diffusion of pests31, the marginal impact of weather can be influenced by the level of pesticides. In both cases, future research should explore the suitability of nonlinear functions—rather than adopting the linear approximation discussed here—to consider, for example, decreasing marginal gains from the application of chemical inputs, or their interactions with other factors such as temperature. The level of pesticides and fertilizers could in principle be a proxy for other aspects of management such as mechanization or advanced cultivars, but only if there is correlation between these factors and fertilizers or pesticides in a significant number of countries.

Additional adaptation options

The wide range of marginal impacts from temperature increases seen across the 18 crops suggests that replacing highly sensitive crops with those more resilient to temperature increase is a potential adaptation strategy to rising temperatures. While likely to take place across countries, this substitution may severely impact the diversity of crops used in agriculture. This is an aspect that should be assessed as a matter of urgency by empirical studies. Development of crop varieties matched to not only current conditions but also those likely to develop in the coming decades is an area of substantial current research interest32. Notably in Africa, where many countries worst affected by rising temperatures are located, the green revolution has been harder to establish due to a broad range of environmental and socio-economic factors23. Maize yields in the United States were found to be less sensitive to extreme heat days in hotter climates33, demonstrating that the response to temperature can be substantially reduced by the choice of cultivars. On the other hand, a trade-off between yield levels and the robustness to heat has also been found among new varieties34. Typically associated with higher environmental and/or economic costs, increased use of agricultural chemicals and expansion of cropping area are obvious routes to address food insecurity, which could decrease reliance on imports. From an environmental sustainability perspective, these routes are obviously problematic and could be counterproductive for meeting the SDGs agenda.

With regard to changing growing season, early planting dates failed to increase the US yield of maize, millet and wheat35, but higher yields of US maize could be obtained if high planting rates are combined with delayed planting dates36. This seems an area where further research is also urgently required, especially taking into consideration the impact of changing a crop’s planting and harvest dates on the crops that are planted subsequently. Crop switching is another factor potentially reducing the impact of rising temperatures on crop yield37. The negative welfare impact arising from the climate scenarios for Africa in 2100 could be fully counteracted by switching crops38. Qualitative studies focusing on specific locations however point out obstacles to crop switching, primarily influenced by economic, political and social rather than climate factors39. Benefits arising from crop switching can be highly crop-dependent even when assessed for the same location40.

Another factor that might help counteract the negative impact of rising temperatures is CO2 fertilization. C3 crops (that is, rice, wheat, soybeans, rye, barley, cassava and potatoes) are more sensitive to CO2 compared to C4 crops (that is, maize, sorghum and sugar cane), with low sensitivity in the latter due to CO2 being already saturated, although increases in transpiration efficiency might occur under dry conditions41. Crop response to elevated CO2 remains the largest source of uncertainty in crop yield studies42, but expected gains have been revised downwards by free-air concentration enrichment studies, which are more representative of field growing conditions than earlier chamber studies43. The impact of CO2 fertilization was found to reduce or disappear under wetter, drier and/or hotter conditions when the forcing variable exceeded its intermediate regime44. In addition, increasing CO2 is expected to negatively affect the quality of grains by reducing the overall protein content45 and may require large quantities of fertilizers41. Incorporating the effects of CO2 in empirical modelling is challenging, as CO2 does not have any spatial variation and changes only slowly across time. A number of potential avenues have been discussed previously9. Introduction of CO2 fertilization in process-based models is more straightforward, but without greater clarity on the impact of CO2 from free-air concentration enrichment studies, coefficients used in process-based models are likely to be highly unreliable.

