The probabilistic role of climate change on crop yield potential

No ́e J Nava1

2022 FCSM Research & Policy Conference

1USDA - Economic Research Service

July 5, 2022

The findings and conclusions in these slides are those of the author and should not be construed to represent any

official USDA or U.S. Government determination or policy.

https://noejn2.github.io/ probabilistic crop yield potential

July 5, 2022 The findings and conclusions in th

1 / 16
Table of contents

1 Introduction

Background

Bayesian formulation

Results

2 Bayesian inference

Let us talk about Bayes

3 A Bayesian formulation of the Ricardian approach

4 Results

The role of probabilistic distributions on crop yields

Findings

5 Concluding remarks

https://noejn2.github.io/ probabilistic crop yield potential

July 5, 2022 The findings and conclusions in th

2 / 16
Introduction Background

A Ricardian approach

Source: Mendelsohn, Nordhaus, and Shaw’s (1994) The impact of Global Warming on Agriculture: A Ricardian Analysis.

https://noejn2.github.io/ probabilistic crop yield potential

July 5, 2022 The findings and conclusions in th

3 / 16
Introduction Background

Popularity

Due to its simplicity, several studies report employing the Ricardian approach to estimate the impact of

climate change on agriculture in different regions such as,

Canada (Reinsborough, 2003),

China (Wang et al., 2009),

Europe (Van Passel, Masseti, and Mendelsohn, 2016), and

South Africa (Gbetibouo and Hassan, 2005).

https://noejn2.github.io/ probabilistic crop yield potential

July 5, 2022 The findings and conclusions in th

4 / 16
Introduction Background

(A few) Methodological limitations

Available methodologies have been proven to have limitations:

McIntonsh and Schlenker (2006),

Do estimated parameters reflect a long-run or short-run responses to weather variations?

Deschenes and Greenstone, (2007),

A-temporal unobserved mechanisms cannot be controlled for by the researchers.

Schlenker and Roberts (2009),

The relationship between crops’ growth and heat is highly non-linear.

Ortiz-Bobea (2020), and

Non-farm influences have been growing in importance in the valuation of farmland prices.

M ́erel and Gammans (2021).

Estimated parameters do not reflect long-run responses to weather variations.

https://noejn2.github.io/ probabilistic crop yield potential

July 5, 2022 The findings and conclusions in th

5 / 16
Introduction Bayesian formulation

Bayesian formulation of the Ricardian approach

A Byesian formulation of the Ricardian approach can circumvent several limitations that practitioners

encounter when studying crop yields by incorporating model structure (Gelman, 2008; Gelman, Lee, and

Guo, 2015; Van de Schoot et al., 2021).

Previous crop yield studies exploit the fact that Bayesian inference does not dependent on

asymptotic approximations (e.g., large number of observations).

Ozaki et al., 2008 apply their methodology to Brasil, and

Ramsey (2020) combines a Bayesian framework with a quantile regression.

My study constructs a Bayesian formulation that integrates agronomic evidence on the

yield-weather interaction.

Parametrizing the dependence between unit-level produciton and global parameters permits

flexibility in the model design.

https://noejn2.github.io/ probabilistic crop yield potential

July 5, 2022 The findings and conclusions in th

6 / 16
Introduction Results

Preview of results

Crop yield projections from Midwestern and Eastern U.S. counties for 2022, 2027, and 2032 indicate

that,

Soybean farmers in Midwestern counties will shift to corn production,

Findings corroborate existing evidence regarding U.S. agricultural outlooks, and

Short-term productivity gains are associated with the largest producers.

https://noejn2.github.io/ probabilistic crop yield potential

July 5, 2022 The findings and conclusions in th

7 / 16
Bayesian inference Let us talk about Bayes

Posterior distributions: The math

Posterior distributions are sampled, point estimates are estimated:

p(θi|yit, xit)

| {z }

Posterior

∝ p(yit, xit|θi)

| {z }

Likelihood

p(θi)

| {z }

Prior

where

yit denotes crop yield realizations,

xit denotes observed weather, and

θi denotes estimate values.

https://noejn2.github.io/ probabilistic crop yield potential

July 5, 2022 The findings and conclusions in th

8 / 16
Bayesian inference Let us talk about Bayes

Poserior distributions: The viz

Source: NSS (2016) Bayesian statistics explained to beginners in simple English in Analytics Vidhya.

https://noejn2.github.io/ probabilistic crop yield potential

July 5, 2022 The findings and conclusions in th

9 / 16
Bayesian inference Let us talk about Bayes

Can we expand the probability?

