Using Climate Analogues to Obtain a Causal Estimate of theImpact of Climate on Agricultural Productivity

Nicholas A. PotterDoctoral student

School of Economic SciencesWashington State Universitynicholas.a.potter@wsu.edu

Michael BradyAssistant Professor

School of Economic SciencesWashington State University

Kirti RajagopalanAssistant Research Professor

Center for Sustaining Agriculture and Natural Resources

Selected Paper prepared for presentation at the 2018 Agricultural & Applied EconomicsAssociation Annual Meeting, Washington, D.C., August 5-August

Copyright 2018 by Potter, Brady, and Rajagopalan. All rights reserved. Readers may makeverbatim copies of this document for non-commercial purposes by any means, provided that

this copyright notice appears on all such copies.

Abstract

Matching has several benefits for estimating the effects of climate on agriculture. Improved

covariate balance reduces bias. It does not require a functional form, so is useful in the complex

case of estimating farmer adaptation to climate. And it allows for comparision between matched

observations to gain insight into how producers adapt to different climates. We describe and apply

the application of the statistical method of matching to contribute to the literature predicting future

impacts of climate change on agricultural production. The matching approach can be viewed as an

extension of the concept of “climate analogues”. We demonstrate the advantages of the approach

to the Fruitful Rim in the western United States where there is a large diversity in crop mix and

temperature regimes. While existing methods are likely preferable for studying some regions, we

demonstrate the advantages of matching to studying this type of region. We consider projected

climate in 2040, 2060, and 2080. We find that on average the projected climate in the Fruitful Rim

will lead to increased agricultural productivity due to warmer temperatures. A major caveat is that

the potential for decreased surface water diversions due to reduced snowpack is not yet incorporated

into our analysis.

1

Introduction

The importance of understanding how climate change will affect food production in total and differ-

entially across the globe is apparent, and there is now a significant literature across disciplines on the

topic. Three major approaches to estimating the effect of climate on agricultural productivity have

developed (Blanc and Reilly 2017). Agroeconomic analyses focus on agronomic/crop science based

controlled experiments investigate the effect of warmer temperatures and higher CO2 concentrations

on yields (Antle and Stöckle 2017). These physical systems models capture the response of crops in

trials, but may miss the complexities involved in production and the adaptations farmers may make

in trying to optimize. The cross-sectional approach applies a Ricardian logic, arguing that under

competition the productivity of farmland is equal to net farm revenue (Mendelsohn and Massetti

2017). The panel data approach exploits existing cross-sectional and temporal variation in climate,

yields, net farm revenue to project future outcomes. Assumed in all three approaches, but often to

varying degrees, is the assumption that farmers adapt to changing climate by altering crop and tech-

nology choices. While yields respond to higher temperatures and different precipitations patterns

(Schlenker and Roberts 2009), agriculture producers adapt with new technologies and different

and hardier crops (Mendelsohn, Nordhaus, and Shaw 1994). Yet farmers are constrained in their

adaptation by soil type and water availability. The adaptation assumption is important because any

study that projects climate induced changes in productivity keeping crop and technology choices

constant is going to be overly pessimistic. It is also possible for the cross-sectional Ricardian

approach to be overly optimistic since it assumes that farmers make the best possible changes

without delay (Kelly, Kolstad, and Mitchell 2005).

In contrast to the cross-sectional Ricardian approach, fixed-effects models have the benefit of

establishing a causal relationship, particularly because they account for omitted variables. However,

because farm income can vary substantially from year to year as farmers store harvests in response

to prices, it is difficult to use fixed-effects models to capture the relationship between climate

and net income (Blanc and Schlenker 2017). As a result, estimates using fixed-effects models

do not allow for farmer adaptation by switching crops or technologies. This implies that, where

2

Ricardian approaches are likely optimistic in their estimates of impacts, fixed-effects models are

likely pessimistic (Mendelsohn and Massetti 2017).

