Factors determining the supply of agricultural labor

The economic literature suggests that the labor supply (e.g., the number of hours worked) of a worker depends on several factors, which are expressed in the following equation [14]:

(1)

where H is the worker’s hours, W is their income, V is other non-labor income, X is a vector containing other determinants of agricultural labor supply such as farm and community characteristics (e.g., travel distance to the farm, community quality of life), and e is a stochastic term. In this model, an individual´s labor supply response to income could be either positive or negative, depending on the price and income effects and the type of labor contract (e.g., daily quotas). This framework also suggests that the labor supply response to changes in income from other sources, V (e.g., income from other household members), should be negative. The vector X, in equation (1), includes well-known variables, but it could also include exogenous factors that affect the ability of agricultural laborers to work, such as frequent occurrences of extreme heat, COVID-19, as well as a combination of both. Recent studies find that both extreme heat and the COVID-19 pandemic have significantly impaired agricultural workers’ health and reduced their participation in the labor market [1,5,6,15].

In this study, we examine how the combination of extreme heat and the COVID-19 pandemic affected the labor participation of farmworkers in the California Central Valley communities of Coalinga, Avenal, and Huron.

Empirical evidence on extreme heat affecting agricultural labor supply

Outdoor workers in California faced multiple hazards during summer of 2020 in addition to COVID-19. Because of fossil fuel consumption [16], average summer temperatures in California during 2020 were considerably higher than before significant human interference in the climate system. While it was very hot in the study region, it was not quite at unprecedented temperatures. Fig 1 shows the average summer temperature and the annual maximum of the running three-day average of the daily maximum modified heat index [17] at the Visalia weather station 723896 in California [18]. The hottest three-day period of 2020 at 112.8^oF (44.9C) was the third highest on record behind 2006 and 2017. This value is deemed “very hot” by the National Oceanic and Atmospheric Administration, which warns that “with prolonged exposure and/or physical activity, people in high-risk groups are likely to experience sunstroke, heat cramps, or heat exhaustion, and heatstroke is a possibility” [19].

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Fig 1. Average summer temperature (dashed line) and the annual maximum of the running three-day average of the daily maximum modified heat index (solid line) at the Visalia, California weather station.

This station is within 100km east of the study area and also within the Central Valley of California (Units: Fahrenheit).

https://doi.org/10.1371/journal.pclm.0000770.g001

Prolonged exposure to extreme heat poses a significant risk to farmworkers and has been shown to affect their productive capacity [20]. Agricultural workers, who work outdoors, are at particularly high risk of developing extreme, acute heat-related illnesses, as well as chronic conditions, such as kidney disease and cardiorespiratory problems, associated with extreme heat [5,12]. As extreme heat events become more frequent and intense due to climate change, long-term health risks for these workers are exacerbated and lead to increases in their socioeconomic impacts such as reduced productivity, increase in heat related health expenses, and even death [7].

Other studies support the classification of occupational heat stress as a public health problem [20]. Nonetheless, deficiencies remain in adaptation and control strategies to mitigate the effects of heat stress on outdoor workers [11].

Empirical evidence on the impact of COVID-19 on labor supply

Farmworkers played a key role in sustaining the food supply chain during the pandemic. They were designated as essential to society during the pandemic; nevertheless, their work hours were negatively impacted. A study conducted in June 2020 surveyed 92 farmworkers in central Florida and found that 91% of workers continued to work despite health restrictions, and 75% reduced their work hours due to the pandemic [8]. COVID-19 posed a unique challenge for farmworkers, who continued to work in hazardous conditions as part of an essential production sector. In particular, the risk was exacerbated by vulnerabilities associated with their socioeconomic status, on-farm working conditions, and off-farm inequities such as housing and legal status. This vulnerability resulted in higher infection rates compared to the rest of the population [13].

Empirical evidence on the combined effect of extreme heat and COVID-19 on agricultural labor supply

In this section we propose a conceptual framework that describes how simultaneous exposure to extreme heat and COVID-19 exacerbates the adverse effects on the health and labor productivity of migrant farmworkers.

A few studies have also examined the health impacts of exposure to extreme heat and COVID-19 infections together. Such investigations concluded that susceptibility to conditions such as COVID-19 and heat stress tends to increase with different factors such as pre-existing health problems [6,9,21].

