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Heat‐related illness (HRIs) for agricultural workers include dizziness, fatigue, fainting, nausea or vomiting, and headaches, among others. The incidence of HRIs is geographically contextual: in California, where humidity is often not a factor, the prevalence of some HRIs are different from that of Georgia or North Carolina, where humidity levels are generally higher. Studies show that the incidence of HRIs and the resulting overall impact on worker’s health is also a function of the resources and regulations that limit or enhance workers’ ability to adjust their workload to the occurrence of heat waves (Fleischer et al., 2013; Mirabelli et al., 2010; Stoecklin‐Marois et al., 2013). When appropriate regulations and compliance with those regulations take place, the impact of heat on worker’s health decrease in severity. Regular breaks, access to water, access to personal feeding times, and the use of proper clothing and protection equipment all reduce the impact of heat waves on worker’s health (Crowe et al., 2013; Kjelltrom et al., 2015).

      Excessive heat (above 95⁰F to 100⁰F) can also affect worker productivity levels, possibly due to heat’s impact on workers’ health. Impact on occupational performance can be in the form of more mistakes while working and/or increases in the incidence of work‐related injuries. Research on the impact of heat on worker’s productivity has concentrated on paid agricultural work, but there is no reason to believe that heat does not affect those engaged in subsistence farming activities (Kjellstrom et al., 2016). Research has also shown that workers do not have to show HRI for productivity to decrease, because cognitive functions decline with minor elevations of body temperatures (Varghese et al., 2018). Geographically, research shows that excessive heat has significant negative impacts on the labor force located in most tropical and mid‐latitude regions of the world (Dunne et al., 2013). A research topic that has received little attention up to now is the impacts of heat on school‐age children’s ability to learn during heat wave occurrence. The long‐term impact of heat on school‐age children might very well include reductions in future labor productivity.

      Although productivity impacts of heat on agricultural workers can be significant, few studies have estimated the impacts of heat on specific activities, such as harvesting. Most have estimated impacts of heat on metabolic rates in humans and assumed that after a particular metabolic threshold rate the ability of the worker to perform an activity decreases. For sugar cane harvesting workers, the metabolic threshold rate has been estimated at 261 W/m² with a corresponding wet bulb global temperature (WBGT) for harvesting at 100% effort of 79^OF. In Costa Rica the threshold values were reached, on average, at 9 am (Crowe et al., 2013). A study of the impact of heat on the productivity of rice harvesters in India found that the hourly number of rice bundles collected declined 5% per each increase in one degree in the WBGT (Sahu et al., 2013). Although these and other studies provide benchmarks of the impact of heat on productivity, they have generally assumed a linear relationship between productivity and temperature. The relationship between the onset of HRI and heat, however, is known to be nonlinear, and one could expect that the relationship between productivity and heat would be nonlinear.

      Nonlinear models have been used when analyzing the impact of heat on the productivity of industrial labor (Cai et al., 2018; Somanathan et al., 2018). Research results also indicate that the impact of temperature on overall economic output in the Caribbean basin is statistically significant and of important magnitude for some sectors such as wholesale, retail, restaurants, and hotels, whereas for agriculture, hunting, and fishing the magnitude is less clear and of no statistical significance (Hsiang, 2010).

      The impact of heat in agricultural labor productivity would be more complete if we were to consider a theoretical framework where other inputs required for crop production are included. In the context of the agricultural sector, this would likely require including some technological component and/or other factors of production besides labor, particularly capital and land. The next section proposes such a framework.

2.4. CONCEPTUAL FRAMEWORK

      We propose a production function framework to analyze the impact of heat waves on specific crops in California. Specifically, we are proposing the framework to determine the impact of heat stress on agricultural labor and the resulting impact on crop production. The analysis of the impact of excess temperature on plant productivity has been extensive (Lobell et al., 2011; Schlenker & Roberts, 2009), but the impact of heat on the productivity of the agricultural outdoor labor less so. In essence, the analysis here complements prior work on the impact of high temperatures on crops themselves. The crops in the area under analysis are heavily irrigated, so that the impact of high temperature on crops themselves is less severe than in other geographical areas where irrigation is not the norm. Our starting point is the conceptual framework implemented by other researchers who have used output production functions to analyze the impact of heat on industrial/indoor labor (Somanathan et al., 2018), adjusted to the reality of the California agricultural sector. For example, the seasonality of harvesting activities contrasts sharply with the ability of non‐agricultural workers to work indoors most of the year, especially with air conditioning. In addition, we take into consideration the role of product differentiation with respect to crop prices and requirements for land and labor. Finally, we include specific seasonality of agricultural production for different crops, particularly with respect to harvesting periods.

A generalized production function shows the relationship between output quantity Y and the required inputs and their quantities such as labor L, capital K, and fertilizer X for example:

(1)

Eq. (1) can take many functional forms. As we indicated previously, the relationship between outdoor temperature and outdoor labor productivity is likely to be nonlinear. A Cobb‐Douglas specification for Eq. (1) would therefore seem reasonable:

      (2)

      where:

       Y= Crop production level

       L(T)= Function indicating the relationship between labor and temperature in the production of Y

       T= Observable outdoor temperature

       E= Area harvested in the production of crop Y

       A= capital requirement to produce crop Y

      Because the relationship between the HI and a worker’s ability to complete a task is assumed to be nonlinear, one can hypothesize the existence of a threshold heat index value, HI_c, after which labor productivity declines (Somanathan et al., 2018). If workers are able to perfectly adapt to the outdoor temperature via proper clothing, regular breaks, water availability at all times, and regular water intake, then workers would be unlikely to be affected by high temperatures, in essence, negating the existence of HI_c or making HI_c of such value that it does not affect their work. HI_c is then a value we need to estimate empirically. Our ongoing fieldwork experience and published research indicates that this is not the case and that in fact there is such a value, HI_c, after which productivity declines (Crowe et al., 2013; Kjellstrom et al., 2016; Stoecklin‐Marois et al., 2013).

      We hypothesize that a decline in labor productivity due to high temperature is reflected in declines in output and/or increases in labor costs. If the outdoor heat index HIis less than the critical value HI_c there is no impact on productivity and/or labor costs. If, however, HI > HI_c, then we would expect labor productivity to decline. We note that this heat index extreme, HI_c, is crop and geographically specific because there are crops that are more labor intensive than others and temperatures vary across regions. We expand on this notion in Section 2.6. The contextual

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