# Assessing the Effectiveness of the Actuaries Climate Index for Estimating the Impact of Extreme Weather on Crop Yield and Insurance Applications

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Statistical Models for Crop Yields Prediction

#### 2.2. Machine Learning-Based Methods and Simulation Approaches for Crop Yields Prediction

#### 2.3. Extreme Weather Events for Crop Yields Prediction

#### 2.4. Other Variables Affect Crop Yields

#### 2.5. Extreme Weather Events and Insurance Applications

## 3. Background of the Actuarial Climate Index

## 4. Data

#### 4.1. Crop Yields Data

#### 4.2. The Actuaries Climate Index Data

#### 4.3. The High-Level Resolution Climate Data

## 5. Statistical Models

#### 5.1. Linear Regression Model

#### 5.2. Generalized Linear Model—Probit Regression Model

- Step 1: Compute the 25th percentile of the detrended corn yields;
- Step 2: Set the yields lower than the 25th percentile as “1”, which means there is a loss, and the part above the 25th percentile data as “0”, which means there is no loss.

## 6. Empirical Analysis

#### 6.1. Midwest Analysis with the Combined Actuaries Climate Index

^{2}value of 0.8917 and two significant variables, July and September ACI. The coefficient of the July ACI illustrates that extreme weather conditions may have negative effects on corn yields. The coefficient of the September ACI is positive. One possible reason is that high daytime warm temperatures might offset the adverse effects of cold nights in September. The coefficients of ACI_4, ACI_5, ACI_6, and ACI_8 are not significant. Column 3 shows the linear regression results without the insignificant variables, dropping variables starting from the one with the highest p-value, step by step. All remaining variables are significant, and the R

^{2}value is as high as 0.8901. The fit of the linear regression model implies that changes in ACI variables explain about 89% of the changes in corn yields across the Midwest. Overall, the model is significant, as shown by the significance of the F-test statistic at a 0.1% significance level.

^{2}value of 0.1617 is calculated by the formula:

^{2}. The lower pseudo R

^{2}might imply that the combined ACI might have fewer insights when modeling corn yield losses since a pseudo R

^{2}value between 0.2 and 0.4 could represent a very good fit.

#### Midwest Analysis with Individual Component Variables of the Actuaries Climate Index

^{2}value is as high as 0.9548 and the F-test statistic is high enough to imply that all explanatory variables together significantly explain corn yields. The R

^{2}values are comparable to those reported in existing studies, such as [43], indicating reasonable goodness of fit. Furthermore, the R

^{2}values using the individual components are higher than using the original ACI variables. This indicates that relaxing the predetermined weights of the variables in the ACI construction could improve the predictive accuracy of corn yields.

^{2}of 0.9535 and five significant variables, shown in Table 2, column 4.

^{2}and pseudo R

^{2}. This paper continues to use the manual selection method in the following analysis but provides the results from backward stepwise selection for comparison and reference in the Appendix A.

^{2}value of the probit model indicates a good fitness since it is close to 0.4. Furthermore, even though the pseudo R

^{2}is gradually decreasing, the AIC value and p-value of the Chi-square test are both declining as well. It might demonstrate that the simplest model, as a whole, has a better fit compared to the original probit model (ANOVA chi-square test is based on the current model and the null model). The backward stepwise selection results are the same as the simplest model and are shown in Table A4, column 3.

#### 6.2. Midwest Analysis with Annual State-Level Data

- Step 1: Calculate the mean and standard deviation of CDD in the reference period 1961 to 1990, written as ${\mu}_{f}$ and ${\sigma}_{f}$;

- Step 2: Calculate the standardized CDD for year i in each state k within the Midwest from 1961 to 2016, using the formula $\frac{CD{D}_{\left(i,k\right)}-{\mu}_{f}}{{\sigma}_{f}}$.

^{2}value of the linear regression model is 0.7504, and the pseudo R

^{2}value of the probit regression model is 0.0739. After adding a state effect variable to the linear regression model, the R

^{2}value grows to 0.7607, and the significance of the state variable might imply that locations are highly correlated to crop yields. However, all of these R

^{2}s are still smaller than the results in Section 6.1. This result might be due to the fact that yearly data is an averaged evidence of the entire year and ignores the monthly or daily extrema. In addition, the state-level might still be a large spatial scale and may eliminate local extrema.