Our objective in this paper is to propose the use of the statistical methodology of matching to

estimate the effect of climate change on food production. This can be viewed as an extension of the

concept of climate analogues (Hallegatte, Hourcade, and Ambrosi 2007) – areas that are climatically

similar across time – to estimate the effect of projected climate on agricultural productivity. Though

Easterling et al. (1993) employed an analogue to estimate the effect of climate in the Missouri-Iowa-

Nebrask-Kansas (MINK) region, to our knowledge we are the first to create climate analogues using

matching methods and estimate impacts at the county level, and in particular to focus on crops other

than the major grains.

Our study region is the Western “Fruitful Rim”, an area primarily in Idaho, Washington, Oregon,

California, and Arizona. This is a particularly interesting and ideal region for exploring the

analog/matching approach for two reasons. There is an enormous diversity in crops grown, which

allows for considerable adaptation through changing crop mix. This is very different than many

other production regions, like the Cornbelt and Great Plains in the U.S., that are highly specialized

in wheat, corn, and soybeans. One of the reasons that a matching approach could be a valuable

addition to the climate/agriculture toolbox is that it can relate economic outcomes to agronomic

decisions more directly. This is possible because of the “one-to-one” matching. Simultaneously,

an economic effect can be estimated by comparing cash rents between the location of interest and

its analog. Then, comparing all of the locations in the “treatment group” to their analogs permits

estimating an average treatment effect, in the parlance of the matching literature. Irrigated rents

are typically negotiated on a ten-year contract and as a result reflect the expected productivity

of the land over this period regardless of production methods and crop choice. This Ricardian

approach allows producers to employ the best mix of crops, inputs, and technologies that they can

to maximize the productive value of the land. It is also possible to use the analog to predict future

crop mix. This would not be possible in a standard regression approach.

Another reason to focus on the Western Fruitful Rim is that the region has a North-South

3

orientation. This leads to a considerable range in temperature regimes in terms of length of growing

season and temperature ranges during the season. This will be critical for achieving covariate

balance in the matching procedure. Also, the Western Fruitful Rim is dominated by surface water

driven irrigated production systems. This reduces the number of factors that need to be incorporated

into the matching process. Another reason to focus on this region is that it accounts for a very large

share of the total value of agricultural production for the country as a whole.

A final reason for our regional focus is that fruit and vegetable production is common through-

out, and these systems almost always require local downstream processing infrastructure. Costs

associated with reinvestment resulting from changing crop mix could be an important, yet currently

underappreciated question in the literature. A method that only considers farm-level economic

outcomes (net returns) cannot be used to consider this question. In contrast, the matching approach

can be applied in this way.

An important limitation of our study is that we have not yet incorporated changing irrigation

water availability due to changes in future snowpack. This is known to be a significant potential

climate change impact on this region. We plan to account for this in future research.

There are a couple of additional potential advantages to using matching estimators to analyze

climate change impacts on agriculture. To the extent that there is a correlation between included

covariates and omitted variables, matching’s improved covariate balance between control and

treatment groups reduces the potential for bias. Also, matching relaxes the assumption of a

functional form, which is useful when the relationship is particularly complex.

To preview results, we find that climate change will increase irrigated land rents by 24% in

2040, declining to 23% in 2060 and 2080. These results support the idea that on average the

projected climate in the fruitful rim will lead to increased agricultural productivity due to warmer

temperatures.

4

Data

We focus on the 177 counties in Washington, Idaho, Oregon, and California with valid irrigated

land rent data available from the USDA National Agricultural Statistics Service (NASS, 2017). As

a reference group we include all 599 counties with centriods1 west of the 100° meridian, which

receives significantly less precipitation than the eastern United States. These 599 counties form the

basis of our units of analysis.

For each county, we collect data from the USDA National Agricultural Statistics Service (NASS,

2017) on irrigated acres (available every five years from 1997 to 2017) and irrigated cropland rent

(available from 2008 to 2017)2. County demographic information on population, housing units,

and income are from the U.S. Census3. United States Census Bureau (2017) provides static county

characteristics on land area, water area, and the latitude and longitude of the county centroid.

