# Climate, Agriculture and Food
Submitted as a chapter to the Handbook of Agricultural Economics

Ariel Ortiz-Bobea Associate Professor, Charles H. Dyson School of Applied
Economics and Management, Cornell University. Email<EMAIL_ADDRESS>I am
thankful for useful comments provided by the editors Christopher Barrett and
David Just as well as by Thomas Hertel and Christophe Gouel. Code and data
necessary to reproduce the figures and analysis discussed in the chapter are
available in a permanent repository at the Cornell Institute for Social and
Economic Research (CISER): https://doi.org/10.6077/fb1a-c376.

###### Abstract

Agriculture is arguably the most climate-sensitive sector of the economy.
Growing concerns about anthropogenic climate change have increased research
interest in assessing its potential impact on the sector and in identifying
policies and adaptation strategies to help the sector cope with a changing
climate. This chapter provides an overview of recent advancements in the
analysis of climate change impacts and adaptation in agriculture with an
emphasis on methods. The chapter provides an overview of recent research
efforts addressing key conceptual and empirical challenges. The chapter also
discusses practical matters about conducting research in this area and
provides reproducible R code to perform common tasks of data preparation and
model estimation in this literature. The chapter provides a hands-on
introduction to new researchers in this area.

May 2021

Keywords: climate change; impacts; adaptation; agriculture.
Approximate length: 31,200 words.

###### Contents

  1. 1 Introduction
  2. 2 Basic concepts and data
    1. 2.1 Weather and climate
    2. 2.2 Adaptation
    3. 2.3 Weather data
    4. 2.4 Climate models
    5. 2.5 Degree-days and agriculture
  3. 3 Climate change impacts and adaptation
    1. 3.1 Biophysical approaches
    2. 3.2 The Ricardian approach
    3. 3.3 Panel profit and productivity approaches
    4. 3.4 Statistical crop yield models
    5. 3.5 Mixed statistical and biophysical approaches
    6. 3.6 Joint estimation of short and long run responses
    7. 3.7 Retrospective climate change impacts
    8. 3.8 Statistical crop quality models
    9. 3.9 Modeling planting and harvesting decisions
    10. 3.10 Irrigation and other input adjustments
    11. 3.11 Market equilibrium and trade
    12. 3.12 Understudied problems and unsettled questions
  4. 4 Coding and other empirical matters
    1. 4.1 Aggregation of point weather data
    2. 4.2 Aggregation of gridded weather data
    3. 4.3 Estimating non-linear effects
    4. 4.4 Estimating within-season varying effects
    5. 4.5 Spatial dependence
    6. 4.6 Common robustness and sensitivity checks
  5. 5 Conclusion

##  1 Introduction

Climate has always been critical to the development of agriculture. For
instance, changes in climate are believed to have played an imporant role in
the origin of agriculture (Gupta, 2004; Matranga, 2017). More recently, the
story surrounding the territorial expansion of agriculture over the past few
centuries was also one about adapting farming practices and existing crops to
new climates (e.g. Olmstead and Rhode, 2011).

But climate is now changing at an unprecedented rate overwhelmingly due to
human causes (Pachauri et al., 2014). And even as the extent of global
agricultural land stabilizes, and agricultural productivity continues to rise,
climatic shocks continue to play a central role in explaining fluctuations in
agricultural production (Lesk et al., 2016). In fact, recent climate change
appears to have already substantially slowed down global agricultural
productivity growth (Ortiz-Bobea et al., 2021). In this context, research is
needed not only to understand potential future impacts of anthropogenic
climate change on agriculture, but also to identify efficient strategies to
enhance adaptation to a changing climate. This includes identifying market
failures and possible barriers to adaptation.

Unlike mitigation of climate change, which requires a coordinated
international effort to reduce greenhouse emissions, adaption is generally
framed as a local matter, something that only local private agents have to
deal with. However, farmers rely directly or indirectly on public
infrastructure, and buy technologies and sell products in markets with
important government presence and regulation. Moreover, the increasing
globalization of agricultural markets and technologies challenge this view. So
agricultural adaptation to climate change goes beyond the boundaries of the
farm.