#### 6.3. Iowa Analysis with Standardized High-Level Resolution Climate Data

- Step 1: Calculate the mean and standard deviation of PDSI for each month m in the reference period 1961 to 1990, written as ${\mu}_{f}\left(m\right)$ and ${\sigma}_{f}\left(m\right)$;
- Step 2: Calculate the standardized PDSI for month m of year i in each county k within Iowa from 1961 to 2018, using the formula $\frac{pds{i}_{\left(m,i,k\right)}-{\mu}_{f}\left(m\right)}{{\sigma}_{f}\left(m\right)}$.

^{2}is 0.7982, indicating that this model with standardized high-level resolution climate data is appropriate. Further, except for two insignificant variables, July PDSI and June precipitation, all other variables are statistically significant. In addition, the F-test statistic is high enough to imply that all explanatory variables together significantly explain corn yields. Moreover, we remove pr_6 and pdsi_7 in the next two steps to get better-fit models as a result (shown in Table 5, columns 3 and 4), the significance level of the estimated coefficients is the same as the second column, and the R

^{2}value of 0.7982 does not change. Compared to the results in Section 6.1, this simplest linear regression model contains more effective coefficients. The backward stepwise selection results in the same as the simplest model and is shown in Table A6, column 2.

^{2}values of the original probit model and simplest probit model, 0.2867 and 0.2864, are very close and could represent that both models are a good fit.

#### 6.4. Midwest Analysis with Standardized High-Level Resolution Climate Data

^{2}value of 0.7126 is acceptable, although it is smaller than the R

^{2}values of the models using ACI data. It might imply that changes in high-level resolution weather variables could explain about 71.26% of the corn yield changes across the Midwest. The F-test statistic is significant and demonstrates that all these variables together fit and explain corn yields well.

^{2}of the simplest model, 0.2341, is the same as the pseudo R

^{2}of the original probit regression and could represent a good fitness.

^{2}of these two models is moderately improved to 0.2536. In addition, the AIC value and p-value of the ANOVA Chi-square test of the probit regression model with more variables (Lasso selection) are smaller than the values of the probit model only with self-selected variables and demonstrate that the probit model with more variables could better explain the effectiveness of the high-level resolution ACI for estimating corn yield losses (the ANOVA Chi-square test is based on the current model and the original probit regression). The backward stepwise selection method is applied to the original probit model and the probit model with the variables selected based on both the Lasso approach and experience. The results are the same as the simplest models and are shown in Table A7, columns 3 and 4.

#### 6.5. Rolling Window Predictive Analysis

## 7. Conclusions and Discussion

## 8. Future Research

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Variable Abbreviation | Variable Description |
---|---|

CDD | Maximum number of consecutive dry days in a year with precipitation less than one millimeter |

Rx5Day | Maximum rainfall per month in five consecutive days |

T10 | Change in frequency of cooler temperatures below the 10th percentile |

Tn10 | Percentage of days when the daily minimum temperature is less than the 10th percentile of the reference period |

T90 | Change in frequency of warmer temperatures above the 90th percentile |

Tx90 | Percentage of days when the daily maximum temperature is greater than the 90th percentile of the reference period |