Data on historical and projected climate consists of daily measures of minimum and maximum

temperature, total precipitation, and average wind speed on a 6-kilometer resolution latitude-

longitude gridded dataset. Historical climate data is from the VIC model and covers the period from

1979-2016 over 102,268 grid points that includes all points in counties with centroids west of the

100° meridian. Projected climate is from the MACAv2-METDATA (Abatzoglou 2011) and covers

30,140 grid points in Washington, Idaho, Oregon, and California from 2016-20994. To capture the

uncertainty in projected climate, we use six climate models5 that encompass a range of assumptions.

Each model projects climate data for four representative concentration pathways (RCPs), each of

which reflect atmospheric carbon concentration levels relative to pre-industrial levels. The RCPs

are 2.6, 4.5, 6.0, and 8.5, of which we include the 4.5 and 8.5 scenarios6.

For each grid point and each year, we calculate the length of the growing season as the dates

1Centroids are from United States Census Bureau (2017)2NASS data are retrieved using the R package rnassqs (Potter 2017).3Retrieved using the R package censusapi (Recht 2017).4The MACAv2-METDATA are derived from global climate model (GCM) data from the Coupled Model Intercom-

parison Project 5 (CMIP5, Taylor, Stouffer, and Meehl 2012) and statistically downscaled using a modification of theMultivariate Adaptive Constructed Analogues (MACA, Abatzoglou and Brown 2012) method with the METDATA(Abatzoglou 2011) observational dataset as training data.

5The climate models are: bcc-csm1-1, BNU-ESM, CanESM2, CNRM-CM5, GFDL-ESM2G, and GFDL-ESM2M.6We selected 4.5 and 8.5 for brevity’s sake and also because we are considered to be beyond the 2.6 scenario.

5

from the last day with a temperature below 0°C in the spring to the first day below 0°C in the fall.

For this growing season, we then calculate number of days, total growing degree days, average

minimum and maximum temperature, total accumulated precipitation, and number of hours at

each degree of temperature. Growing degree days (GDD) are the sum of the maximum daily

temperature between 0 and 32°C over the course of the growing season. Average minimum and

maximum temperature is the average of daily minimum or maximum temperature respectively. Total

accumulated precipitation is the sum of all precipitation over the growing season. Number of hours

at each degree is estimated following Schlenker and Roberts (2009) using a linear interpolation

between minimum and maximum temperatures and summing the number of hours over all days in

the growing season in each 1-degree temperature bin.

Soil data are from the Soil Survey Geographic Database (SSURGO, 2017), and contain in-

formation on drainage, elevation, land classification, and soil type and agricultural suitability for

geographic map units. SSURGO map units are irregular shapes comprising areas of similar soil

characteristics. We assign soil characteristics to each climate grid point based on the map unit that

the grid point falls within.

To create county-level climate and soil variables, we summarize over all points within the

county in two ways: taking the mean over all points, or selecting the location with the maximum

GDD within that county. Averaging over all points within a county provides a better estimate

of the average county characteristics, but won’t reflect the agricultural potential of mountainous

counties with substantial low-elevation agricultural land. Using the maximum GDD point within a

county to represent the county as a whole does not provide a good estimate of the average county

characteristics, but may provide a better estimate of county characteristics for agricultural areas

within the county.

The resulting data set consists of climate, agricultural, demographic, and soil for 599 counties

with centroids west of the 100° meridian from 1979-2017, though data on irrigated rents is only

available from 2008-2017. In addition, for each of the six climate models and two RCP scenarios, the

dataset contains records 30-year averages of projected climate variables for three time periods: 2040

6

(2025-2055), 2060 (2045-2075), and 2080 (2065-2095) as well as the current soil and geographic

characteristics for each county in the Fruitful Rim.

Method

Previous research has focused on yields or farm profits, with the issues of identification and

adaptation being a primary concern. Here we focus on irrigated rents, which allow for adaptation,

but employ matching as an identification strategy. Our approach is to first match the projected

climate and soil characteristics of counties in the Western Fruitful Rim to the current climate and

soil characteristics of counties west of the 100° meridian. The difference in irrigated land rent

between the matched counties is the treatment effect of projected climate.

