Empirical specification and estimation strategies

The main empirical specification to determine how higher temperatures affect corn yield response to planting density is defined as follows:

(1)$$\ln( y_{ilzt}) = \alpha_z + f( {\bf tmin}_{lzmt},\; {\bf tmax}_{lzmt},\; {\bf PDSI}^w_{lzmt} ,\; {\bf PDSI}^d_{lzmt},\; {\bf D}_{lzt}) + \gamma {\bf X}_{ilzt} + \eta t + \varepsilon_{ilzt}$$

where ln(y _ilzt) is the natural log of corn yield in bushels per acre (bu/acre) for plot i, field trial location l, production zone z, and year t.Footnote ⁶ We estimate equation 1 using ordinary least squares (OLS) regression that includes a production zone fixed effect α_z to eliminate any concerns about time-invariant unobservables at the production zone level.Footnote ⁷ We also include a linear time trend ηt to account for the technological improvement over time. Control variables that represent input use (or practices) are included in the vector X_ilzt (e.g., fertilizer, tillage, and other variables in Table 1).

We call f( · ) in equation 1 the “weather-plant-density” function, which includes as arguments the following weather-related variables: tmin, tmax, PDSI^w, and PDSI^d for field trial location l, production zone z, month m, and year t. Note that PDSI^w refers to positive PDSI values that measure the degree of wetness (w), while PDSI^d refers to the absolute value of negative PDSI values that reflect the degree of dryness (d). Large PDSI^d values usually reflect drought conditions, and large PDSI^w typically reflect extremely wet conditions (i.e., flooding).Footnote ⁸ The planting density variable (in ’000s of plants per acre) is also included in f( · ) and is represented by D_lzt.

In particular, the “weather-plant-density” function is defined as follows:

(2)$$\eqalign{& \delta {\bf D}_{lzt} + \sum^5_{m = 1} \beta_{1m}{\bf tmin}_{lzmt} + \sum^5_{m = 1} \beta_{2m}{\bf tmax}_{lzmt} + \sum^5_{m = 1}\psi_{1m}{\bf ( tmin}_{lzmt}\times {\bf D}_{lzt}) \cr & \quad + \sum^5_{m = 1}\psi_{2m}{\bf ( tmax}_{lzmt}\times {\bf D}_{lzt}) + \sum^5_{m = 1}\beta_{31m}{\bf PDSI}^w_{lzmt} + \sum^5_{m = 1}\psi_{31m}{\bf ( PDSI}^w_{lzmt}\times {\bf D}_{lzt}) \cr & \quad + \sum^5_{m = 1}\beta_{32m}{\bf PDSI}^d_{lzmt} + \sum^5_{m = 1}\psi_{32m}{\bf ( PDSI}^d_{lzmt}\times {\bf D}_{lzt}) .}$$

The growing season is specified as spanning 5-months (m = 1, 2, …, 5) from May to September. The ψ parameters associated with the interaction terms in equation 2 give us insight into how weather variables affect corn yield response to planting densities. To facilitate inference, we utilize Eicker–Huber–White (EHW) heteroskedasticity robust standard errors.Footnote ⁹

The specification in equations 1 and 2 is consistent with previous studies that examined crop yield effects of weather variables (see Peng et al. Reference Peng, Huang, Sheehy, Laza, Visperas, Zhong, Centeno, Khush and Cassman2004; Lobell and Field Reference Lobell and Field2007; Schlenker and Lobell Reference Schlenker and Lobell2010; Welch et al. Reference Welch, Vincent, Auffhammer, Moya, Dobermann and Dawe2010; Lobell, Schlenker, and Costa-Roberts Reference Lobell, Schlenker and Costa-Roberts2011; Tack, Barkley, and Nalley Reference Tack, Barkley and Nalley2015). These studies typically use the following variables in their specifications: tmin, tmax, and a weather variable that reflects water availability (e.g., typically quadratic functions of precipitation or rainfall). However, in contrast with these aforementioned studies, our specification above utilizes a drought index, specifically the PDSI, as a measure of water availability rather than quadratic functions of precipitation or rainfall levels.Footnote ¹⁰ A drought index like PDSI is appropriate as a measure of water/moisture availability because its values are referenced to local climate, which allows one to calculate dryness or wetness relative to local norms (Xu et al. Reference Xu, Hennessy, Sardana and Moschini2013; Kolář et al. Reference Kolář, Trnka, Brázdil and Hlavinka2014). In addition, local soil attributes are partly accounted for when calculating drought indices, which is an important factor in a crop's ability to handle extreme dryness or wetness. Using both the positive and negative PDSI values in our specification also adequately accounts for nonlinearities in the effects of water availability (i.e., typically reflected by having a quadratic precipitation term in previous studies).