WP90 | Frequency of wind speed above the 90th percentile |

psdi | Palmer Drought Severity Index |

pr | Precipitation |

tmmn | Average monthly minimum temperature |

tmmx | Average monthly maximum temperature |

soil | Soil moisture |

time | Estimation year |

Midwest ACI Data | ||||

N = 58 | ||||

Variables | Min. | Max. | Mean | Std. dev. |

CDD_6 | −1.5200 | 1.6200 | −0.2228 | 0.826686 |

CDD_7 | −1.5100 | 1.5800 | −0.2228 | 0.837129 |

Rx5Day_5 | −2.3600 | 3.1700 | 0.2216 | 1.075954 |

Rx5Day_6 | −2.8600 | 2.7900 | 0.3293 | 1.086263 |

Rx5Day_7 | −1.9500 | 2.4500 | 0.1081 | 1.013655 |

Rx5Day_8 | −1.8600 | 2.6100 | 0.0603 | 1.026407 |

T10_4 | −1.5800 | 5.3400 | 0.0966 | 1.257771 |

T10_5 | −1.5000 | 2.0600 | −0.0107 | 0.931239 |

T10_9 | −1.7300 | 2.9100 | −0.1960 | 0.947877 |

T90_6 | −1.4900 | 3.4200 | 0.0419 | 0.869365 |

T90_7 | −1.4200 | 3.3100 | −0.0452 | 1.072289 |

T90_8 | −1.1400 | 3.2300 | −0.0090 | 0.916306 |

WP90_6 | −2.0000 | 2.4700 | −0.0519 | 0.959081 |

Midwest State-Level ACI Data | ||||

N = 448 | ||||

Variables | Min. | Max. | Mean | Std. dev. |

Rx5Days | −3.0069 | 3.3768 | 0.1416 | 7.055175 |

Tn10 | −3.4417 | 2.6049 | −0.6697 | 2.834646 |

Tx90 | −2.6841 | 3.5244 | −0.0742 | 3.126361 |

CDD | −1.7955 | 3.2369 | −0.0929 | 5.162458 |

Iowa | Midwest | |||||||
---|---|---|---|---|---|---|---|---|

N = 5742 | N = 39,567 | |||||||

Variables | Min. | Max. | Mean | Std. Dev. | Min. | Max. | Mean | Std. Dev. |

pdsi_5 | −2.2089 | 2.4257 | 0.2369 | 0.9235 | −2.8968 | 2.7909 | 0.2197 | 0.9634 |

pdsi_6 | −2.1255 | 2.8809 | 0.2810 | 0.9640 | −3.0956 | 3.2119 | 0.2450 | 0.9805 |

pdsi_7 | −2.0579 | 3.1031 | 0.2855 | 1.0049 | −3.3342 | 3.4489 | 0.2567 | 1.0043 |

pr_5 | −2.1374 | 4.1245 | 0.2233 | 1.0853 | −2.0385 | 4.9146 | 0.1300 | 1.0406 |

pr_6 | −1.9785 | 4.4164 | 0.2075 | 1.1000 | −2.0814 | 5.6135 | 0.1683 | 1.0733 |

pr_7 | −2.1185 | 4.7036 | −0.0063 | 1.0682 | −2.1026 | 5.3021 | 0.0378 | 1.0226 |

pr_8 | −1.6730 | 3.9577 | 0.0393 | 1.0099 | −2.0023 | 4.9549 | −0.0004 | 0.9564 |

pr_9 | −1.6081 | 3.4128 | −0.1191 | 0.8677 | −1.7247 | 5.2737 | −0.0442 | 0.9430 |

tmmn_4 | −4.2684 | 3.0962 | 0.0633 | 1.0847 | −3.7637 | 3.3897 | 0.0744 | 1.0185 |

tmmn_5 | −2.3074 | 3.3706 | 0.1385 | 0.9498 | −3.5180 | 3.3233 | 0.1413 | 0.9930 |

tmmn_6 | −3.2213 | 3.9836 | 0.3211 | 1.0449 | −5.1971 | 3.4176 | 0.2040 | 0.9881 |

tmmn_7 | −3.2254 | 3.5331 | 0.0854 | 1.0876 | −4.7108 | 3.1205 | 0.1064 | 1.0149 |

tmmn_8 | −2.9774 | 3.8303 | 0.1778 | 1.0520 | −3.6873 | 3.3509 | 0.1649 | 1.0146 |

tmmn_9 | −3.0840 | 3.0610 | 0.1807 | 1.0536 | −3.3779 | 3.0657 | 0.0988 | 0.9565 |

tmmx_5 | −2.3430 | 2.9852 | −0.0271 | 0.9485 | −3.9462 | 2.9478 | 0.0162 | 0.9473 |

tmmx_6 | −3.6915 | 3.0492 | −0.0573 | 0.9724 | −5.0084 | 2.8003 | 0.0058 | 0.9499 |

tmmx_7 | −3.8262 | 3.5587 | −0.1971 | 1.1176 | −5.0404 | 4.2726 | −0.0735 | 1.0334 |

tmmx_8 | −2.6017 | 3.7864 | −0.0768 | 0.9583 | −3.6573 | 3.6903 | 0.0115 | 0.9895 |

tmmx_9 | −3.9046 | 2.7694 | 0.1893 | 1.0727 | −4.0176 | 2.6574 | 0.0828 | 0.9721 |

soil_6 | −1.4541 | 3.6462 | 0.3125 | 1.0964 | −1.5698 | 4.4239 | 0.1609 | 1.0362 |

soil_7 | −1.3344 | 4.8123 | 0.2354 | 1.1375 | −1.3969 | 6.0008 | 0.1532 | 1.0864 |