In our model, the outcome irrigated land rents in a county is a non-linear function of expected

productivity, which depends on the climate and soil characteristics of the county, such that

Yit = g (Xit, S i) ,

where Yit is the irrigated land rent in county i at year t, Xit is the set of time-varying climate

variables, and S i is a set of time-invariant soil characteristics.

Our measures of climate in Xit consist of the length of the growing season as well as temperature

and precipitation. The growing season is defined as the time period from the last day in the spring

to the first day in the fall at which minimum temperature falls below 0°C. Following Schlenker and

Roberts (2009), we account for temperature by estimating the number of hours over the growing

season within a three-degree temperature range. For each day, we linearly interpolate between the

minimum and maximum temperature and sum the number of hours in each bin across all days in

the growing season, normalizing by the total number of hours in the growing season. Temperature

bins are the set {< 0, 0 − 3, 3 − 6, . . . , 36 − 39, > 39}. Precipitation is measured as accumulated

precipitation over the course of the growing season. Soil variables in S i consist of drainage class

and the share of silt, sand, and clay type soils. These capture the time-invariant properties of the soil

7

that limit the extent to which producers can adapt by switching crops or employing other strategies.

Matching

To estimate the effect of projected climate, we want to find

Yit − Yi,2012

, where t ∈ {2040, 2060, 2080} for each climate model and RCP scenario. This is the central problem

from a causal framework: we observe only the treated or the untreated outcome for a given unit

of observation. That is, Yobsi = Yi(Wi) and Ymis

i = Yi(1 −Wi), where Wi ∈ {0, 1} indicates treatment

(here we use a similar notation to G. W. Imbens and Rubin (2015)). This is in a sense a missing

data problem, where the goal is to estimate E [Yi(1) − Yi(0)], but either Yi(1) or Yi(0) is unobserved.

Both regression and matching rely on finding a set of covariates X such that Wi y (Yi(0),Yi(1))|Xi.

In other words, regression and matching require meeting the unconfoundedness assumption.

Unconfoundedness implies that missing and observed observations are equal in distribution,

that is(Ymis

i |Wi = w, Xi

)∼

(Ymis

i |Wi = 1 − w, Xi

). No amount of observed data allows us to infer the

distribution of Ymisi .

In our case, as is the the case for any outcome that has not yet taken place, the missing outcomes

are also the treatment outcomes, so Yi(1) = Ymisi , where Yi(1) ∈ {Yi,2040,Yi,2060,Yi,2080}. A necessary

step in matching is limiting the sample to treatment and control observations that have a common

support in the matching covariates. Given that all treatment outcomes are unknown (e.g. we don’t

know the irrigated rent value in the future for any county), this is particularly important.

Since Yit is unknown, it must be estimated via some method. In previous literature on climate, a

common strategy is to estimate an effect and apply general trends to estimate outcomes in future

years. An effect x per degree of temperature multiplied by the projected temperature change is the

projected effect. A more specific estimate is derived by first estimating a model using historical data

and using that model to predict future outcomes using projected climate. Here we use matching to

8

derive an estimate of projected irrigated land rents, where

Yit = minj

D(Zit,Z j,2012).

Here D(·) can be any distance function, which can include the propensity score. We use a

generalized distance function that is a weighted combination of propensity score and mahalanobis

distance described and implemented in Sekhon (2011) and Diamond and Sekhon (2013), where

D(Zi,Z j,K) =

√(Zi − Z j)T (S −1/2)T (KI)S −1/2(Zi − Z j).

Here Z = [π(X), X], where π(X) is the propensity score. Weights for each covariate and the

propensity score are contained in the vector K, so that KI is a k × k diagonal matrix of weights and

k = rank(Z). K is estimated via a genetic algorithm to maximize balance over the set of covariates

Z.

Yit can be estimated as a weighted average of the n nearest neighbors, where if m = 1 then the

value of the observation with the minimum distance is used. The estimate of the effect of projected

climate in future years is then E[Yit − Yi,2012] for each climate model and RCP scenario.