Another feature of the specification in equation 2 is the linear relationship between planting density (D) and crop yields. Previous studies have typically assumed a quadratic specification for planting density (see Assefa et al. (Reference Assefa, Carter, Hinds, Bhalla, Schon, Jeschke, Paszkiewicz, Smith and Ciampitti2018) for example). However, a linear specification is appropriate in our case given that the range of our planting density data does not usually reach the reported “optimal” planting density levels recommended for Wisconsin (i.e., the yield-maximizing planting density level where corn yields plateau (the “turning point”) and consequently decreases in a quadratic specification). For example, Stanger and Lauer (Reference Stanger and Lauer2006) suggest that the optimal planting densities for Wisconsin are approximately 39,984 plants per acre for non-GM corn and 42,290 plants per acre for GM corn with the Bt trait (for the period between 2002 and 2004). Based on field trial data locations across the corn belt, Assefa et al. (Reference Assefa, Carter, Hinds, Bhalla, Schon, Jeschke, Paszkiewicz, Smith and Ciampitti2018) indicate that optimal planting density ranges from 30,500 plants per acre (in 1987) to about 37,900 plants per acre in the 2007–2016 period. In our field trial data from 1990 to 2010, the range of planting density values is from about 18,250 plants per acre to around 33,409 plants per acre. This data range is more consistent with the upward sloping (and close to linear) part of the corn yield response function to planting density, which again supports our linear specification. Furthermore, a straightforward regression of the natural log of corn yield on planting density using our data set indicates a relationship that is very close to linear and without a turning point (see Supplementary Figure S5).

Marginal effects

To achieve the study objective of assessing how the yield impact of planting density changes with temperature, we calculate the marginal effect of planting density on corn yields under different temperature scenarios based on the empirical model specified in equations 1 and 2. The marginal percentage effect of increasing plant density is the percentage change in corn yields as a result of a 1 unit (in this case, 1,000 plants per acre) increase in planting density. This marginal effect calculation can be expressed as follows:

(3)$${\partial \ln( {y_{t}}) \over {\bf \partial D}_{t}} = \delta + \sum^5_{m = 1}\psi_{1m}{\bf tmin}_{mt} + \sum^5_{m = 1}\psi_{2m}{\bf tmax}_{mt} + \sum^5_{m = 1}\psi_{31m}{\bf PDSI}^w_{mt}$$

if PDSI in each month is positive, and:

(4)$${\partial \ln( {y_{t}}) \over {\bf \partial D}_{t}} = \delta + \sum^5_{m = 1}\psi_{1m}{\bf tmin}_{mt} + \sum^5_{m = 1}\psi_{2m}{\bf tmax}_{mt} + \sum^5_{m = 1}\psi_{32m}{\bf PDSI}^d_{mt}$$

if all monthly PDSIs are negative.