Implications for food security and productivity

Our results investigate the relationship between the impact of rising temperatures and the existing level of crop yields for a large set of crops and over a wide temperature range. In fact, we look explicitly at the existing level of crop yield rather than using proxies such as latitude and gross domestic product42,46. There are a number of institutional routes to address the impacts of warming temperatures on food security and productivity, although substantial costs and barriers may be associated with them. These include increasing technology transfer to the worst affected countries and sharing targeted agronomic research advances. International donors might facilitate these processes and coordinated action to raise yields through improved agronomic practices and modernization of the agronomic system, while managing potentially negative effects of farming intensification47. This is particularly important in countries with prevailing low productivity and inadequate diets48.

Changing harvesting area is also an important consideration for food security and productivity. Our research flags the countries that are likely to stop production of a certain crop (that is, those with high marginal negative impact and low productivity). New marginal producers (that is, countries with climatic conditions similar to those with the highest positive marginal impact49) are also likely to emerge. Finally, the role of international trade in this context should also be explored, bearing in mind that rising temperatures are likely to impact international trading patterns as the absolute advantage to trade is projected to change across countries.



The models described below explore the sensitivity of crop yield to a number of factors, including weather, but also irrigation and management practices such as the use of pesticides and fertilizers, by making use of a dataset that spans the 1986–2012 period. The analysis is implemented for 18 crops: barley, cassava, cotton, groundnuts, maize, millet, oats, potatoes, pulses, rapeseed, rice, rye, sorghum, soybeans, sugar beet, sunflowers, sweet potatoes and wheat. This set of crops uses all of the data (with the exception of yams) available in a commonly used gridded crop calendar50, which is required to compute weather variables as described below. The specification search, which follows the general-to-specific framework51 in terms of the modelling approach and the variables used in the model, incorporates considerations related to statistical significance, and therefore the precision of the estimates, as well as the sign of the estimated marginal impacts from agronomic literature and previous studies. Our analysis covers at most the years between 1986 and 2012, although the specific start and end years vary across countries and modelled crops, as a result of shorter available time span for some of the variables (see below). The time period used in this study is comparable to that of previous contributions11,12,13,17,18 and is considered adequate to analyse the implications of weather factors for crop yields. The countries covered in the dataset vary across crops, reflecting requirements in terms of growing conditions and dietary habits.


Crop yield is defined as the harvested production per unit of harvested area with data collected from the online dataset of the Food and Agriculture Organization of the United Nations (FAO); that is, FAOSTAT Database Agricultural Production. These are annual time series at the country level. Weather variables are included in terms of their monthly average weighted across the growing season. Data for irrigation, pesticides and fertilizers are available only for total agricultural activity (for example, tons of fertilizers used in the agricultural sector as a whole, rather than in the cultivation of a specific crop). In addition, fertilizer data are available for a limited number of countries compared to the set of countries for which crop yield data are available. These are limitations of the available datasets that influence the way in which specification search is implemented, as discussed below.

  • Information for pesticides, defined as the average use per area of cropland (kilograms per hectare), is taken from FAOSTAT Database Inputs. Annual data are available at the earliest from 1990 onwards for 164 countries, although the actual start year of the dataset varies across countries.

  • Data for irrigation (area irrigated in hectares) are obtained from the Global Map of Irrigation Areas used by FAO’s Information System on Water and Agriculture (AQUASTAT). This dataset is available for the year 2005 for 196 countries. We computed irrigated agricultural areas as a percentage of agricultural areas by using agricultural area retrieved from FAOSTAT Database Inputs and we then divided countries into two groups, those with intensive irrigation systems (that is, countries with more than 10% of their agricultural area being irrigated (a group of 39 countries)) and those not characterized by an intensive irrigation system (that is, countries with less than 10% of their agricultural area being irrigated (resulting in a set of 157 countries)).

  • Data for fertilizers, taken from IFASTAT of the International Fertilisers Association, are expressed as consumption (in metric tons) of grand total nitrogen in 2005 for 109 countries. By using cropland information from FAOSTAT Database Inputs, we express consumption of fertilizers per hectare of cropland, to obtain data comparable to those available for pesticides.

