The value of undocumented farm labour

Stricter US federal and local immigration policies in recent years have established procedures for apprehending the employment of undocumented immigrants. Employment verification systems and monitored hiring procedures were defined, along with harsher sanctions (involving higher civil fines and criminal penalties) for violators among employers (Reference Smith and SugimoriSmith and Sugimori, 2015). However, even as immigration enforcement efforts have led to many arrests and deportations, the share of undocumented workers has dropped in only a few industries, such as production and construction (Reference PasselPassel, 2015). Undocumented workers are eight times more likely than local residents to work in the farm sector (Reference BumpBump, 2015). The following sections explore possible explanations for this trend.

Data and variable measurement

This study’s data were compiled from the National Agricultural Workers Survey (NAWS), which is the only nationally representative cross-sectional survey of hired agricultural labourers in the US. Use of data collected from 1993 to 2012 resulted in a sample size of 56,976 observations. The geographical affiliation of the respondents is categorised under six different regions: East, Southeast, Midwest, Southwest, Northwest and California. ^{Footnote 1} The analysis focuses on the employment time allocation of farm workers categorised as citizens, green card holders and undocumented, accounting for 26%, 26% and 46%, respectively, of the total observations.

In order to investigate the employment time allocation decisions of US farm workers, a threefold classification of time allocation decisions is used, namely, farm employment weeks, non-farm employment weeks and unemployment (not working) weeks. In addition, for the sake of comparability of time allocation decisions among classes of hired farm workers, the number of employment weeks for each work alternative is divided by the total weeks of residence in the US to generate the share of employment time allocation decision for each legal status category.

Panel (A) in Table 1 shows the dependent variables capturing the time allocation decisions for farm workers. Figure 1 presents a graphical representation of such allocation decisions made by different legal categories of workers.

Table 1. Summary statistics of dependent and independent variables.

a The baseline for education categorical variable is zero years of education.

b Speaking and Reading are categorical variables that measure how well a farm worker speaks and reads English; proficiency categories are defined as follows: 1 = Not at all; 2 = A little; 3 = Somewhat; and 4 = Well.

c The baseline for farm task categorical variable is pre-harvest task.

d The baseline for the crops at farm work categorical variable is field crop.

Figure 1. Hired farm workers’ actual workweek allocations, by legal status (1993–2012).

Source: National Agricultural Workers Survey.

As can be gleaned from Figure 1, undocumented farm workers devoted the highest proportion of their employment time to farm work at approximately 83%, followed closely by green card holders at 79%. Citizen farm workers had the lowest allocation of time to farm work, but registered the most time spent in unemployment. Undocumented farm workers had the shortest period of unemployment. As for employment time allocated to non-farm work, citizens and green card holders recorded more time spent on non-farm jobs than undocumented farm workers.

In addition to the patterns noted in general allocation of employment time, Figure 2 presents the intertemporal trends and disparities of farm workers’ time allocation between farm and non-farm jobs. The contrasting trends in the upper and lower plots (Figure 2) indicate the shifting of time allocation of farm workers between farm and non-farm sectors. Undocumented and green card holders in general had more stable labour time allocation trends over the years compared to citizens. Citizen farm workers registered a lower share of time devoted to farm work prior to 1998 (with the lowest point at 59.4% in 1995); thereafter, the share started increasing to levels comparable to those of green card holders (with the highest point at 82.1% in 2006).

Figure 2. US farm workers’ annual workweek allocation trends, by legal status.

Source: National Agricultural Workers Survey.

Panel (B) in Table 1 lists the independent variables considered in this study. As suggested by Reference Acquaye, Alston and PardeyAcquaye et al. (2003), there are substantial differences in agricultural input requirements and productivity growth rates among regions in the US such that labour demand and utilisation patterns across regions could vary as well. To control for this regional variation in labour use, this article applies regional fixed effects, in addition to the inclusion of time (year) fixed effect.

Education is usually regarded as an important factor in promoting non-farm employment and thus enhancing income diversification opportunities for rural and farm households (Reference De Janvry and SadouletDe Janvry and Sadoulet, 2001; Reference Mishra and El-OstaMishra and El-Osta, 2016; Reference Yunez-Naude and TaylorYunez-Naude and Taylor, 2001). In this study’s sampled data, citizen farm workers have higher average educational attainment levels as majority of these workers have had more than 10 years of education experience. Undocumented workers have significantly lower educational attainment and low English speaking and reading proficiency levels which, in turn, reduce their ability to compete for non-farm jobs.