In order to examine how temperature changes influence the yield response to planting density, we calculate marginal effects under two higher-temperature scenarios: (1) a scenario where both tmin and tmax change by 1°C increments, and (2) a scenario where tmin and tmax change separately by 1°C increments. To calculate the marginal effects of planting density under the first high-temperature scenario, we first assume that both the monthly tmin and tmax variables deviate from their means by the following amounts: − 1°C, − 2°C, − 3°C, − 4°C, +1°C, +2°C, +3°C, +4°C. This calculation structure allows us to see how corn yield response to planting density changes as both the minimum and maximum temperatures change (holding PDSI constant at its mean).Footnote ¹¹ The marginal effect of planting density under the first high-temperature scenario can then be expressed as follows:

(5)$${\partial \ln ( {y_{t}}) \over {\bf \partial D}_{t}} = \delta + \sum^5_{m = 1}\psi_{1m}( [ 1.1] {\overline{\bf tmin}}_{mt} + k) + \sum^5_{m = 1}\psi_{2m}( \xoverline[ 1.1] {\overline{\bf tmax}}_{mt} + k) + \sum^5_{m = 1}\psi_{31m}\xoverline[ 1.1] {\overline{\bf PDSI}}_{mt}$$

where $\xoverline [ 1.1] {\overline{\bf tmin}}_{mt}$, $\xoverline [ 1.1] {\overline{\bf tmax}}_{mt}$, and $\xoverline [ 1.1] {\overline{\bf PDSI}}_{mt}$ are set at the means in month m and year t, and the nine assumed temperature deviations are where k = −4, − 3, …, 0, …, + 3, + 4.Footnote ¹²

Under the second higher-temperature scenario, the marginal effects of planting density are calculated assuming that tmin and tmax separately change in 1°C increments (where k = −4, − 3, …, 0, …, + 3, + 4). The marginal effect of planting density when only tmin changes can be calculated as follows:

(6)$${\partial \ln( {y_{t}}) \over {\bf \partial D}_{t}} = \delta + \sum^5_{m = 1}\psi_{1m}( \xoverline[ 1.1] {\overline{\bf tmin}}_{mt} + k) + \sum^5_{m = 1}\psi_{2m}\xoverline[ 1.1] {\overline{\bf tmax}}_{mt} + \sum^5_{m = 1}\psi_{31m}\xoverline[ 1.1] {\overline{\bf PDSI}}_{mt},\; $$

where tmax and the PDSIs are held at their mean values. On the other hand, the marginal effect of planting density when only tmax changes can be expressed as follows:

(7)$${\partial ln( {y_{t}}) \over {\bf \partial D}_{t}} = \delta + \sum^5_{m = 1}\psi_{1m}\xoverline[ 1.1] {\overline{\bf tmin}}_{mt} + \sum^5_{m = 1}\psi_{2m}( \xoverline[ 1.1] {\overline{\bf tmax}}_{mt} + k) + \sum^5_{m = 1}\psi_{31m}\xoverline[ 1.1] {\overline{\bf PDSI}}_{mt}$$

where tmin and the PDSIs are held at their mean values.

The marginal effect calculations above assume that changes in temperature occur in all months of the season. However, previous literature has argued that the June to August months are the critical months for corn growth. During this period, crop growth is frequently affected by environmental stresses such as high temperatures (McWilliams, Berglund, and Endres Reference McWilliams, Berglund and Endres1999). Since silking occurs in the summer time, stress conditions that happen two weeks before or after silking typically lead to substantial reductions in yield (see McWilliams, Berglund, and Endres Reference McWilliams, Berglund and Endres1999). Therefore, we also calculate the marginal effects of increasing planting density under both the scenarios described above, but only imposing changes in the temperatures for the June to August months (i.e., and where temperatures in the other months are set at their means).

Another issue of interest in this study is to determine the role of GM corn varieties, especially those that have RW-resistant traits, with regard to how corn yield responds to planting density under different high-temperature scenarios (i.e., the “quadruple” inter-relationship among corn yields, planting density, GM traits, and high temperatures). Given this interest, we modify the “weather-planting-density” function in (2) to allow for “triple” interaction terms among the planting density variable, the weather variables, and GM corn varietal dummy variables. In this case, the corn varieties in the field trial data set are categorized into three groups: conventional varieties, GM-RW hybrids, and other GM hybrids. Note that GM-RW hybrids are those varieties that have RW resistance, either as a single-trait GM crop with only RW resistance, or a “multi-stack” variety with RW resistance combined with other traits (i.e., such as a double-stack GM with combined above-ground corn borer resistance together with below-ground RW resistance). The “other GM hybrids” category includes those GM varieties with GM traits, but specifically without the RW resistance trait (e.g., single-trait Bt corn with resistance only to European corn borers).