Authors argue that the effects of COVID-19 and climate change vary by income and suggest that responses to the pandemic should address the negative impacts by considering the interrelationship between the two. In summary, studies have been limited to literature reviews or descriptive approaches, without producing an empirical analysis that would conclusively validate the impact of these two phenomena on the labor supply. Overall, detailed empirical research on the combined impact of extreme heat and the COVID-19 pandemic on farmworkers’ labor force participation and working hours remains notably scarce [6,9]. This gap in the literature is particularly important because the interaction between extreme heat and COVID-19, along with the occupational, socioeconomic, and health vulnerability of farmworkers, significantly alters labor supply patterns and production in the agricultural sector.

Survey data and variables

The survey includes data from 280 workers across three communities in California’s Central Valley: Coalinga, Avenal, and Huron. Data were collected during August and September 2020, a period coinciding with the early stages of the COVID-19 pandemic. The survey comprised a total of 130 variables. Among these, two key features stand out: (1) each worker’s decision to participate in the agricultural labor market during the summer of 2020, and (2) the number of hours worked per week during the same period. The labor market participation variable is a binary indicator, taking the value of one if the worker decided to work during this period and zero if not. The variable measuring hours worked captures the number of hours each worker reported working per week.

Three variables related to labor market participation and labor supply: 1) a binary variable that takes the value of one if the worker stopped working due to the occurrence of extreme heat and zero if not, 2) a binary variable that takes the value of one if the worker reported a positive COVID-19 test result with an antigen test and zero if not, and 3) a variable that takes the value of one if the worker stopped working due to extreme heat and COVID-19 and zero if not. All other variables included in the survey are reported in the appendix (see S1 Table).

Other variables included in the survey are: worker demographics (i.e., sex, age, other), household characteristics, housing and working conditions, health insurance coverage, health-related habits, and community characteristics. Household characteristics include weekly household income, number of persons per household, home ownership status, etc. Information on workers’ health includes whether they received medical care at work due to high temperatures, the types of illnesses associated with extreme heat, and the availability of the COVID-19 vaccine. This unexplored dataset provides a valuable opportunity to analyze the combined effect of COVID-19 and extreme heat on labor force participation and hours worked.

The survey was developed after completing focus groups and completing a pre-survey process. To interview farmworkers the survey was incorporated into mobile devices (tablets). The data was administered by enumerators who completed a comprehensive training process. Participant farmworkers were selected by randomly choosing potential respondents at work sites and farmworker recruitment centers. The fieldwork was conducted as part of the project: “The compounded socio-economic impacts of COVID-19” and “heat stress on agricultural workers.” The project was also approved by Institutional Review Board (IRB: protocol number 30-19-0468) of the University of California at Santa Barbara. Verbal consent was obtained from potential respondents prior to completing the survey.

To facilitate the selection of the most relevant variables to include in the labor supply models, from the set of 130 available per worker, we use the machine learning algorithm known as the Least Absolute Shrinkage and Selection Operator (LASSO). This algorithm allows us to select the relevant variables by applying a penalty factor, LAMBDA, which reduces the coefficients of the least significant regressors to zero [23]. We used LASSO to select the determinants of the selection equation of the Heckman model (probability of working) and the determinants of the outcome equation of the same model (number of hours worked). In the final model, we include only salient variables (see S2 Table in the appendix). The variables selected using the LASSO process are consistent with the theoretical and empirical models described by Equation 1. It is worth mentioning that we assessed multicollinearity after the LASSO selection process for both equations (selection equation: Variance Inflation Factor (VIF)=1.24; outcome equation: VIF = 1.55).

Heckman regression model for estimation of the combined effect of extreme heat and COVID-19 infection on labor supply and participation of agricultural workers

We model the combined effect of extreme heat and COVID-19 on the farmworkers’ ability to participate in the labor market and the number of hours offered as part of their participation in the labor market. Typically, to estimate the labor supply model in equation (1), the Ordinary Least Squares method is used with a random sample of workers who participated in the labor market, which guarantees unbiased estimates of the effects of interest on hours worked. In our case, the sample collected may contain workers who self-select to work based on unobservable factors such as their job vulnerability (associated with different power positions between them and their employers), their perception of their health, their perception of their tolerance to heat, or even observable factors such as their financial needs [14]. Self-selection issues may lead to biased estimates of the effects of interest unless we control for these by using appropriate statistical methods.