This chapter is primarily aimed to introduce new researchers to the analysis
of climate change impacts on the agricultural sector. Most of the content
should be highly accessible but familiarity with matrix algebra is necessary
to take fully advantage of the content. Importantly, the chapter provides code
and data to reproduce common tasks while conducting research in this area,
including data preparation and cleaning as well as the estimation of semi-
parametric models. All of the figures illustrating these techniques are fully
reproducible in R. R is a an increasingly popular open source statistical
software that will ensure a wide access to this material to all researchers.

The chapter is organized in 3 main sections. Section 2 covers important basic
concepts and terminology regarding climate change and agriculture and
discusses various aspects regarding common datasets used in economic analysis
in the field. Subsection 2.1 defines weather as a random variable and climate
as describing the moments of the underlying distribution of that weather
variable. Weather change and climate change mean different things and this
clarification will allow a more precise discussion surrounding these concepts
throughout the chapter. Subsection 2.2 defines what we mean by adaptation to
climate change following the formal definition adopted by the
Intergovernmental Panel of Climate Change (IPCC).

Conducting research in this area also require familiarity with different types
of weather data. Subsection 2.3 discusses important features about historical
weather datasets including their format (e.g. gridded, weather stations). I
also provide the names of common datasets used in the literature. Subsection
2.4 also discusses the basics of General Circulation Models (GCM) and how the
climate science community improves these models over time within global inter-
comparison projects that feed into the IPCC reports. Subsection 2.5 covers
some basic concepts regarding the use and interpretation of degree days. As it
will become apparent, temperature has been found to be a critical driver of
agricultural production. The use of degree days is not new in agriculture
science, and I provide a historical perspective on the concept and how its use
has evolved in the more recent economic literature.

Section 3 dives into specific areas of research or methodologies to assess the
economic impacts of extreme weather or climate change on agriculture. An
important emphasis in some of the techniques and approaches presented in this
section deal with the extent to which farmer adaptations are captured and
represented. Subsection 3.1 provides an overview of process-based biophysical
approach of modeling crop yields and how these are integrated into economic
models to simulate climate change impacts to the agricultural sector. That
presentation provides an overview of the early literature as well as recent
trends toward the adoption of multi-model ensembles and inter-comparison
projects.

Subsection 3.2 transitions to discuss the cross-sectional Ricardian approach,
one of the first econometric approaches introduced to evaluate the impact of
climate change on agriculture. Here I discuss some the advantages and pitfalls
of this approach including recent advances. The following subsection 3.3 deals
with models estimating the effects of weather fluctuations on agricultural
profits or aggregate measures of productivity based on panel data. Because
these models include location fixed effects, they provide a more credible
identification of the effect of weather than correctional approaches. I also
provide an overview of their limitations.

Subsection 3.4 discusses the rise of statistical crop yield models in
agricultural economics and related fields. These models are also based on
panel data but their focus on specific crop yields allows researchers to
engage in more detailed crop-specific treatment of weather variables. I try to
provide a historical perspective of the origin of these models before the
renewed interest in the context of climate change. I also briefly discuss new
creative ways to combine statistical and biophysical approaches to modeling
crop yields in subsection 3.5. These new efforts provide exciting new
frontiers of collaboration with natural scientists.

In subsection 3.6 I discuss an emerging area of research proposing new methods
to overcome certain perceived limitations of both cross-sectional and panel
approaches. I describe these recent advances and their limitations. I
highlight new work that clarifies the theoretical interpretation of panel
estimates. I also provide a brief overview to retrospective climate change
studies in subsection 3.7. Most of the research emphasis has focused on
assessing future potential impacts of climate change on the sector. However,
anthropogenic forces have already changed climate which is about 1°C warmer
than in pre-industrial times. As climate continues to change, such
retrospective studies are likely to increase in popularity. I provide a brief
overview of early and more recent studies. The rest of section 3 is less about
methods, and more about various aspects of capturing climate change impacts
and farmer and market responses.

There is a vast literature assessing impacts on crop yields, but there is much
less work focusing on the impact on crop quality. Subsection 3.8 presents
recent work on this topic and lays out some challenges for future work.
Subsection 3.9 discusses the analysis of planting and harvesting decisions,
ranging from the timing of planting, to the decision to increase cropping
frequency (e.g. double cropping). Naturally, irrigation is central to
agriculture and is often perceived as an important mechanism for farmers to
adapt a water scarcity in a changing climate. I cover this topic in subsection
3.10, where I discuss early studies but also provide a look to more recent
work based on new data sources collected from satellites or providing high-
frequency information about water use at the farm level. I also discuss the
role of trade in the analysis of climate change impacts on agriculture in
subsection 3.11.