With the GM variety categorization above, the “weather-planting-density” specification in (2) is modified as follows (to include the GM variety dummies and triple interaction terms):

(8)$$\eqalign{& \delta {\bf D}_{lzt} + \sum^2_{r = 1} \zeta_r{\bf V}^r_{ilzt} + \sum^2_{r = 1}\eta_r ( {\bf D}_{lzt}\times {\bf V}^r_{ilzt}) + \sum^5_{m = 1} \beta_{1m}{\bf tmin}_{lzmt} + \sum^5_{m = 1} \beta_{2m}{\bf tmax}_{lzmt} \cr & \quad + \sum^5_{m = 1}\beta_{31m}{\bf PDSI}^w_{lzmt} + \sum^5_{m = 1}\beta_{32m}{\bf PDSI}^d_{lzmt} + \sum^2_{r = 1}\sum^5_{m = 1}\theta_{1rm}( {\bf tmin}_{lzmt}\times {\bf V}^r_{ilzt}) \cr & \quad + \sum^2_{r = 1}\sum^5_{m = 1} \theta_{2rm}( {\bf tmax}_{lzmt}\times {\bf V}^r_{ilzt}) + \sum^2_{r = 1}\sum^5_{m = 1}\theta_{31rm}( {\bf PDSI}^w_{lzmt}\times {\bf V}^r_{ilzt}) \cr & \quad + \sum^2_{r = 1}\sum^5_{m = 1}\theta_{32rm}( {\bf PDSI}^d_{lzmt}\times {\bf V}^r_{ilzt}) + \sum^5_{m = 1}\psi_{1m}( {\bf tmin}_{lzmt}\times {\bf D}_{lzt}) \cr & \quad + \sum^5_{m = 1}\psi_{2m}( {\bf tmax}_{lzmt}\times {\bf D}_{lzt}) + \sum^5_{m = 1}\psi_{31m}( {\bf PDSI}^w_{lzmt}\times {\bf D}_{lzt}) + \sum^5_{m = 1}\psi_{32m}( {\bf PDSI}^d_{lzmt}\times {\bf D}_{lzt}) \cr & \quad + \sum^2_{r = 1}\sum^5_{m = 1}\kappa_{1rm}( {\bf tmin}_{lzmt}\times {\bf D}_{lzt}\times {\bf V}^r_{ilzt}) + \sum^2_{r = 1}\sum^5_{m = 1}\kappa_{2rm}( {\bf tmax}_{lzmt}\times {\bf D}_{lzt}\times {\bf V}^r_{ilzt}) \cr & \quad + \sum^2_{r = 1}\sum^5_{m = 1}\kappa_{31rm}( {\bf PDSI}^w_{lzmt}\times {\bf D}_{lzt}\times {\bf V}^r_{ilzt}) + \sum^2_{r = 1}\sum^5_{m = 1}\kappa_{32rm}( {\bf PDSI}^d_{lzmt}\times {\bf D}_{lzt}\times {\bf V}^r_{ilzt}) }$$

where $V^r_{ilzt}$ represents the GM variety dummy variables for plot i, field trial location l, production zone z, and year t. In the specification above, conventional corn hybrids are designated as the base group (e.g., the omitted category) and V ^r are dummy variables that represent the two GM varietal groups, where r = 1 corresponds to the GM-RW hybrids, and r = 2 refers to the other GM hybrids. Among the 28,521 plots in the field trial data, there are 17,680 with conventional corn, 4,044 with GM-RW hybrids, and 6,797 with the other GM hybrids. The change in varietal adoption rate over time for the four production zones is shown in Figures S6, S7, and S8.

