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temperature on labor productivity enables us to pose two general hypotheses:

       Temperature impacts on agricultural labor productivity or crop production should be higher for labor‐intensive crops.

       The negative impact of temperature on labor productivity should occur for relatively high heat index values.

2.5. DATA SOURCES AND DESCRIPTION

      Starting with data from the California Department of Food and Agriculture (CDFA) and the US Department of Agriculture (USDA) we constructed a county panel data set consisting of crop production, acreage harvested, and output prices for two crops: onions and melons (all types). We also constructed panel data sets for almonds, grapes, lettuce, and citrus. Those are not reported here, because the directional results are as expected but not statistically significant. We use acreage harvested, as opposed to acreage planted, to reflect the actual acreage contributing to crop production. The difference between acreage harvested and acreage planted is minimal in most years. We complement this data with estimated crop labor requirements, labor and equipment costs obtained from a variety of cost studies collected by the authors, and other costs obtained from the University of California at Davis Agricultural Issues Center (University of California Davis, 2020). Unfortunately, there are not cost studies available for all crops in all counties for each year, so we started by using cost studies completed during the period of analysis. If no cost study was available for the period of analysis, we used available studies adjusted for inflation. In addition, experts were consulted, specifically labor contractors and extension specialists familiar with the crops and geographical areas included in the study. Nominal crop prices over time are available from the indicated sources. We adjusted crop prices and costs of production using sectorial‐specific deflators.

The panel data set is for the 1994–2014 period and includes five California counties: Fresno, Kern, Yolo, Imperial, and San Joaquin. For onions and melons, the panel data starts in 1997. As Figure 2.2 shows, counties included in the study span a wide geographical area that include both the Northern Central Valley and the southernmost area of the state. All of these rank among the top 10 agricultural producers by value in the state.

Total labor for each crop is determined by using county‐level data collected by the California Employment Development Department (CEDD) for all agricultural‐related activities including harvesting, administrative, and managerial activities. Using crop labor harvest requirement specific for each crop, we estimate the fraction of this total in each county associated with specific crops in the specific months they are harvested. We did this because climate‐related data (specified later) are reported daily, and to associate socioeconomic data with climate‐related data, we need to downscale the annual labor data to monthly units while scaling up the daily climate data to the same basis. For example, melon harvesting for Fresno County is assumed to take place during the July–September period whereas in Imperial County the same crop is assumed to be harvested during the May–July period. Onions in Imperial County are harvested during the April–May period, and so on. Harvesting months are reported in the Annual County Agricultural Reports (https://www.cdfa.ca.gov/statistics/). Similar analysis was carried out for the remaining crops and counties included in the study. Appendix 2.1 shows the counties, crops, and harvesting months for each of the crops included in the analysis. We note that we consulted with extension specialists and others with knowledge of the labor sector in California agriculture and we concluded that the crop labor requirements do not change across counties.

Figure 2.2 California counties included in this study.

2.6. EMPIRICAL ESTIMATION AND RESULTS

      We are interested in estimating the impact of heat on agricultural output. If we were to use the heat index value as an independent variable directly impacting output, we are likely to encounter endogeneity problems due to the feedback between production and labor and vice versa. Results of an ordinary least squares (OLS) estimation using the heat index value as an independent variable directly against output may then yield spurious results. To correct for the endogeneity problem, we estimate the impact of heat on agricultural production using a two‐stage least squares (2SLS) instrumental variable (IV) method. We hypothesize that extreme heat affects agricultural productivity via impacts on labor employed in each crop. To capture this effect, we first estimate the impact of heat on labor requirements via the following specification:

(3)

The specific model for 3 is:

(3.1)

In these equations, D₁, D₂ are defined as the number of days that the heat index exceeds specific HI value thresholds for any given month during the harvesting season such that 95 ≤ HI < 100 andHI₂ > 100. Thus, for any given crop, D₁ is the number of days that the heat index exceeded values between 95 and 100^OF during any given harvesting month. D₂ is interpreted similarly for values exceeding 100^OF. X_Ct and X_At are defined as the cost of production and the harvested acreage at year t respectively. Finally, L_it denotes the crop labor requirement for each crop i at time t. The second stage of the specification shows the relationship between the estimated impacts of heat on labor on agricultural output:

(4)

The specific model for 4 is:

(4.1)

We estimate Eqs. (3.1) and (4.1) using a panel‐fixed effect approach. Results for both stages of the estimation are specified in Table 2.3. Prior to estimation, we tested for endogeneity for both crops for all variables. Results of the endogeneity test reject the null hypothesis of “all variables in the model are exogenous” with values obtained of p < 0.01. Panel A shows the results for the first stage of the estimation, Eq. (3.1), and panel B indicates the results for Eq. (4.1). In addition to melons and onions, we estimated the model for grapes and almonds. Although the directional results were in tandem with the literature previously mentioned, the estimations did not yield significant statistical results.

Table 2.3 Instrumental Variable (IV) Estimation,

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