Model-based Estimates for Farm Labor Quantities

Lu Chen∗,#, Nathan B. Cruze+, Linda J. Young#

∗National Institute of Statistical Sciences (NISS)

#United States Department of Agriculture

National Agricultural Statistics Service (NASS)

+NASA Langley Research Center

FCSM Session C-3: Advances in Small Area Estimation

October 25, 2022

“. . . providing timely, accurate, and useful statistics in service to U.S. agriculture.” 1
Disclaimer and Acknowledgment

The findings and conclusions in this presentation are those

of the authors and should not be construed to represent any

official USDA or US Government determination or policy.

I This research was supported by the U.S. Department of

Agriculture, National Agricultural Statistics Service.

I The authors thank Theresa Varner and Jennifer Rhorer NASS,

USDA for their contributions of the success of the 2020

publication.

I They also acknowledge Andreea Erciulescu for her

contributions in the early stage of the research.

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Outline

Motivation

Data and Modeling Procedure

Models

Case Study

Concluding Remarks

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Motivation

”Improving Farm Labor Estimates using small area models.“

I The Farm Labor Survey conducted by NASS, USDA

I Important official statistics to various data users

I Required tabulations at different levels

I Sparse sample in some states for some cells

I Multiple data sources available

Question: How to construct modeling process to produce reliable

and coherent estimates with measures of uncertainty for all

required tabulations in the publication?

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Motivation: Quantities of Interest

I Regional and US level estimates:

I NASS Worker Types; the Standard Occupational

Classification (SOC)

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Traditional USDA NASS Official Statistics

Agricultural (Farm) Labor Survey

I Time: biannual official statistics for four quarters

I May (April and January) and November (October and July)

I Quantities: number of workers, hours/week, wage rate

I Expert assessment

I Point estimates only (no measures of uncertainty∗

)

I Domains: region, US, worker-type

I Different worker types: field, livestock, supervisor and others

I Aggregation based on finer geographical or worker-type domain

*quality measures were historically published for some selective survey

estimates.

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Current Modeling Application

I Model estimates as the key indicators for official statistics

I Hierarchical Bayesian sub-area small area models produce all

levels estimates by different NASS worker types

I Associated measures of uncertainty published on quality

measures

I Harmony among nested levels and consistent ratio definitions

I Geographic: State → Regional → US

I Worker types: field + livestock, all hired

I Transparent and reproducible method

I Increase precision and reliability

I Published articles: Chen et al. (2022); Young and Chen

(2022)

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Direct Estimates — Number of Workers

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Direct Estimates — Wage Rates by Types

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Modeling Procedure

Log Modeling Modeling Modeling Aggregation

number

of workers

finer level

hours/week

finer level

wage rates

Required

aggregated

estimates

Input

I Finer level survey summaries: state × worker-type

I Previous year, same quarter, the official values and sample

sizes: state × worker-type

Output

I Finer level and domain-level estimates

I Point estimates, measures of uncertainty, distributions
Notation

I i = 1, . . . , m index for areas (i.e. regions)

I j = 1, . . . , ni

index for sub-areas (i.e. states) within area i

I k = 1, ...K index for different NASS worker types

I yˆijk , σˆ

2

ijk,y

Farm Labor direct estimates by worker types

I xijk known auxiliary information: the previous year, same

quarter, official estimates; number of positive responses; and

worker types

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Model for Number of Workers

The sub-area model:

θˆ

ijk = log(ˆyijk )|θijk

ind∼ N(θijk , σˆ∗

2

ijk ), k = 1, . . . ,K,

θijk |β, νi, σ2

μ

ind∼ N(x0

ijkβ + νi

, σ2

μ

), j = 1, . . . , ni,

νi|σ

2

ν

iid∼ N(0, σ2

ν

), i = 1, . . . , m,

β ∼ MN(βˆ, 1000 × Σˆ

βˆ),

σ

2

μ∼Uniform(R

+), σ2

ν∼Uniform(R

+),

where σˆ∗

2

ijk = (ˆyijk )

−2σˆ2

ijk,y

serves as estimate for the sampling

variances.