Given the “weather-planting-density” specification in equation 8, the marginal yield effect of increasing planting density for conventional corn under the first high-temperature scenario (for k = −4, − 3, .., 0, .., + 3, + 4) can then be calculated as follows:

(9)$${\partial \ln( {y_{t}}) \over {\bf \partial D}_{t}} = \delta + \sum^5_{m = 1}\psi_{1m}( \xoverline[ 1.1] {\overline{\bf tmin}}_{mt} + k) + \sum^5_{m = 1}\psi_{2m}( \xoverline[ 1.1] {\overline{\bf tmax}}_{mt} + k) + \sum^5_{m = 1}\psi_{31m}\xoverline[ 1.1] {\overline{\bf PDSI}}_{mt}$$

where the weather variables are set at their mean values in all 5 months of the growing season. On the other hand, the marginal effect of increasing planting density for the GM-RW hybrids can be written as:

(10)$$\eqalign{& {\partial \ln( {y_{t}}) \over {\bf \partial D}_{t}} = \delta + \eta_1 + \sum^5_{m = 1}\psi_{1m}( \xoverline[ 1.1] {\overline{\bf tmin}}_{mt} + k) + \sum^5_{m = 1}\psi_{2m}( \xoverline[ 1.1] {\overline{\bf tmax}}_{mt} + k) \cr & \quad + \sum^5_{m = 1}\kappa_{11m}( \xoverline[ 1.1] {\overline{\bf tmin}}_{mt} + k) + \sum^5_{m = 1}\kappa_{21m}( \xoverline[ 1.1] {\overline{\bf tmax}}_{mt} + k) + \sum^5_{m = 1}\psi_{31m}\xoverline[ 1.1] {\overline{\bf PDSI}}_{mt} \cr & \quad + \sum^5_{m = 1}\kappa_{311m}\xoverline[ 1.1] {\overline{\bf PDSI}}_{mt}}$$

where the weather variables are again set at their mean values in all 5 months of the growing season. Similarly, the marginal effect of increasing planting density for the other GM hybrids can be calculated as follows:

(11)$$\eqalign{& {\partial \ln( {y_{t}}) \over {\bf \partial D}_{t}} = \delta + \eta_2 + \sum^5_{m = 1}\psi_{1m}( \xoverline[ 1.1] {\overline{\bf tmin}}_{mt} + k) + \sum^5_{m = 1}\psi_{2m}( \xoverline[ 1.1] {\overline{\bf tmax}}_{mt} + k) \cr & \quad + \sum^5_{m = 1}\kappa_{12m}( \xoverline[ 1.1] {\overline{\bf tmin}}_{mt} + k) + \sum^5_{m = 1}\kappa_{22m}( \xoverline[ 1.1] {\overline{\bf tmax}}_{mt} + k) + \sum^5_{m = 1}\psi_{31m}\xoverline[ 1.1] {\overline{\bf PDSI}}_{mt} \cr & \quad + \sum^5_{m = 1}\kappa_{312m}\xoverline[ 1.1] {\overline{\bf PDSI}}_{mt}}$$

where the weather variables are again set at their mean values in all 5 months of the growing season. Although not shown here, similar marginal effect calculations can also be computed for the second high-temperature scenario, and for the case where we only consider temperature changes in June to August months.

High-temperature effects

To determine the influence of higher temperatures on the yield effects of planting density, we calculate the marginal effects of increasing planting density under the two scenarios described in the previous section and present results in Table 3. For the first high-temperature scenario, where both tmin and tmax are assumed to change by 1°C increments, we find that the yield benefit of increasing planting density is reduced by 1.86 percent (95 percent CI [1.67, 2.05]) for every 1°C increase in the minimum and maximum temperatures in each month of the cropping season. This result suggests that the yield benefits of increasing planting density diminish in the presence of higher temperatures.