Region | KPSS Test for Stationarity |
---|---|

p-Value | |

Midwest | Below 0.01 |

IL | Below 0.01 |

IN | Below 0.01 |

IA | Below 0.01 |

MI | Below 0.01 |

MO | Below 0.01 |

OH | Below 0.01 |

WI | Below 0.01 |

Variables | Simplest Linear Regression | Simplest Probit Regression |
---|---|---|

Intercept | 67.32980 *** | −0.7595 *** |

CDD_6 | ||

CDD_7 | ||

Rx5Day_5 | ||

Rx5Day_6 | ||

Rx5Day_7 | 1.98864 ^{†} | |

Rx5Day_8 | 2.79095 * | |

T10_4 | ||

T10_5 | 0.4222 ^{†} | |

T10_9 | −2.85146 * | 0.4200 ^{†} |

T90_6 | ||

T90_7 | −5.45714 *** | 0.7353 ** |

T90_8 | −5.76785 *** | 0.4278 |

WP90_6 | ||

Time | 1.83177 *** | |

N | 58 | 58 |

R^{2} (Pseudo R^{2}) | 0.9535 | 0.3451 |

AIC | 411.2117 | 53.426 |

F-test statistic/ANOVA Chi-square test (p-value) | 174.2 *** | 0.0001338 *** |

^{2}(Pseudo R

^{2}) values, and F-test statistics during each step. “

^{†}”, “*”, “**”, and “***” indicate significance at 10%, 5%, 1%, and 0.1% levels, respectively.

Variables | Simplest Linear Regression | Simplest Probit Regression |
---|---|---|

Intercept | 65.01863 *** | −0.83610 *** |

pdsi_6 | 2.68789 *** | −0.25164 *** |

pdsi_7 | ||

pr_5 | −2.77632 *** | 0.26529 *** |

pr_6 | ||

pr_7 | 4.03047 *** | −0.21372 *** |

pr_8 | −2.83344 *** | 0.20966 *** |

tmmn_4 | −0.61710 * | |

tmmn_5 | −0.56257 ^{†} | 0.05174 * |

tmmn_9 | 5.08391 *** | −0.23903 *** |

tmmx_6 | 0.60951 ^{†} | |

tmmx_7 | −5.00016 *** | 0.37875 *** |

tmmx_8 | −9.62043 *** | 0.59262 *** |

soil_6 | 3.04412 *** | |

soil_7 | −8.29728 *** | 0.38068 *** |

Time | 1.89820 *** | |

N | 5742 | 5742 |

R^{2} (Pseudo R^{2}) | 0.7982 | 0.2864 |

AIC | 49,193.75 | 4777.72 |

F-test statistic/ANOVA Chi-square test (p-value) | 1738 *** | 0.7723 |

^{2}(Pseudo R

^{2}) values, and F-test statistics during each step. “

^{†}”, “*”, and “***” indicate significance at 10%, 5%, and 0.1% levels, respectively.

Variables | Simplest Linear Regression (Lasso Selection) | Simplest Probit Regression | Simplest Probit Regression (Lasso Selection) |
---|---|---|---|