To deal with potential selection bias, Heckman [22] proposed a two-stage model consisting of estimating two equations: 1) a selection equation that models the probability of participating in the labor market conditional on a set of observable factors (a probit model), and 2) an outcome equation that corresponds to a linear regression model of the number of hours worked. The latter is estimated only for those workers who decided to participate in the labor market. This two-stage method can be applied only if there is a significant correlation between the error terms of the two equations, thus allowing the problem of self-selection bias to be corrected [24–26].

As a first step, we estimate the selection equation for participation in the agricultural labor market, which is represented by the following relationship:

(2)

Where z_i* is a latent variable that captures the difference between the utility of participating in the agricultural labor market, U₀, and the utility of not participating in this market, U₁. Thus, the farmworker’s decision to participate in the market requires that the following condition be satisfied:

(3)

Since z_i* is a latent variable, in an estimable (probit) model, it is replaced by a binary variable that takes the value of one if the worker has decided to work in the agricultural labor market and zero if not. Meanwhile, x_i is a vector that includes the observable variables that could affect the probability of participating in the agricultural labor market, and μ_i is a random error term. Thus, in the first stage, equation (2) is a probit model that determines the probability of a worker entering the labor market as a function of a set of observable variables that influence the decision to enter or not to enter the labor market.

In the second stage, the outcome equation is modeled as follows:

(4)

Where: S_i = Number of hours worked (logarithmic scale)

    X_i = Vector of explanatory variables.

    z_i = Dichotomous variable indicating labor market participation.

    ε_i = The random error term with normal distribution.

    λ = Inverse Mills ratio.

At this stage, the estimation of the probit model is incorporated into a regression model of the number of hours worked, equation (4), conditional on a vector of explanatory variables X_i and an additional regressor denoted by “λ”, which is defined as “the ratio of the density of a standard normal distribution to the cumulative probability at the tail of such distribution” [27]. The variable λ is the inverse Mills ratio and corrects for potential bias due to self-selection [22]. The dependent variable in this equation (S_i) represents the number of hours worked by farmworkers who chose to work.

Preliminary analysis of the variables

Below is a descriptive analysis of some selected survey variables.

Table 1 shows that 66% of the surveyed workers who reported being exposed to extreme heat chose to work, while 34% chose not to work. Similarly, 72% of the workers who reported a positive COVID-19 test chose to work while testing positive, whereas the remaining 28% chose not to work. Finally, 77% of the workers who reported exposure to both extreme heat and COVID-19 chose to work, while the remaining 23% chose not to work. It is important to emphasize that when temperature reaches 95°F degrees or even more, agriculture employers are required to provide extra cool-down rest periods, in addition to the required breaks [28].

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 1. Decision to work based on the type of condition: extreme heat, COVID-19, and both.

https://doi.org/10.1371/journal.pclm.0000770.t001

In summary, a large percentage (66%, 72%, and 77%, respectively) of workers who experienced extreme heat, COVID-19, or both conditions chose to work. This result suggests that most workers in the surveyed communities chose to work in conditions of extreme duress, exemplified by the dual burden of extreme heat and COVID-19. Likely, this is partially due to their financial vulnerability and working conditions, resulting from structural socio-economic conditions present in the agricultural labor market [13].

Table 2 shows the average weekly hours worked by workers who chose to work and reported experiencing the effects of extreme heat, COVID-19, or both conditions, as well as the hours worked by those who reported not being exposed to either of these conditions. The differences in hours worked between the two groups and their p-values are also reported.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 2. Average weekly hours worked by exposed and unexposed individuals.