The present analysis also considers the possible effects of other demographic and structural attributes on the time allocation decisions of farm workers. Reference Ahituv and KimhiAhituv and Kimhi (2006) find that older and female workers are less inclined to work on farms. Reference Lien, Kumbhakar and HardakerLien et al. (2010) suggest that younger and married individuals would exhibit a greater preference for off-farm employment. Notably, undocumented farm workers in our sample are predominantly male and generally 10 years younger than their documented peers.

The number of dependants among family members, such as children, has been found to reduce a farm household’s exposure to off-farm activities (Reference Bjørnsen and BiørnBjørnsen and Biørn, 2010; Reference Goodwin and MishraGoodwin and Mishra, 2004; Reference Lien, Kumbhakar and HardakerLien et al., 2010). The responsibility of taking care of dependants does not necessarily affect the time allocation to and performance of farm work as both tasks can usually be done together in a well confined farm business and household setting (Reference Lien, Kumbhakar and HardakerLien et al., 2010).

As suggested by some studies, a variable measuring the number of years of residence in the US is also added here to capture the immigrant/foreign worker’s cultural and social assimilation (Reference Hamermesh and TrejoHamermesh and Trejo, 2013; Reference VargasVargas, 2016). In this study’s dataset, 88.7% of green card workers and 90.2% of undocumented farm workers are from Mexico. The predominance of a single source of foreign farm labour reduces the measurement error of characteristics across different immigration cohorts when analysing the overall population (Reference VargasVargas, 2016).

Reference Serra, Goodwin and FeatherstoneSerra et al. (2005) indicate that more labour-intensive activities on farms could decrease the share of time allocated to non-farm sectors for farm households. For instance, fruit and vegetable farm workers would usually be required to devote more time at the work site than grain crop workers due to the labour-intensive nature of the former operations. Thus, work time allocation decisions even within the farm sector may also be differentiated according to the nature and type of farming enterprises.

In considering the income effect, the present analysis utilises expected (instead of actual) individual income owing to the suspicion that individual income may be modelled endogenously with the time allocation between farm and off-farm activities. It follows the approach proposed by Reference El-Osta, Mishra and AhearnEl-Osta et al. (2004), which uses the predicted value for the possible endogenous variable to address endogeneity. In this article, expected individual income is constructed as a function of a series of factors based on previous models (Reference Ahearn, El-Osta and MishraAhearn et al., 2013; Reference Atamanov and Van den BergAtamanov and Van den Berg, 2012; Reference De Janvry and SadouletDe Janvry and Sadoulet, 2001) and an exclusive covariate (country of origin). Reference Adsera and ChiswickAdsera and Chiswick (2007) examine the impact of country of origin on labour market outcomes, including immigrants’ work earnings, and find significantly large differences among immigrants originating from various countries. This study does not expect to find any country of origin effect on the time allocation decisions of farm workers, except through changes in individual incomes. In the sample used in this analysis, undocumented farm workers have statistically lower incomes than documented workers (Table 1).

The conceptual and empirical framework

The model of farm and non-farm labour supply decisions of different classes of farm workers assumes the following utility function of individuals

(1) $U_i=U_i(W_i,A_i|X)$

where i = 0, 1, 2, … represents the first to the Nth production sector. Given the characteristics of individuals X, utility is affected by such factors as the sectoral wage rate $W_i$ and sectoral amenities $A_i$ . In this article, farm workers maximise their utilities by choosing between farm and non-farm employment. If the utility that can be derived from farm sector is higher than non-farm sector, such as

(2) $\Delta U=U_{FARM}-U_{NONFARM}$

when $\Delta U>0$ , farm workers will continue to work on the farm; when $\Delta U<0$ , farm workers will transfer to non-farm sectors.

This study identifies factors that may influence the farm workers’ decisions on allocation of time (measured in terms of weeks and referred to in this article as ‘workweek’ ^{Footnote 2} ) for farm and non-farm employment alternatives. The allocation decisions of different classes of workers according to their legal stature will be scrutinised using different estimation techniques. The analysis employs fractional multinomial logit (FMLOGIT) estimation given the model’s suitability to this study’s proportional response dependent variable. A secondary modelling approach, a seemingly unrelated generalised linear modelling framework (SUR-GLM), is also employed to account for possible contemporaneous correlation among errors of the three estimating equations.