  • The weather variables include country-level temperature (measured in degrees Celsius) and precipitation (measured in millimetres). We follow established practice in the literature11,17 to construct weather variables by averaging monthly weather observations based on a constant crop growing season39 and areas where the crop is cultivated19. Thus, only weather fluctuations specific to the production of each crop are considered, leading to a precise identification of the impact of temperature and precipitation on yield. This implies combining three different datasets:

  1. (1)

    monthly average of temperature and precipitation on a grid of 30-min resolution, collected from the Climate Research Unit of the University of East Anglia52;

  2. (2)

    a map of cropland at 5-min resolution19; and

  3. (3)

    a crop calendar, which provides the growing season for each crop at 5-min resolution39.

The weather variables correspond to daily (or diurnal) average temperature and total precipitation, by combining monthly anomalies and monthly climatology41. All crops have one growing season in the crop calendar39, apart from maize, rice and wheat—which have main and secondary seasons and for which we used the main season (similarly to ref. 11). The possibility of multiple cropping on the same land plot should not have an impact on the outcome of this analysis, as the focus is the crop yield and not land requirements for cropping.

Our analysis uses country-level datasets owing to the obvious difficulty of accessing global datasets at the sub-country level. The need to use datasets covering multiple countries also influenced our choice of weather variables. As historical hourly weather data are challenging to aggregate across a variety of growing regions26, our study follows the established practice of using monthly averages of temperature and precipitation in linear and quadratic terms11,13,18. Such specifications align with the agronomic literature with regard to crops best growing within a range of temperature and precipitation, beyond which weather factors become harmful for production. We pool together all countries growing a specific crop, as previous analyses with specific country groups11 have shown that the estimated impact of temperature and precipitation is comparable across groupings.

The choice of the time span for this study (1986 to 2012) mirrors other studies in the literature11. However, for the models including pesticides, the start year of the sample in this study is 1990 owing to data availability. Our analysis covers at most the time span from 1986 to 2012 to maintain comparability with existing studies12,17,18,53 and across models estimated in this article. We followed the majority of contributions in the literature by adopting panel approaches to benefit from a much higher number of observations, a dataset incorporating more variation compared to a single time series, and the ability to control for omitted variables—especially if their variation across time is limited. On the one hand, estimation is also more straightforward as, from a statistical perspective, there is no need to deal with stochastic or deterministic trends as one would when dealing with a single time series. On the other hand, given the global coverage of our dataset and the possibility of large differences in cultivars and agronomic practice between countries, optimal growing conditions could vary considerably. Evidence against this possibility has been explored in a dataset similar to the one used in this study11. Subgrouping of countries in the panel was not found to be very influential on the results of that analysis. In addition, the optimal temperature in the case of sugar beet estimated here is very similar to those we obtained using a time-series approach for single European countries, as part of the follow-up study to ref. 7. It is important to mention that a different optimal temperature does not necessarily imply a change in the value of the marginal effect, which is the key metric in this study, as the marginal effect for a specific country is determined not only by the optimal temperature but also by the curvature of the parabola being estimated.

Statistical models

This study makes use of a comprehensive collection of panel data models, with the subscripts i and t indicating country and year, respectively. The most general model includes a country-specific quadratic trend (t, t2), an individual specific time-invariant component, αi, a common time-variant component, λt, and a set of observed variables potentially affecting crop yield, included in the vector Xit. This specification, in which yit represents the logarithm of crop yield and εit represents a random disturbance, reads as follows:

$$y_{it} = \alpha _i + \lambda _t + \rho _{1i}t + \rho _{2i}t^2 + {{{\bf{\upbeta}}{\bf{X}}}}_{it} + \varepsilon _{it}$$

where β and ρ are the related set of paramaters. In the second-most general model, the common time-variant component, λt, is dropped so that:

$$y_{it} = \alpha _i + \rho _{1i}t + \rho _{2i}t^2 + {{{\bf{\upbeta}} {\bf{X}}}}_{it} + \varepsilon _{it}$$

while by dropping the country-specific quadratic trend and reinserting the common time-variant component, λt, one obtains:

$$y_{it} = \alpha _i + \lambda _t + {{{\bf{\upbeta}} {\bf{X}}}}_{it} + \varepsilon _{it}$$