https://doi.org/10.1371/journal.pclm.0000770.t002

The average number of hours worked per week for agricultural workers not exposed to extreme heat was 42.52 hours per week, while the average number of hours worked per week for those exposed to extreme heat was 41.87 hours. The difference between the two groups is 0.65 hours, suggesting that extreme heat may be associated with fewer hours worked. This finding is consistent with evidence showing that extreme heat not only affects workers’ physical health, such as dehydration, exhaustion, and heat stroke, but also negatively affects their hours worked and work rate [5,7]. This difference of 0.65 hours worked per week is not statistically significant. However, this small difference may not reflect the true impact of heat and COVID-19 because farmworkers self-select to participate in the agricultural labor market based on unobservable and observable characteristics. For example, unobservable characteristics such as the different power standings between employers and farmworkers that result in the latter working under duress. This usually results in working for longer hours and fewer breaks, even on hot days [5]. It is also possible that financial and job vulnerability, and other individual observable characteristics, force them to self-select to work in conditions that are highly hazardous to their health. Thus, in the next section, we re-estimate these differences using a model that checks for observable and unobservable effects that may affect workers’ labor market participation and hours worked, such as the Heckman two-stage model [23]. This model provides unbiased estimates of the impacts of heat and COVID-19 in the presence of self-selection.

Similarly, the average number of hours worked by those who experienced only COVID-19 was 41.08, lower than the average of 42.43 hours for workers unaffected by COVID-19. This finding is consistent with the literature, which argues that COVID-19 had a negative impact on workers’ active hours [8]. It should be noted that the difference in hours between the two groups is 1.35 hours per week. Again, this difference is not large, which is probably explained by observable and unobservable factors that force farmworkers infected with COVID-19 to work almost the same number of hours as uninfected workers.

We note that workers exposed to extreme heat were less affected (0.65 hours) than those affected only by COVID-19 (1.35 hours). This difference may indicate that extreme heat, although harmful, has a less limiting, shorter-term effect on working time than does COVID-19, which enervates physical energy and the ability to work long hours [6].

Finally, the data in Table 2 show that workers exposed to both COVID-19 and extreme heat worked an average of 39.76 hours per week, which is lower than the average total hours worked by unaffected workers (42.75). Again, the difference between these figures is not statistically significant, which may be associated with estimation issues due to potential self-selection of workers based on unobservable and observable which we controlled by employing the Heckman selection model, below. This difference is also small (2.98), representing about 7% of the hours in a typical 40-hour work week, suggesting that workers exposed to both effects worked, on average, approximately the same amount of time as unaffected workers. This figure indicates that the combination of the two factors could also have a negative effect on the number of hours worked; however, those exposed still worked on average a similar number of hours as those who were not exposed.

Econometric estimation of the combined effect of extreme heat and COVID-19 on agricultural labor supply: The two-stage Heckman model

The descriptive analysis in the previous section reveals two empirical facts: 1) extreme heat, COVID-19, and the combination of both appear to be associated not only with the decision to participate in the agricultural labor market, but also with average weekly hours worked; and 2) since a large majority of the surveyed workers decided to work despite extreme heat and COVID-19, it is possible that there is self-selection bias, which as mentioned earlier, could be explained by various reasons, such as the different power standings between employers and farmworkers, socio-economic and on the job vulnerabilities, and other observable and non-observable worker characteristics.

Because of self-selection the OLS estimates result in biased estimates of the parameters of the labor supply model. To correct for this, we use the Heckman model [22], which solves this problem by estimating the model in two stages (see equations 2 and 4). Table 3 presents the final results of the OLS and Heckman models.

Download:

• PPT
  PowerPoint slide
• PNG
  larger image
• TIFF
  original image

Table 3. The determinants associated with the Probability of Working and the Average Number of Hours Worked by Agricultural Workers.

https://doi.org/10.1371/journal.pclm.0000770.t003

The outcome equation: Explanatory factors for average hours worked

The outcome equation links the number of hours worked once workers have decided to participate in the labor market with factors that influence the decision to work, even under harsh conditions. The results in Table 3 show how extreme heat reduces weekly hours worked (-0.186). Similarly, the effect of COVID-19 on weekly hours worked is negative, at about -0.173, confirming that the pandemic had very similar adverse effects to those caused by extreme heat [1]. Meanwhile, the combined effect of extreme heat and COVID-19 reduces hours worked by about -0.218. Thus, the combined effect of both conditions is similar in magnitude to the individual effects of extreme heat and COVID-19. Overall, after accounting for possible endogeneity due to self-selection, we find statistically significant results. Specifically, we find that extreme heat, COVID-19, and the combination of the two reduced hours worked by very similar amounts.