Intercept | 63.593053 *** | −0.756608 *** | −0.726714 *** |

pdsi_5 | −7.356485 *** | 0.626712 *** | |

pdsi_6 | 14.471175 *** | −0.019064 ^{†} | −0.906566 *** |

pdsi_7 | −6.178364 *** | 0.269595 *** | |

pr_5 | 0.663937 *** | −0.105575 *** | −0.065205 *** |

pr_6 | 2.120822 *** | −0.280150 *** | −0.111829 *** |

pr_7 | 8.913359 *** | −0.439158 *** | −0.443344 *** |

pr_8 | −0.730487 *** | 0.041241 *** | |

pr_9 | 1.169836 *** | ||

tmmn_4 | −0.425323 * | −0.137153 *** | −0.063977 *** |

tmmn_5 | −0.153493 *** | −0.066655 * | |

tmmn_6 | 4.916094 *** | ||

tmmn_7 | 6.375701 *** | −0.328385 *** | |

tmmn_8 | 7.210296 *** | −0.226689 *** | |

tmmn_9 | −4.729296 *** | −0.155197 *** | 0.034804 ^{†} |

tmmx_5 | 4.394181 *** | −0.075420 ** | |

tmmx_6 | 4.189060 *** | −0.352383 *** | −0.411686 *** |

tmmx_7 | −11.271298 *** | 0.321780 *** | 0.555092 *** |

tmmx_8 | −17.524793 *** | 0.479800 *** | 0.708800 *** |

tmmx_9 | 7.564631 *** | −0.134287 *** | |

soil_6 | 0.910250 ** | 0.073061 *** | 0.066103 ** |

soil_7 | −8.339541 *** | 0.430947 *** | 0.410685 *** |

Time | 1.566997 *** | ||

N | 39,567 | 39,567 | 39,567 |

R^{2} (Pseudo R^{2}) | 0.7297 | 0.2341 | 0.2536 |

AIC | 350,336.1 | 35,293 | 34,406 |

F-test statistic /ANOVA Chi-square test (p-value) | 5085 *** | 0.2529 | <2.2 × 10^{−16} *** |

^{2}(Pseudo R

^{2}) values, and F-test statistics during each step. “

^{†}”, “*”, “**”, and “***” indicate significance at 10%, 5%, 1%, and 0.1% levels, respectively.

**Figure A1.**Annual weighted average corn yields in the Midwest (N = 58). Note: The 1958–2018 annual weighted average corn yields in the Midwest show an upward trend.

**Figure A2.**Distribution of annual weighted average corn yields in the Midwest (N = 58). Note: The 1958–2018 annual weighted average corn yields in the Midwest show a roughly right-skewed distribution.

**Figure A3.**Distribution of annual state-level corn yields in the Midwest (N = 448). Note: The annual corn yields from 1958 to 2018 of all states in the Midwest show an approximately right-skewed distribution.

**Figure A4.**Distribution of annual county-level corn yields in Iowa (N = 5742). Note: The annual corn yields from 1958 to 2018 of all counties in Iowa show a roughly normal distribution.

**Figure A5.**Distribution of annual county-level corn yields in the Midwest (N = 39,567). Note: The annual corn yields from 1958 to 2018 of all counties in the Midwest show a right-skewed distribution.

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Variables | Linear Regression | Linear Regression | Probit Regression |
---|---|---|---|

Intercept | 66.8829 *** | 67.15695 *** | −0.76085 |

ACI_4 | 3.5330 | −0.44542 | |

ACI_5 | −1.5629 | 0.09833 | |

ACI_6 | −3.2987 | 0.80559 | |

ACI_7 | −6.9927 * | −6.24302 ^{†} | 0.76382 ^{†} |

ACI_8 | −5.6327 | −6.16164 ^{†} | 0.55087 |

ACI_9 | 8.2069 * | 7.80479 * | −1.11165 * |

time | 1.8737 *** | 1.86356 *** | |

N | 58 | 58 | 58 |

R^{2} (Pseudo R^{2}) | 0.8917 | 0.8901 | 0.1617 |

AIC | 69.582 | ||

F-test statistic | 58.82 *** | 84.22 *** |

^{†}”, “*”,and “***” indicate significance at 10%, 5%, and 0.1% levels, respectively.

Variables | Linear Regression | Linear Regression without CDD | Simplest Linear Regression |
---|---|---|---|

Intercept | 67.11794 *** | 67.17533 *** | 67.32980 *** |

CDD_6 | 2.14337 | ||

CDD_7 | −1.86621 | ||

Rx5Day_5 | 0.41072 | 0.40784 | |

Rx5Day_6 | −0.46413 | −0.47983 | |

Rx5Day_7 | 1.98230 | 1.98341 | 1.98864 ^{†} |

Rx5Day_8 | 2.86024 * | 2.83325 * | 2.79095 * |

T10_4 | −0.45676 | −0.44421 | |

T10_5 | 0.11886 | 0.01343 | |

T10_9 | −2.54756 ^{†} | −2.61742 ^{†} | −2.85146 * |

T90_6 | 0.72151 | 0.66719 | |

T90_7 | −5.77264 *** | −5.78398 *** | −5.45714 *** |

T90_8 | −6.13024 *** | −6.09450 *** | −5.76785 *** |

WP90_6 | −0.62446 | −0.57842 | |

Time | 1.84387 *** | 1.83969 *** | 1.83177 *** |

N | 58 | 58 | 58 |

R^{2} | 0.9548 | 0.9547 | 0.9535 |

AIC | 425.5799 | 421.6728 | 411.2117 |

F-test statistic | 64.82 *** | 79.01 *** | 174.2 *** |

^{†}”, “*”, and “***” indicate significance at 10%, 5%, and 0.1% levels, respectively.