It is worth noting that the coefficients of the quadratic time trends are allowed to differ across countries, while the coefficients of all other components are assumed to be constant across countries11. By including country-specific time trends, we aim to account for factors such as technological advance or other time-varying features that could possibly influence crop productivities. We capture country-based unobserved effects by estimating models using either fixed effects or random effects; the choice between the two is based on the Hausman test. In the case of soybeans, omitted variable bias is absorbed by estimating the model in first differences. A global trend is included in this case, instead of a country-specific trend, based on the relative fit of the model. We also estimated models pooling the dataset and providing estimates based on country-specific averages across time (individual between estimator) or time-specific averages across countries (time effects between estimator).

Set of explanatory variables

In our analysis of the impact of weather factors and management practices on crop yield, the most general set of control variables, \({\mathbf{X}}_{it}^1\), includes:

  1. 1.

    temperature and precipitation incorporated in both their levels and their squared terms11;

  2. 2.

    an indicator of the extent to which irrigation is deployed in the whole agricultural sector, with the indicator taking a value equal to one for countries with more than 10% of their agricultural area being irrigated and a value equal to zero otherwise. This indicator is interacted with the linear terms of the weather variables, so that temperature and precipitation are allowed to have a different optimal value in countries making extensive use of irrigation;

  3. 3.

    use of pesticides and fertilizers in the whole agricultural sector.

$$\begin{array}{l}{{{\bf{\upbeta}} {\bf{X}}}}_{{it}}^1 = \left[ \beta _1{\rm{Temp}}_{it}^2 + \beta _2{\rm{Temp}}_{it} {\rm{Irr}}_i + \beta _3{\rm{Temp}}_{it} + \beta _4{\rm{Prec}}_{it}^2 + \beta _5{\rm{Prec}}_{it} {\rm{Irr}}_i\right.\\\qquad\qquad\qquad\left. + \beta _6{\rm{Prec}}_{it} + \beta _7{\rm{Pest}}_{it} + \beta _8{\rm{Fert}}_{it} \right]\end{array}$$

When the full vector of controls was not used, our attention was primarily focused on the interaction between irrigation and temperature, following recent studies exploring such a relationship12. For this reason, we chose to start dropping the factors related to management practices (that is, Pestit and Fertit), and only if no viable models are delivered by the search specification below, we drop the interaction term between irrigation and weather factors (that is, TempitIrri and PrecitIrri), so that the set of variables included in the models are respectively:

$$\begin{array}{l}{{{\bf{\upbeta}} {\bf{X}}}}_{{it}}^2 = \left[ \beta _1{\rm{Temp}}_{it}^2 + \beta _2{\rm{Temp}}_{it} {\rm{Irr}}_i + \beta _3{\rm{Temp}}_{it} + \beta _4{\rm{Prec}}_{it}^2\right.\\\qquad\qquad\qquad\left. + \beta _5{\rm{Prec}}_{it} {\rm{Irr}}_i + \beta _6{\rm{Prec}}_{it} \right]\end{array}$$
$${{{\bf{\upbeta}} {\bf{X}}}}_{{it}}^3 = \left[ {\beta _1{\rm{Temp}}_{it}^2 + \beta _3{\rm{Temp}}_{it} + \beta _4{\rm{Prec}}_{it}^2 + \beta _6{\rm{Prec}}_{it} + \beta _7{\rm{Pest}}_{it} + \beta _8{\rm{Fert}}_{it}} \right]$$