A challenge of estimating posterior distributions is that wide distributions are unreliable (think about

the trade-off between bias and variance).

p(θi, τ |yit, xit)

| {z }

Posterior

∝ p(yit, xit|θi)

| {z }

Likelihood

p(θi, τ )

| {z }

Prior//hyper−prior

where

τ is a probabilistic structure above the priors.

https://noejn2.github.io/ probabilistic crop yield potential

July 5, 2022 The findings and conclusions in th

10 / 16
A Bayesian formulation of the Ricardian approach

Likelihood

I assume that farmer maximizes output by varying inputs as a funciton of variations in weahter,

yit ≡ Ψ(xit, γ∗(xit)), and γ

∗

(xit) is optimal output employment as a reponse to observed

weather.

I propose a Beta-type probability distribution that builds upon the work of Nelson and Preckel

(1989), and Cribari-Neto and Zeileis (2010):

B(μ, φ) = Γ(φ)

Γ(μφ)Γ((1 − μ)φ)

×

y

μφ−1

it (yu − yit)

(1−μ)φ−1

y

(φ−1)

u

where

1 > μ > 0 is the location parameter,

φ > 0 is the spread parameter, and

yu is an upper limit for crop yield realizations defined by the researcher.

https://noejn2.github.io/ probabilistic crop yield potential

July 5, 2022 The findings and conclusions in th

11 / 16
A Bayesian formulation of the Ricardian approach

Priors

I relate data on crop yield and weather observations with my prior structures about the effect of

weather on cropm yields.

ln( μ

1 − μ

) ∼ N(β

GDD

i GDD + β

EDD

i EDD + β

PPT

i PPT + Ψ(t), σ)

where

my weather variables of interest are GDD, EDD and PPT,

Ψ(t) is a temporal structure that controls for non-weather variation, and

A link function, g(μ) : R 7→ (0, 1) to keep B(μ, φ) well defined.

https://noejn2.github.io/ probabilistic crop yield potential

July 5, 2022 The findings and conclusions in th

12 / 16
A Bayesian formulation of the Ricardian approach

(A peak to the) Hyper-priors

A variance-covariance matrix regulates the spatial and temporal effect of weather on crop yields.





β

GDD

i

β

EDD

i

β

PPT

i



 ∼ N(M, Σ)

where

M is a vector of means, and

Σ is a variance-covariance matrix.

https://noejn2.github.io/ probabilistic crop yield potential

July 5, 2022 The findings and conclusions in th

13 / 16
Results The role of probabilistic distributions on crop yields

Posterior distributions and example simulations

https://noejn2.github.io/ probabilistic crop yield potential

July 5, 2022 The findings and conclusions in th

14 / 16
Results Findings

Corn and soybean yield trends in Midwestern and Eastern counties

https://noejn2.github.io/ probabilistic crop yield potential

July 5, 2022 The findings and conclusions in th

15 / 16
Concluding remarks

Bayesian formulation:

Previous crop yield studies exploit the fact that Bayesian inference does not dependent on

asymptotic approximations (e.g., large number of observations),

My study constructs a Bayesian formulation that integrates agronomic evidence on the

yield-weather interaction, and

Flexibility in the model design.

Results:

Soybean farmers in Midwestern counties will shift to corn production,

Findings corroborate existing evidence regarding U.S. agricultural outlooks, and

Short-term productivity gains are associated with the largest producers.

https://noejn2.github.io/ probabilistic crop yield potential

July 5, 2022 The findings and conclusions in th

16 / 16