Variables | Probit Regression | Probit Regression without CDD | Simplest Probit Regression |
---|---|---|---|

Intercept | −0.83975 ** | −0.84186 ** | −0.7595 *** |

CDD_6 | −0.52693 | ||

CDD_7 | 0.66512 | ||

Rx5Day_5 | 0.12407 | 0.10113 | |

Rx5Day_6 | 0.09689 | 0.08025 | |

Rx5Day_7 | −0.22456 | −0.21207 | |

Rx5Day_8 | −0.08674 | −0.11425 | |

T10_4 | 0.21453 | 0.18391 | |

T10_5 | 0.35710 | 0.35282 | 0.4222 ^{†} |

T10_9 | 0.42315 | 0.39679 | 0.4200 ^{†} |

T90_6 | 0.15687 | 0.18821 | |

T90_7 | 0.75301 * | 0.76816 * | 0.7353 ** |

T90_8 | 0.48152 | 0.48877 | 0.4278 |

WP90_6 | 0.24637 | 0.22502 | |

N | 58 | 58 | 58 |

Pseudo R^{2} | 0.4015 | 0.3973 | 0.3451 |

AIC | 67.686 | 63.963 | 53.426 |

ANOVA Chi-square test (p-value) | 0.01402 * | 0.005767 ** | 0.0001338 *** |

^{†}”, “*”, “**”, and “***” indicate significance at 10%, 5%, 1%, and 0.1% levels, respectively.

Variables | Linear Regression | Linear Regression | Probit Regression |
---|---|---|---|

Intercept | 67.87581 *** | 76.29208 *** | −0.62538 *** |

Rx5Day | 0.10005 | −0.63556 | 0.06065 |

Tn10 | −2.32393 * | −2.51860 * | 0.09919 ^{†} |

Tx90 | −5.73952 *** | −5.80187 *** | 0.29302 *** |

CDD | 1.47515 | 0.77219 | −0.06731 |

Time | 1.67055 *** | 1.66590 *** | |

State | −0.29164 *** | ||

N | 448 | 448 | 448 |

R^{2} (Pseudo R^{2}) | 0.7504 | 0.7607 | 0.0739 |

AIC | 3809.78 | 3792.93 | 492.89 |

F-test statistic | 265.8 *** | 233.7 *** |

^{†}”, “*”, and “***” indicate significance at 10%, 5%, and 0.1% levels, respectively.

**Table 5.**Iowa analysis with standardized high-level resolution climate data using the linear regression model.

Variables | Linear Regression | Linear Regression without pr_6 | Simplest Linear Regression |
---|---|---|---|

Intercept | 65.01353 *** | 65.01403 *** | 65.01863 *** |

pdsi_6 | 3.07422 * | 3.06977 * | 2.68789 *** |

pdsi_7 | −0.46299 | −0.45688 | |

pr_5 | −2.78124 *** | −2.77376 *** | −2.77632 *** |

pr_6 | −0.02197 | ||

pr_7 | 4.14047 *** | 4.13523 *** | 4.03047 *** |

pr_8 | −2.83129 *** | −2.83299 *** | −2.83344 *** |

tmmn_4 | −0.61862 * | −0.62150 * | −0.61710 * |

tmmn_5 | −0.54592 ^{†} | −0.56722 ^{†} | −0.56257 ^{†} |

tmmn_9 | 5.08470 *** | 5.08345 *** | 5.08391 *** |

tmmx_6 | 0.60512 ^{†} | 0.60769 ^{†} | 0.60951 ^{†} |

tmmx_7 | −5.01798 *** | −5.01431 *** | −5.00016 *** |

tmmx_8 | −9.61604 *** | −9.61887 *** | −9.62043 *** |

soil_6 | 3.12003 *** | 3.09629 *** | 3.04412 *** |

soil_7 | −8.29489 *** | −8.28874 *** | −8.29728 *** |

Time | 1.89845 *** | 1.89844 *** | 1.89820 *** |

N | 5742 | 5742 | 5742 |

R^{2} | 0.7982 | 0.7982 | 0.7982 |

AIC | 49,197.69 | 49,195.69 | 49,193.75 |

F-test statistic | 1506 *** | 1614 *** | 1738 *** |

^{†}”, “*”, and “***” indicate significance at 10%, 5%, and 0.1% levels, respectively.