The time spent in the US within the last year before the interview for hired farm workers j = 1, 2, … J is divided into three categories: farm work, non-farm work and not working. The basic models are structured as follows

(3) $\frac{FARMWEEK{S}_{jtr}}{USWEEK{S}_{jtr}}={\alpha }_1+{X^{\prime }}_{jtr}\gamma +{\rho }_t+{\phi }_r+{\epsilon }_{jtr}$

(4) $\frac{NONFARMWEEK{S}_{jtr}}{USWEEK{S}_{jtr}}={\alpha }_2+{X^{\prime }}_{jtr}\mu +{\rho }_t+{\phi }_r+{ϵ}_{jtr}$

(5) $\frac{NOWORKWEEK{S}_{jtr}}{USWEEK{S}_{jtr}}={\alpha }_3+{X^{\prime }}_{jtr}\sigma +{\rho }_t+{\phi }_r+e_{jtr}$

where $FARMWEEK{S}_{jtr}$ , $NONFARMWEEK{S}_{jtr}$ and $NOWORKWEEK{S}_{jtr}$ represent the number of farm work, non-farm work and not working weeks devoted by individual $j$ in year $t$ and region $r$ , respectively. $USWEEK{S}_{jtr}$ is the total number of weeks an individual spends in the US, which is the sum of farm employment, non-farm employment and not working weeks. The observed shares on the left side of equations (3), (4) and (5) have two common characteristics: (a) they are bounded between 0 and 1, inclusive, and (b) the sum of all three share components for any farm worker should be 1. ${\rho }_t$ is the year trend effect, while ${\phi }_r$ controls for regional fixed effects. The vector ${X^{\prime }}_{jtr}$ captures the demographic characteristics of farm workers as well as other covariates listed in Table 1.

The fractional regression model, introduced by Reference Papke and WooldridgePapke and Wooldridge (1996), expands the generalised linear model (GLM) and combines it with a quasi-likelihood maximisation econometric method to generate robust estimates and inferences for proportional responses. Moreover, in the application of the model to the analysis of the share of participation in 401(k) as dependent variable, Reference Papke and WooldridgePapke and Wooldridge (1996) show that such an estimation technique would produce fully robust and relatively efficient results.

The univariate version of the fractional regression model is used as starting point for developing the multivariate fractional regression model. Under the fractional logit model, the share/proportional value of time allotted to each activity can be specified by the following functional form whereby the expectation of the share time allocation $S_{jtr}$ is conditional on a series of covariates and fixed effects

(6) $E\left(S_{jtr}|X_{jtr}\right)=G\left(X_{jtr}\beta \right)$

where $X_{jtr}$ are the covariates that would affect the time allocation decisions of farm workers. $G(·)$ is the cumulative distribution function (cdf) that follows the logit cdf. To estimate the $\beta$ parameters, the Bernoulli likelihood can be specified as follows and its log-likelihood can be maximised by using the quasi-maximum likelihood estimation methods

(7) $L_j={\left[G\left(X_{jtr}\beta \right)\right]}^{S_{jtr}}{\left[1-G\left(X_{jtr}\beta \right)\right]}^{1-S_{jtr}}$

The quasi-maximum likelihood estimation will produce consistent estimates of $\beta$ even if the Bernoulli likelihood is incorrectly specified as long as the link function is in the correct form (Reference Hausman and LeonardHausman and Leonard, 1997). In addition, all GLM equations could be estimated in an equation system resembling a seemingly unrelated regression form in order to address the possible issue of correlated error terms associated with time allocation decisions for different activities.

In addition to the fractional regression model that separately estimates the share of time allocated to three activities, an extended model that accommodates both the proportional responses and multiple correlated choices can also be used. In this model, $S_{jtr}∊[0,1]$ , ${\sum }_{m=1}^M{S}_{jtrm}=1$ , where m represents the category on which the allocation share is calculated. Moreover, the probability of observing boundary solutions in outcomes (i.e. 0 and 1) is essential. Since all $\beta$ cannot be estimated separately under multinomial quasi-likelihood methods (Reference MullahyMullahy, 2015), normalisation is used by setting the coefficient of Mth category to be zero. As a result, the expectation value of share dependent variable conditional on covariates can be constructed as the following form

(8) $E\left(S_{jtrn}|X\right)=\left[\frac{exp\left(X_{jtr}{\beta }_n\right)}{1+\sum _{m=1}^{M-1}exp\left(X_{jtr}{\beta }_m\right)}\right],n=1,2,\dots ,M-1$

and

(9) $E\left(S_{jtrM}|X\right)=\left[\frac{1}{1+\sum _{m=1}^{M-1}exp\left(X_{jtr}{\beta }_m\right)}\right]$

The multinomial logit likelihood function is therefore defined as

(10) $L=\prod _{j=1}^J\prod _{m=1}^{M}E{\left(S_{jtrm}|X_{jtr}\right)}^{S_{jtrm}}$

The parameter could be estimated by maximising the log-likelihood form of equation (10), and the multinomial logit quasi-maximum likelihood estimation will provide consistent estimates of $\beta$ following the contention presented by Reference Papke and WooldridgePapke and Wooldridge (1996).