Table 3. Estimated changes in the effects of plant density on yield as a result of 1°C increase in temperatures

Notes: (1) The results here are estimated through our main specification in equations 1 and 2. (2) The first column indicates what weather variables the marginal effects of plant density are based on. The first row indicates a 1°C increase in both tmin and tmax. The second row refers to a scenario where only tmin increases by 1°C. The third row refers to a 1°C increase in tmax. (3) The second and the third column report coefficients and p-values of the changes in the marginal effects of plant density as a result of higher temperatures (both tmin and tmax increase, and tmin and tmax separately increase) where the temperature of each month of the May–September growing season increases by 1°C. The last two columns provide coefficients and p-values of the changes in the marginal effects where the temperature of each month from June to August increases by 1°C.

As described in the previous section, we also calculate the marginal effect of increasing planting density as temperature deviates from the mean by 1°C increments (see equation 5). The results of these marginal effect calculations are graphically presented in Figure 2. The mean temperature result in Figure 2 indicates that, for average weather conditions in the study area (e.g., average minimum and maximum temperatures, as well as average PDSI), increasing planting density would negatively affect corn yields (albeit by a relatively small percentage amount). Moreover, as the minimum and maximum temperatures increase relative to the mean, increasing planting density becomes more detrimental to corn yields (e.g., a 1,000 plants per acre increase in planting density results in more than 5 percent yield reduction when minimum and maximum temperatures increase by more than 3°C from the mean). On the other hand, note that increasing planting density has a positive marginal effect on yield when temperatures are lower than the mean. The diminishing marginal effect of increasing planting density in a higher-temperature environment is consistent with the idea that inter-plant competition for nutrients and resources (i.e., water) intensifies as planting density increases, and this competition escalates further when temperatures increase.

Figure 2. Marginal Percentage Effect of Plant Densities as tmin and tmax of Each Month Deviate from the Mean by 1°C Increments. Notes: The main specification in equations 1 and 2 is implemented. The Impacts are reported as the percentage change in yield. The vertical solid lines show 90 percent confidence interval.

To better contextualize the magnitudes of our estimates, we conduct a simple back-of-the-envelope calculation. First, consider the average corn yields (176.4 bu/acre) and the average planting density in the sample (28,440 plants/acre). Then, from Figure 2, we make the assumption that when tmin and tmax are at their means, increasing planting density does not change yields (i.e., there is close to zero yield impact of increasing planting density). Thus, if we increase average planting density by 1,000 plants/acre (to 29,4400) and our temperature variables remain at the mean, then yields will still be around 176.4 bu/ac. Now suppose that tmin and tmax increase by 1°C (as in our first scenario), then our findings suggest that yields will fall by 1.86 percent compared to the scenario where there are no changes in mean temperatures. In this case, yields will be around 173.11 bu/ac (= 176.4 × 0.9814) where 0.9814 = 1 − 0.0186. This suggests that when tmin and tmax increase by 1°C, increasing planting density will result in a yield reduction of about 3.29 bu/ac. This does not seem like a large reduction, but if a farmer operates 1,000 acres and corn price is at $5/bu (consistent with prices in spring 2021), this is a revenue loss of $16,450 in one cropping season. For farms with thin margins, this revenue loss from high temperatures is substantial.

Results from the second higher-temperature scenario, where we assume that tmin and tmax increase separately in 1°C increments in all months, are fairly consistent with the marginal effect estimates calculated in the first scenario described above (see Table 3). But we note that increases in tmax tend to have a larger negative impact on the yield effects of increasing planting density (as compared to the impact of increases in tmin). This suggests that increases in daytime temperatures are more likely to negatively influence yield response to increasing planting density. This result is in line with Kucharik and Serbin (Reference Kucharik and Serbin2008) where they find that tmax plays a stronger role than tmin in creating variability for Wisconsin corn.

For the case where the two higher-temperature scenarios are applied only to the critical growth months of June to August, the marginal effect estimates are still largely consistent with the results from the earlier results where increasing temperatures affect all growing season months (see Table 3 and Supplementary Figure S11). The general pattern of results in Supplementary Figure S11 is almost the same as in Figure 2. However, the magnitudes of the temperature effects are relatively smaller for the case where increasing temperatures are only felt in the June to August months.