**Table 6.**Iowa analysis with standardized high-level resolution climate data using the probit regression model.

Variables | Probit Regression | Probit Regression without soil_6 | Simplest Probit Regression |
---|---|---|---|

Intercept | −0.837520 *** | −0.83781 *** | −0.83610 *** |

pdsi_6 | −0.192399 | −0.18535 | −0.25164 *** |

pdsi_7 | −0.060811 | −0.07146 | |

pr_5 | 0.265546 *** | 0.26434 *** | 0.26529 *** |

pr_6 | −0.009730 | −0.01235 | |

pr_7 | −0.214757 *** | −0.20945 *** | −0.21372 *** |

pr_8 | 0.213755 *** | 0.21389 *** | 0.20966 *** |

tmmn_4 | 0.031181 | 0.03109 | |

tmmn_5 | 0.043589 ^{†} | 0.04375 ^{†} | 0.05174 * |

tmmn_9 | −0.239507 *** | −0.23952 *** | −0.23903 *** |

tmmx_6 | −0.020039 | −0.01969 | |

tmmx_7 | 0.362900 *** | 0.36229 *** | 0.37875 *** |

tmmx_8 | 0.602808 *** | 0.60295 *** | 0.59262 *** |

soil_6 | −0.009438 | ||

soil_7 | 0.395052 *** | 0.39028 *** | 0.38068 *** |

N | 5742 | 5742 | 5742 |

Pseudo R^{2} | 0.2867 | 0.2867 | 0.2864 |

AIC | 4785.19 | 4783.22 | 4777.72 |

ANOVA Chi-square test (p-value) | 0.8769 | 0.7723 |

^{†}”, “*”,and “***” indicate significance at 10%, 5%, and 0.1% levels, respectively.

**Table 7.**Midwest analysis with standardized high-level resolution climate data, the linear regression model.

Variables | Linear Regression | Linear Regression (Lasso Selection) | Simplest Linear Regression (Lasso Selection) |
---|---|---|---|

Intercept | 62.41806 *** | 63.696265 *** | 63.593053 *** |

pdsi_5 | −7.358564 *** | −7.356485 *** | |

pdsi_6 | 4.87800 *** | 14.477384 *** | 14.471175 *** |

pdsi_7 | −3.88711 *** | −6.178563 *** | −6.178364 *** |

pr_5 | 1.26769 *** | 0.676166 *** | 0.663937 *** |

pr_6 | 5.45665 *** | 2.114477 *** | 2.120822 *** |

pr_7 | 9.70496 *** | 8.912569 *** | 8.913359 *** |

pr_8 | 0.49006 *** | −0.733426 *** | −0.730487 *** |

pr_9 | 1.170014 *** | 1.169836 *** | |

tmmn_4 | 1.80134 *** | −0.418122 * | −0.425323 * |

tmmn_5 | 4.53892 *** | −0.097777 | |

tmmn_6 | 4.952973 *** | 4.916094 *** | |

tmmn_7 | 6.389840 *** | 6.375701 *** | |

tmmn_8 | 7.222588 *** | 7.210296 *** | |

tmmn_9 | 2.99060 *** | −4.724990 *** | −4.729296 *** |

tmmx_5 | 4.479994 *** | 4.394181 *** | |

tmmx_6 | 7.97478 *** | 4.156479 *** | 4.189060 *** |

tmmx_7 | −7.27719 *** | −11.281069 *** | −11.271298 *** |

tmmx_8 | −9.84868 *** | −17.532366 *** | −17.524793 *** |

tmmx_9 | 7.555767 *** | 7.564631 *** | |

soil_6 | 0.52865. | 0.909000 ** | 0.910250 ** |

soil_7 | −8.86023 *** | −8.340331 *** | −8.339541 *** |

Time | 1.67237 *** | 1.566900 *** | 1.566997 *** |

N | 39,567 | 39,567 | 39,567 |

R^{2} | 0.7126 | 0.7297 | 0.7297 |

AIC | 352,752.4 | 350,338.1 | 350,336.1 |

F-test statistic | 6539 *** | 4854 *** | 5085 *** |

**Table 8.**Midwest analysis with standardized high-level resolution climate data, the probit regression model.

Variables | Probit Regression | Simplest Probit Regression | Probit Regression (Lasso Selection) | Simplest Probit Regression (Lasso Selection) |
---|---|---|---|---|