Finally, the simplest set of explanatory weather variables includes only weather factors:

$${{{\bf{\upbeta}} {\bf{X}}}}_{{it}}^4 = \left[ {\beta _1{\rm{Temp}}_{it}^2 + \beta _3{\rm{Temp}}_{it} + \beta _4{\rm{Prec}}_{it}^2 + \beta _6{\rm{Prec}}_{it}} \right]$$

Specification search

We follow the general-to-specific approach38, both in terms of the selection of the explanatory variables and the statistical models being estimated. With regard to the statistical models discussed above, our methodology goes from the most general to the most specific model, by implementing models

  1. 1.

    with both country-specific quadratic time trends and common time effects (equation (1));

  2. 2.

    only country-specific quadratic time trends (equation (2));

  3. 3.

    only common time effects (equation (3));

  4. 4.

    models where data are pooled across either time or countries.

With regard to the explanatory variables used in the estimation, we move from the most general set (that is, \({\mathbf{X}}_{{it}}^1\)) to the most specific (that, is \({\mathbf{X}}_{{it}}^4\)). During the specification search, a model is considered to be congruent to the underlying data-generating process of crop yield if

  1. 1.

    the relationship between yield and temperature has an inverted-U functional shape;

  2. 2.

    coefficients of pesticides, fertilizers and irrigation indicators are statistically significant;

  3. 3.

    the optimal temperature observed in countries with intensive irrigation systems is higher than that in countries where irrigation use is low;

  4. 4.

    the impact of pesticides on crop yield is positive.

Data for irrigation, pesticides and fertilizers are observed for the agricultural sector as a whole rather than for a specific crop. In addition, these variables are available for a limited number of countries and time periods compared to the crop yield and weather. For these reasons, condition (2) above is imposed, so that these variables are retained only if they contribute to explaining the crop yield in a statistically significant fashion. We therefore use statistical significance to discern whether the variables observed for the whole agricultural sector can be used as a proxy for the impact of intensification and management practices for the specific crop at hand, therefore tackling the limitation that crop-specific fertilizer, pesticide and irrigation data are not available at the global scale. As a further criterion to discern the sensible impact of irrigation and pesticides, we require the optimal temperature observed in the countries with intensive irrigation systems to be higher than the optimal level in countries where irrigation use is low12—see condition (3) above. A positive relationship between the use of pesticides and protection of crop quality and yield is well established54, so that we explicitly require the coefficient of pesticides to be positive—condition (4). Yet, evidence on the relationship between the use of fertilizers and crop yield is less conclusive55, so that we do not impose a similar requirement on the coefficient of fertilizers. Condition (1) above arises from the fact that it reflects a plausible assumption for the growing conditions of crops, and is a common assumption in economic studies and increasingly used in the econometric crop yield literature11,13 to indicate that crops benefit from moderate weather changes and are damaged under extreme circumstances. The effect of precipitation is harder to identify compared to the temperature effect, with precipitation coefficients being non-statistically significant18. Furthermore, climate models disagree on the sign of the effect of precipitation changes56, an indication of the uncertainty surrounding the impact of this factor on yield. For this reason, we do not impose condition (1) for precipitation, with our procedure limited to dropping the quadratic term when the coefficient is positive.

Our specification search is therefore the following.

  1. 1.

    We run each statistical model described above with the set of variables in equation (4) and assess the suitability of the estimated models (that is, the N + P + I + W models in Supplementary Fig. 4, where N, P, I and W represent nitrogen/fertilizers, pesticides, irrigation and weather, respectively), based on the conditions above.

  2. 2.

    If none of the models satisfies the search criteria above, we simplify the set of control variables by estimating the I + W models, the N + P + W models dropping either N or P if one contradicts the conditions above, and the W models in Supplementary Fig. 4, in this order.

  3. 3.

    As soon as the applicable conditions are met, we stop the search procedure and select the final model. This occurs in the case of all crops.