I Goal:

I State × type worker: y

wk

ijk = exp (θijk )

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Model for Hours and Wage Rates

The sub-area model for hours/week and wage rates (Erciulescu et

al. 2020):

θˆ

ijk |θijk

ind∼ N(θijk , σˆ

2

ijk ), k = 1, . . . ,K,

θijk |β, νi, σ2

μ

ind∼ N(x0

ijkβ + νi

, σ2

μ

), j = 1, . . . , ni,

νi|σ

2

ν

iid∼ N(0, σ2

ν

), i = 1, . . . , m,

β ∼ MN(βˆ, 1000 × Σˆ

βˆ),

σ

2

μ∼Uniform(R

+), σ2

ν∼Uniform(R

+),

I Goal:

I State × type wage rate: y

wg

ijk = θijk

I State × type hours/week: y

hr

ijk = θijk

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Case Study: 2022 January

I Example:

I 44 states within 18 regions by worker types

I Number of workers; hours/week; wage rates

I Goal: regional and US level estimates by worker types or

combined worker types

I Computation:

I Rjags: 10,000 MCMC samples and 2,000 burn-in, 3 chains,

each thinned every 8 samples, resulting in a number of 3,000

samples for inference

I Convergence diagnostics are conducted: Rhat ≤ 1.1 and

effective sample sizes are around 3,000

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CV Comparisons by Worker Types at State Level

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Model Effectiveness by Worker Types at State Level

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Number of Worker: Posterior Distribution

I US × all hired worker estimates, computed at the h

th draw:

y

wk,(h) =

X

K

k=1

Xm

i=1

Xni

j=1

y

wk,(h)

ijk ,

where h = 1, ...H are the draws.

I Posterior distribution based on y

wk,(h)

:

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Wage Rate: Posterior Distribution

I US × all hired worker wage rate estimates, compuated at

the h

th:

y

wg,(h) =

PK

k=1

Pm

i=1

Pni

j=1 y

wk,(h)

ijk y

hr,(h)

ijk y

wg,(h)

ijk

PK

k=1

Pm

i=1

Pni

j=1 y

wk,(h)

ijk y

hr,(h)

ijk

,

where h = 1, ...H are the draws.

I Posterior distribution based on y

wg,(h)

:

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Concluding Remarks

I NASS incorporated model-based

estimates into the official Farm

Labor publication since 2020

I Increased the accuracy and

improved the precision of estimates

I Harmony among nested levels and

worker types

I Fast computation time within

production window

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Reference

Chen, L., Cruze, N. B., and Young, L. J. (2022).

Model-based estimates for farm labor quantities.

Stats, 5(3):738–754.

Erciulescu, A. L., Cruze, N. B., and Nandram, B. (2018).

Benchmarking a triplet of official estimates.

Environmental and Ecological Statistics, 25:523–547.

Erciulescu, A. L., Cruze, N. B., and Nandram, B. (2019).

Model-based county level crop estimates incorporating auxiliary sources of information.

Journal of the Royal Statistical Society: Series A (Statistics in Society), 182(1):283–303.

Erciulescu, A. L., Cruze, N. B., and Nandram, B. (2020).

Statistical challenges in combining survey and auxiliary data to produce official statistics.

Journal of Official Statistics, 36(1):63–88.

Rao, J. N. K. and Molina, I. (2015).

Small Area Estimation.

2015 John Wiley and Sons, Inc.

USDA NASS.

Farm labor publication.

https://usda.library.cornell.edu/concern/publications/x920fw89s.

Young, L. J. and Chen, L. (2022).

Using small area estimation to produce official statistics.

Stats, 5(3):881–897.

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Thank You!

lu.chen@usda.gov

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