We estimate E[Yit−Yi,2012] in two ways, first as a simple post-match linear regression of the form

Yit = αTit + εit, and repeating the match using the predicted outcomes Yit as the treated outcomes to

estimate Abadie-Imbens standard errors (Abadie and Imbens 2006).

Results

This paper is motivated by a very simple empirical analysis. We identified all of the counties with

an irrigated cash rent estimate, and then calculated the average cash rent for each state as a simple

arithmetic unweighted average. We then plot this against an average measure of temperature for

these same counties for each state. This is shown in Figure 1. For the fruitful rim states, there is a

general nonlinear relationship between temperature as measured by GDD and agricultural land rents.

9

The first panel in Figure 1 plots current irrigated land rent and growing season GDD averaged over

2008-2016. The second and third panels show projected growing season GDD under the RCP 4.5

and RCP 8.5 climate scenarios in 2040, 2060, and 2080. A projected irrigated land rent is estimated

as a second order polynomial in GDD, demonstrating how irrigated land rents may increase in

Oregon, Idaho, and Washington but decrease in California under projected climate scenarios.

10

Table 1: Ratio of the number of unbalanced variables before matching relative to the number ofunbalanced variables after matching. Unbalancedness is determined by a KS test with p < 0.05.

Year RCP 4.5 RCP 8.52040 2.389 1.3662060 1.463 0.8872080 1.198 1

A main benefit of matching is an improvement in the covariate balance between the treatment

and control groups. To the extent that observed covariates are also correlated with any unobserved

covariates, matching reduces the bias introduced by omitted variables. We match projected climate

in counties to all counties in the western United States, resulting in substantially increased balance.

Figure 2 shows the standardized mean difference between the treatment and control groups before

and after matching for matching based on propensity score, mahalanobis distance, and Sekhon’s

(2011) genetic algorithm. The figure shows the differences for climate projections in the CNRM-

CM5 model, but figures for other models are similar.

One could argue that the entire western U.S. is the wrong group to select over, and that indeed

regression models would be better served by using just counties in fruitful rim states as the control

group. Figure 3 repeats the information in Figure 2, except that the region being matched over

is counties in Washington, Idaho, Oregon, California, and Arizona. This eliminates counties that

are geographically distant from counties with projected climate, so unmatched covariate balance

improves relative to the entire western U.S. However, even here matching provides an increase in

covariate balance.

The bootstrap Kolmogorov-Smirnov (KS) univariate test tests the null hypothesis that the

probability densities of each covariate are not different. A p-value less than 0.05 suggests that the

treatment and control are not balanced in that covariate. Table 1 summarizes the results of the

bootstrap KS test across matching covariates.

Effects are calculated by the difference in estimated irrigated rents under projected climate

scenarios and irrigated rents in the same county under current climate. These differences are

summarized in Table 2, where the effect is the effect under all climate models for 2040, 2060, and

11

Figure 1: Irrigated land rent and growing season GDD. Future rents are estimated from a model ofirrigated land rent as a second-order polynomial in growing season GDD.

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2040 2060 2080R

CP

4.5R

CP

8.5

−200 0 200 400−200 0 200 400−200 0 200 400

SiltSandClay

PrecipitationGrowing Season

Hours >40Hours 36−39Hours 33−36Hours 30−33Hours 27−30Hours 24−27Hours 21−24Hours 18−21Hours 15−18Hours 12−15

Hours 9−12Hours 6−9Hours 3−6Hours 0−3Hours <0

PS

SiltSandClay

PrecipitationGrowing Season

Hours >40Hours 36−39Hours 33−36Hours 30−33Hours 27−30Hours 24−27Hours 21−24Hours 18−21Hours 15−18Hours 12−15

Hours 9−12Hours 6−9Hours 3−6Hours 0−3Hours <0

PS

Standardized Mean Difference (CNRM−CM5, West)

● ●Before Matching Propensity Mahalanobis Genetic

Figure 2: Difference in covariates between treatment and control groups before and after matchingfor the CNRM-CM5 climate model. The unmatched control group consists of all counties west ofthe 100 degree meridian. 2040, 2060, and 2080 are 30-year averages about those years.