In addition, we find that the number of hours worked is related to certain specific characteristics of the individual. For example, the number of hours worked is reduced for women (-0.278), for those with a low level of education (-0.484), and for those who speak good English (-0.293). If the worker smokes (-0.335) or drinks alcohol (-0.224), the hours worked are also reduced, possibly because these activities exacerbate negative health outcomes related to COVID-19 and extreme heat. In contrast, hours worked increase with age (0.521), household income (0.398), and whether the worker has health insurance (0.233) or has received medical treatment for extreme heat (0.463). This relationship is consistent with other qualitative studies that show that access to health care helps farmworkers cope more efficiently with health problems, thus allowing them to work during stressful conditions such as extreme heat and COVID-19.

We carried out two alternative models to verify the statistical robustness of our model. First, we estimated a model in which we used a proxy variable for the combined effect corresponding to an interaction between the extreme heat variable and COVID-19. This variable was constructed with different questions of the survey. Second, we estimated another model including PM2.5 to control air pollution obtained from the U.S. Environmental Protection Agency [29–31]. The results of these models also show that the combined effect reduces the number of hours worked by farmworkers and positively affects the decision to work in the agricultural labor market, which confirms the results of our model in Table 3. These results are reported in the supplementary information (see S3 Table).

The selection equation: Factors explaining the probability of employment

The selection equation in Table 3 shows a positive and statistically significant relationship between the combined effect of extreme heat and COVID-19 on the probability that workers participate in the agricultural labor market (6.073). In addition, extreme heat alone is also a factor with a positive and statistically significant effect (0.581).

This finding highlights the fact that the probability of participating in the agricultural labor market is associated with certain household characteristics. For example, a significant inverse relationship exists between the likelihood of working and weekly household income in dollars (-0.360). Similarly, the probability of working increases as the number of people living in the worker’s household increases. These results reflect how financial vulnerability encourages workers to participate more actively in the agricultural labor market despite facing or experiencing negative socioeconomic impacts related to heat and COVID-19.

Regarding worker health, we find that the probability of working decreases when the worker suffers from muscle cramps outside of work (-1.095). The probability of working increases when the worker reports consuming rehydration drinks (0.337), an indication of adaptation to extreme heat and an important finding. We found that this probability also increases if the worker has participated in pistachio planting (0.574), an activity with high exposure to extreme heat when done manually [32]. The probability of working also increases when associated with specific symptoms that could be related to extreme heat, such as nausea or vomiting, during the workday (0.928). Again, these findings suggest that farmworkers are forced to work despite harsh working conditions.

The outcome equation: Factors affecting the average number of work hours offered

In the work hours’ equation, we found that extreme heat, COVID-19 infection, and the combination of both factors had a statistically significant negative effect on the number of hours worked. This negative effect can be explained by the time required to resume work after an employer-ordered break in the event of extreme heat, or by the physical deterioration suffered by workers due to heat. At the time of the study, COVID-19 infection had a negative impact on the number of hours worked since it not only affected the physical capacity of workers but may also have forced them to take temporary leave from work due to health restrictions and the need to recover. The reduction in hours worked reflects not only the direct impact of the symptoms and physical exhaustion associated with COVID-19 but also the fear of disease transmission on the part of both employers and workers themselves, which could lead to the adoption of protective measures affecting work activities.

The combination of extreme heat and COVID-19 was shown to have an effect similar to that of each condition separately, significantly reducing the number of hours worked per week. The combined effect of these two factors is a relevant determinant because it has a greater impact on agricultural workers’ physical capacity and stamina than the individual effects of each variable. Extreme heat imposes a significant physical burden that forces a reduction in work activities to protect workers’ health, while COVID-19 exacerbates this situation because the symptoms and limitations associated with the disease excessively limit the ability of workers to remain active in the field. Thus, the combination of these two opposing factors leads to an additional reduction in working hours, confirming the existence of an additional burden from the combined effects on workers and their working hours, which undoubtedly also reduces productivity in agricultural fields. As well, previous studies suggest that the relationship between heat and COVID-19 may operate in both directions [6]. Contracting COVID-19 can intensify health issues associated with heat exposure, while prolonged heat exposure can increase susceptibility to COVID-19. Under conditions of extreme heat, the adverse effects of COVID-19 infection may be more pronounced. Likewise, during periods of widespread COVID-19 transmission or when individuals carry a high viral load, the negative consequences of heat exposure on worked hours may be amplified [6].