Models delivered by this specification search are comparable to those in the literature when assessed on the basis of the amount of variation in the crop yield explained by the models. For instance, our adjusted R2 is 57% and 35% for maize and sorghum—which are comparable, for instance, to 47% and 29%17.

Marginal effect and optimal level of weather factors

For the final models identified through the specification search described above, we computed the optimal level of each weather factor, taking into account the interaction with the irrigation dummies. In the case of temperature, as an example, the optimal temperature for countries where irrigation use is deemed negligible can be computed as \(V_{{\rm{Temp}}} = - \frac{{\beta _3}}{{2\beta _1}}\), whereas for countries using a high level of irrigation, the optimal level is equal to \(V_{{\rm{Temp}} - {\rm{Irr}}} = - \frac{{(\beta _2 + \beta _3)}}{{2\beta _1}}\). For each model, we computed the coefficient of determination (R2) with and without adjusting for the variables used in the regression. Standard errors robust to heteroscedasticity and serial correlation were estimated to assess the significance of the coefficients in the models, as shown in Supplementary Table 1.

In addition, for each model we computed the effect of temperature and precipitation in relation to a change of 1 °C and 10 mm. As we estimated a quadratic relationship, the effect varies across the level of the weather factor at which the effect is computed. As an example, the impact of a 1 °C temperature increase starting from the level T0 for countries where irrigation use is deemed negligible can be computed as:

$${\rm{ME}}_{{\rm{Temp}}}^{1^\circ\, {\rm{C}}} = 2\beta _1 + \beta _3T_0$$

while for countries using high irrigation, the impact of a 1 °C temperature increase is equal to:

$${\rm{ME}}_{{\rm{Temp}}}^{1^\circ\,{\rm{ C} }}= 2\beta _1 + \left( {\beta _2 + \beta _3} \right)T_0$$

The impact of a temperature increase different from 1 °C can be obtained by simply multiplying \({\mathrm{TE}}_{{\mathrm{Temp}}}^{1^\circ\, {\mathrm{C}}}\) by any specific increase in temperature. Supplementary Table 1 reports the marginal effect evaluated at the global mean, observed over 1986–2012. In Supplementary Table 1, we also present the impact observed in response to a change in temperature and precipitation equal to the average standard deviation, computed by averaging the standard deviation observed in each country in the sample used in this study, to obtain a global average of the standard deviation of the weather factors observed in each country. This has been computed at the global mean.

Data availability

The data used in this study are available through the repository

Code availability

The scripts used in the estimation of the models and the production of the figures displayed in the main body of the paper are available through the repository


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The authors of this work have been supported as follows—P. Agnolucci, C.R., V.D.L. and P.E.: the Grantham Foundation, the UK Energy Research Centre through its Resource and Vectors theme (award EP/L024756/1) and the Addressing the Value of Nature and Energy Together (ADVENT) programme (Award NE/M019799/1); P. Alexander: the Resilience of the UK food system to Global Shocks (RUGS, BB/N020707/1); F.E. and R.H.: the UK Energy Research Centre through its Resource and Vectors theme (Award EP/L024756/1), the Addressing the Value of Nature and Energy Together (ADVENT) programme (Award NE/M019713/1) and the ERC grant SCALEFORES (grant agreement ID: 680176).

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All authors developed the research methodology. P. Agnolucci, V.D.L. and C.R. collected the data and computed the variables used in the estimation. P. Agnolucci and C.R. implemented the estimation. All authors contributed to writing up results.

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Correspondence to Paolo Agnolucci.

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Supplementary information

Supplementary Information

Discussion on the historic variation in yields and model performance, discussion on the effect of weather, irrigation, pesticides and fertilizers on crop yields, Supplementary Figs. 1–4 and Table 1.

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Agnolucci, P., Rapti, C., Alexander, P. et al. Impacts of rising temperatures and farm management practices on global yields of 18 crops. Nat Food 1, 562–571 (2020).

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