13

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2040 2060 2080

RC

P 4.5

RC

P 8.5

0 200 400 0 200 400 0 200 400

SiltSandClay

PrecipitationGrowing Season

Hours >40Hours 36−39Hours 33−36Hours 30−33Hours 27−30Hours 24−27Hours 21−24Hours 18−21Hours 15−18Hours 12−15

Hours 9−12Hours 6−9Hours 3−6Hours 0−3Hours <0

PS

SiltSandClay

PrecipitationGrowing Season

Hours >40Hours 36−39Hours 33−36Hours 30−33Hours 27−30Hours 24−27Hours 21−24Hours 18−21Hours 15−18Hours 12−15

Hours 9−12Hours 6−9Hours 3−6Hours 0−3Hours <0

PS

Standardized Mean Difference (CNRM−CM5, Fruitful Rim)

● ●Before Matching Propensity Mahalanobis Genetic

Figure 3: Difference in covariates between treatment and control groups before and after matchingfor the CNRM-CM5 climate model. The unmatched control group consists of counties in the fruitfulrim states of Arizona, California, Oregon, Washington, and Idaho. 2040, 2060, and 2080 are 30-yearaverages about those years.

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2080 under the RCP 4.5 and RCP 8.5 scenarios.

Table 2: Effect of projected climate on irrigated land rent.

Projected Climate Year

2040 2060 2080

RCP 4.5PS Match 0.25516∗∗∗ 0.24127∗∗∗ 0.24025∗∗∗

(0.05281) (0.05348) (0.05328)

Gen Match 0.7416∗∗∗ 0.83612∗∗∗ 0.83788∗∗∗

(0.04348) (0.04392) (0.04376)

RCP 8.5PS Match 0.2443∗∗∗ 0.23912∗∗∗ 0.23774∗∗∗

(0.05268) (0.053) (0.0531)

Gen Match 0.735∗∗∗ 0.87206∗∗∗ 0.9487∗∗∗

(0.04324) (0.04343) (0.04378)

Note: ∗p<0.1; ∗∗p<0.05; ∗∗∗p<0.01

Discussion

In our approach we seek a method of estimating climate effects that allows for producer adaptation

while minimizing bias in our estimates. In addition, we hope to provide a method of comparison

that allows researchers and stakeholders to evaluate how those adaptations may occur. Matching

to estimate the effect of projected climate on irrigated land rents satistfies these criteria. Matching

reduces bias by improving balance between treatment and control observations. It also matches with

specific county analogues that can be further examined for insight into the strategies that producers

are using to adapt to climate in that location. The strategies that producers employ in california

counties that are the climate analogues for the climate in Washington counties in 2040 provide

suggestions of how producers can adapt and how government policy can be set now to account for

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that adaptation.

Matching is not perfect, however. In particular, if projected climate in the area in question does

not have a good current climate analogue, matches found via minimum distance may still be poor

matches. There may be no good current climate analogues for the projected climate in Arizona

counties, for example. This emphasizes the importance of having a common support between the

projected climate and soil covariates and current climate and soil covariates.

In addition, matching may not be a useful method where adaptation is limited or where a single

crop is vastly more prevalent (and hence more profitable). In some areas of the Middle and Eastern

United States for example, there corn, soybeans, or cotton may be the only crop grown, making it

difficult to estimate effects.

Finally, though matching improves covariate balance for observed covariates and to unobserved

covariates to the extent that unobserved covariates are similarly distributed, it cannot account for

unobserved covariates that are independent of observed covariates. One important case here is that

water availability for irrigation, either via water rights or via available infrastructure, may limit

adaptation. A county could match to another county climatically that has much better access to

irrigation water, and hence higher irrigated land rents. This suggests that our estimates may be an

upper bound on the effect of climate on agricultural productivity as measured by irrigated land rents.

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