Intercept | −0.757158 *** | −0.756608 *** | −0.724359 *** | −0.726714 *** |

pdsi_5 | 0.625632 *** | 0.626712 *** | ||

pdsi_6 | −0.074283 * | −0.019064 ^{†} | −0.900663 *** | −0.906566 *** |

pdsi_7 | 0.064830 | 0.267352 *** | 0.269595 *** | |

pr_5 | −0.107747 *** | −0.105575 *** | −0.064896 *** | −0.065205 *** |

pr_6 | −0.283505 *** | −0.280150 *** | −0.104547 *** | −0.111829 *** |

pr_7 | −0.455160 *** | −0.439158 *** | −0.445186 *** | −0.443344 *** |

pr_8 | 0.001954 | 0.040559 *** | 0.041241 *** | |

pr_9 | −0.014300 | |||

tmmn_4 | −0.136050 *** | −0.137153 *** | −0.060383 *** | −0.063977 *** |

tmmn_5 | −0.152961 *** | −0.153493 *** | −0.051977 ^{†} | −0.066655 * |

tmmn_6 | −0.043355 | |||

tmmn_7 | −0.319458 *** | −0.328385 *** | ||

tmmn_8 | −0.226305 *** | −0.226689 *** | ||

tmmn_9 | −0.156244 *** | −0.155197 *** | 0.051380 * | 0.034804 ^{†} |

tmmx_5 | −0.086972 ** | −0.075420 ** | ||

tmmx_6 | −0.349582 *** | −0.352383 *** | −0.372841 *** | −0.411686 *** |

tmmx_7 | 0.324255 *** | 0.321780 *** | 0.544415 *** | 0.555092 *** |

tmmx_8 | 0.480141 *** | 0.479800 *** | 0.711735 *** | 0.708800 *** |

tmmx_9 | −0.151694 *** | −0.134287 *** | ||

soil_6 | 0.067226 *** | 0.073061 *** | 0.064598 ** | 0.066103 ** |

soil_7 | 0.432060 *** | 0.430947 *** | 0.410868 *** | 0.410685 *** |

N | 39,567 | 39,567 | 39,567 | 39,567 |

Pseudo R^{2} | 0.2341 | 0.2341 | 0.2537 | 0.2536 |

AIC | 35,294 | 35,293 | 34,407 | 34,406 |

ANOVA Chi-square test (p-value) | 0.2529 | <2 × 10^{−16} *** | <2.2 × 10^{−16} *** |

^{†}”, “*”, “**”, and “***” indicate significance at 10%, 5%, 1%, and 0.1% levels, respectively.

Model 1 | Model 2 | Model 3 | Model 5 | |
---|---|---|---|---|

p-value | 0.2616 | 0.0748 | 1.332 × 10^{−8} | <2.2 × 10^{−16} |

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**MDPI and ACS Style**

Pan, Q.; Porth, L.; Li, H.
Assessing the Effectiveness of the Actuaries Climate Index for Estimating the Impact of Extreme Weather on Crop Yield and Insurance Applications. *Sustainability* **2022**, *14*, 6916.
https://doi.org/10.3390/su14116916

**AMA Style**

Pan Q, Porth L, Li H.
Assessing the Effectiveness of the Actuaries Climate Index for Estimating the Impact of Extreme Weather on Crop Yield and Insurance Applications. *Sustainability*. 2022; 14(11):6916.
https://doi.org/10.3390/su14116916

**Chicago/Turabian Style**

Pan, Qimeng, Lysa Porth, and Hong Li.
2022. "Assessing the Effectiveness of the Actuaries Climate Index for Estimating the Impact of Extreme Weather on Crop Yield and Insurance Applications" *Sustainability* 14, no. 11: 6916.
https://doi.org/10.3390/su14116916