Model-Based Estimates for Farm Labor Quantities

Abstract

The United States Department of Agriculture’s (USDA’s) National Agricultural Statistics Service (NASS) conducts the Farm Labor Survey to produce estimates of the number of workers, duration of the workweek, and wage rates for all agricultural workers. Traditionally, expert opinion is used to integrate auxiliary information, such as the previous year’s estimates, with the survey’s direct estimates. Alternatively, implementing small area models for integrating survey estimates with additional sources of information provides more reliable official estimates and valid measures of uncertainty for each type of estimate. In this paper, several hierarchical Bayesian subarea-level models are developed in support of different estimates of interest in the Farm Labor Survey. A 2020 case study illustrates the improvement of the direct survey estimates for areas with small sample sizes by using auxiliary information and borrowing information across areas and subareas. The resulting framework provides a complete set of coherent estimates for all required geographic levels. These methods were incorporated into the official Farm Labor publication for the first time in 2020.

Using Small Area Estimation to Produce Official Statistics

“…Each model is outlined below, and the modeling details are in Chen et al [15]. To estimate the number of workers, let i =1, 2, .…”

“…After obtaining the posterior distribution of θ ijk , the estimators Y wk ijk = exp θ ijk , where wk represents the number of workers, follow from back transformation and are used to obtain the posterior means and measures of uncertainty for the number of workers by each worker type. The aggregated regional level posterior summaries for the number of workers by different worker types are obtained based on state-level MCMC samples (see Chen et al [15] for details).…”

“…After obtaining the posterior distribution of θ ijk , for S ∈ {hr, wg}, where hr and wg represent average hours worked per week and average wage per hour, respectively, the estimators Y S ijk = θ ijk follow from the identity transformation and are used to obtain the posterior means and measures of uncertainty for hr and wg by each worker type. The aggregated regional level posterior summaries for hours and wage rate by different worker types are obtained conditional on the state-level MCMC samples of the number of workers (see Chen et al [15]).…”

“…The detailed model evaluations including model effectiveness, model efficiency, and a comparison between survey estimates and subarea model estimates can be found in Chen et al [15]. Furthermore, a 2020 case study illustrates the improvement in the direct estimates for areas with small sample sizes by using auxiliary information and borrowing information across areas and subareas.…”

“…The convergence was monitored using trace plots, the multiple potential scale reduction factors ( R close to 1), and the Geweke test of stationarity for each chain (see [32,33]). More details can be found in [15,[19][20][21].…”