GM traits and temperature effects

The role of GM traits is examined based on the empirical specification in equations 1 and 8. Parameter estimates for the specification that includes the GM dummy variables (and the corresponding interactions) are presented in Supplementary Table S2. Similar to the results in Supplementary Table S1, the planting density effect on corn yields is positive if GM traits and weather variables are not taken into account.

The marginal effects of increasing planting density that considers GM traits under our two increasing temperature scenarios are presented in Table 4. Results from these marginal effect calculations generally suggest that the negative effect of higher temperatures is more strongly felt for conventional corn varieties, as compared to the GM-RW hybrids and other GM hybrids. That is, the marginal yield effect of increasing planting density is more negatively affected by increasing temperatures when conventional varieties are used. Hence, the adverse effect of higher temperatures on the yield–planting-density relationship is less for GM corn in general.

Table 4. Estimated changes in the effects of plant density on yield as a result of 1°C increase in temperatures (accounting for the type of corn hybrid)

Notes: (1) The table displays coefficients and p-values of the changes in the marginal effects of plant density as a result of 1° in temperatures. The results are calculated from the estimated results of the model specification in equations 1 and 8 (the specifications including interactions among the weather, plant density, and GM varietal dummy variables). (2) The first column indicates what weather variables the marginal effects of plant density are based on. The first row of the first panel indicates a 1°C increase in both tmin and tmax. The first row of the second panel refers to a scenario where only tmin increases by 1°C. The first row of the third panel refers to a situation where only tmax increases by 1°C. (3) The second column indicates the hybrid groups: “RW” is GM hybrids expressing Bt trait for corn rootworm. “other GM” refer to GM hybrids without Bt trait for corn rootworm. (4) The third and fourth column report coefficients and p-values of the changes in marginal effects of plant density as a result of higher temperatures (both tmin and tmax increase, and tmin and tmax separately increase) where the temperature of each month of the May–September growing season increases by 1°C. The last two columns provide coefficients and p-values of the changes in marginal effects where the temperature of each month from June to August increases by 1°C.

To better visualize the role of GM traits, we graph the marginal effects of increasing planting density under the first high-temperature scenario (i.e., increasing both tmin and tmax in all months) but separating it out by the hybrid type—conventional, GM-RW, and other GM (see Figure 3). First, at the mean temperature levels, it is important to note that increasing planting density results in a negative yield impact for conventional corn yields. In contrast, for GM-RW hybrids and other GM hybrids, the marginal yield effect of increasing planting density is positive at mean temperature levels. Second, the positive marginal effect of increasing planting density is higher for GM-RW hybrids as compared to the other GM hybrids. Moreover, even at temperatures above or below the mean level, the positive marginal effect of planting density for GM-RW hybrids is still consistently larger than the other GM hybrids. Lastly, the slope of the marginal effect line for the conventional hybrids is steeper than those of the GM-RW and other GM hybrids, suggesting that the marginal effect of increasing planting density diminishes more rapidly (as temperature rises) for conventional corn, relative to the GM-RW and other GM hybrids. Overall, these results provide some evidence that the typical yield benefits of increasing planting density can be more easily maintained under high-temperature conditions if corn varieties with GM traits are used. This outcome suggests that corn varieties with GM traits (especially GM-RW hybrids) may be more efficient in utilizing nutrients and moisture even under intensified inter-plant competition due to increasing planting density and higher temperatures. Moreover, the GM trait results here support the idea that the use of GM varieties may have facilitated the increases in planting density over time.

Figure 3. Marginal Impacts of Plant Density for the Three Corn Hybrid Groups, as tmin and tmax of Each Month Deviate from the Mean by 1°C Increments. Notes: The figure shows the results of the model specification in equations 1 and 8 (i.e., models including interaction terms among weather, planting density, and GM varietal group dummy variable). Impacts are reported as the percentage change in yield. The vertical solid lines show 90 percent confidence interval.