Results suggest that the number of hours worked is also related to specific worker characteristics, reflecting certain vulnerabilities related to their finances, work, and health. For example, the number of hours worked is reduced if the worker is vulnerable in terms of health, having previously been exposed to extreme heat, smoking, and alcohol consumption. In contrast, workers with access to health insurance tend to work more hours than those who do not, likely because they are less vulnerable. This finding is key to understanding how the conditions of access to medical services influence workers’ decisions to work. Health insurance covers medical care in case of illness and, depending on coverage type, provides financial security and stability for the worker, which translates into a greater willingness to work more hours. As highlighted in previous studies [8,10,15], access to medical services also allows workers to cope with the physical demands of agricultural work in an environment where health risk and the incidence of extreme weather conditions, such as extreme heat, are high.

In addition, results show that different individual characteristics can also influence the number of hours worked in agriculture. For example, the number of hours worked is reduced for women (-0.278), for those with a low level of education (-0.484), and for those who speak English well (-0.293), suggesting that language proficiency may be a factor that significantly affects the number of hours worked. Workers who are proficient in English report working fewer hours than those who are not. One reason for this could be that workers with English proficiency have more job mobility than those who lack proficiency. Weekly household income is positively correlated with the number of hours offered, suggesting that as migrant farmworkers see their incomes increase, they are incentivized to work more hours to improve their financial well-being. This behavior is consistent with economic theory, which postulates that higher compensation creates additional incentives to work more, especially in households where income depends on the contributions of several members. We note that working more is not necessarily an improvement on workers’ well-being as the working conditions for farmworkers are not optimal.

The selection equation: Extreme heat, COVID-19 and other factors affecting the likelihood of working

The estimated model shows a significant relationship between extreme heat and its combined effect with COVID-19 and a reduced probability of working. We note that the results of the two-step model (-0.218) improve the magnitude and lack of statistical results of the OLS estimate (0.043). This discrepancy between the OLS and the Heckman model estimates confirms the hypothesis of the existence of selection bias, associated with self-selection based on unobservable characteristics that result in farmworkers working under hazardous conditions. This finding could be interpreted in several ways. The first is that farmworkers in Huron, Avenal, and Coalinga self-select into the agricultural labor market because of unobservable (but well-documented) factors associated with the different power standings between employers and farmworkers and financial and job vulnerabilities. For example, informal arrangements between farm operators/farm owners and farmworkers may encourage, and provide incentives for, longer hours per day and fewer breaks, even on hot days [5]. Unobservable adaptative skills of workers may allow them to work longer hours, even to their detriment. Self-selection can also be explained by the fact that workers are affected by other structural vulnerabilities that encourage them to work even harder under extreme conditions. These include vulnerabilities related to personal life and employment, especially among migrants, which force them to work despite the risks to their health.

For example, regarding financial vulnerability, the model shows that the likelihood of working increases with the number of people in the household and with a lower household income. Thus, economic necessity forces workers to work despite hazardous conditions when extreme heat and COVID-19 are present. Regarding a worker’s health vulnerability, we find that the likelihood of working decreases if the worker has health problems at work and at home. This last result emphasizes the negative feedback loop in which farmworkers are trapped: working hours are reduced if workers are already facing health problems at home and on the farm; coupled with a lack of access to health insurance and care, the negative effects of COVID-19 and heat are compounded.

As for the COVID-19 variable, it was not found to be a determining factor on its own in the decision to work, possibly because being infected makes it less likely to adapt to work as workers may do in the face of extreme heat. However, a significant synergy was found between COVID-19 and extreme heat, increasing the likelihood that workers would decide to work despite the adverse conditions.

Limitations

Our empirical study is limited by some data issues. Our sample size is relatively small for a two-stage model. In the context of a Heckman selection model, limited sample sizes can produce less precise parameter estimates and larger standard errors. Nevertheless, despite these constraints, the results obtained provide some valuable information on how extreme heat, COVID-19, and both effects produce a negative impact in worked hours from farmworkers. On the other hand, LASSO may have a problem with collinearity among the regressors. However, after running LASSO we tested for multicollinearity using the VIF test, which suggested the absence of collinearity problems.