I conclude section 3 addressing various questions that still seem unsettled
and where more research is likely needed (subsection 3.12). For instance,
there is insufficient work on the economic of agricultural innovation in the
context of a changing climate. For instance, it is unclear whether current
levels and the current nature of agricultural R&D is adequate in a rapidly
changing climate. In addition, there are many lingering uncertainties
regarding the important of changing pest pressure as well as the rise of soil
salinity in a warming world. There is also little emphasis on climate justice.

Section 4 provides more practical and hands-on guidance regarding common
empirical tasks in this area of research. The chapter is accompanied with
reproducible R code that illustrates how to perform many of these tasks in a
systematic way. Providing the accompanying code seems important for new
researchers entering this field because many of the data management and
estimation techniques are yet not standard in agricultural economic curricula.
The code provided can be easily adapted to new projects and accelerate the
learning curve of new entrants. For instance, the section provides an overview
on how to efficiently aggregate point and gridded weather datasets
(subsections 4.1 and 4.2). The techniques that I introduce are based on matrix
algebra and sparse matrices to speed up aggregation relative to standard
“canned” functions in R packages.

An important empirical consideration in the analysis of the effects of extreme
weather and climate change on agriculture is the presence of nonlinearities
and thresholds. Climate change will lead to more frequent extreme weather and
thus capturing such nonlinearities is critical. Importantly, temporal and
spatial averaging of weather conditions can conceal exposure to extreme
weather and thus more advanced techniques are required to overcome such
obstacles. In subsection 4.3 I describe how to estimate non-linear effects of
weather variables semi-parametrically based on bins representing the entire
distribution of time exposure to varying environmental conditions (e.g.
temperature). I also describe how to construct these datasets. The R code
provided illustrates not only how to construct these data but also how to
estimate these models. I also clarify certain misconceptions and confusion
regarding the estimation of these models. In subsection 4.4 I also present a
two-dimensional generalization of the semi-parametric model above that allows
simultaneously for non-linear and within-season varying effects. This is
particularly valuable when trying to capture varying sensitivities to
environmental conditions within the growing season.

A common feature of agricultural and climate data is spatial dependence, which
generally translates into spatial dependence in a regression setting.
Subsection 4.5 introduces a few approaches to deal with this by either
correcting for spatial dependence or by harnessing spatial dependence to
obtain a more efficient estimator. Finally, subsection 4.6 discusses common
robustness checks in the literature as well as strategies to present these in
a concise manner in a “specification chart”. I also provide reproducible code
to conduct these sensitivity checks.

I finally conclude in section 5 where I provide some final thoughts about the
potential for new collaborations and for enhancing the impact of economic
research in this field.

##  2 Basic concepts and data

Here I discuss basic concepts and terminology regarding climate change and how
farmers respond to it. This preliminary step is critical in helping new
researchers understand the common language used in this field.

###  2.1 Weather and climate

Throughout this chapter I refer to “weather” and “climate” which are related
but distinct concepts. A useful way to characterize their relationship is to
think about weather as a random variable representing the state of the
atmosphere. That random variable could represent, say the “average temperature
during the month July in Ithaca, NY”. The value taken by this variable on a
given year represents weather conditions.

In contrast, “climate” refers to the moments of the probability distribution
of that random variable. Thus, quantities such as the “long term average” or
the “inter-annual variability” of this random variable relate to climate. It
is often the case that climatologists (and economists by extension) refer to
“climatology” as the 30-year average of a weather variable, and as “climate
variability” as the inter-annual variance of a weather variable. This concept
is different from the term “intra-annual weather variability” which refers to
the variability of weather conditions between contiguous time periods within a
season or the year.

As a result, the term “climate change” refers to the change in the long term
distribution of weather conditions at a given location. By definition, it is a
long term process because climatologies are defined over several decades. It
follows that climate change eventually results in the rising frequency of
weather events that were previously considered unusual or extreme. That being
said, because of natural variability in the climate system, a sequence of
extreme weather events is not evidence of climate change per se. Indeed,
assessing changes in climate requires a relatively long time series of weather
observations.

In addition, the term “climate change” should also not be conflated with
“weather change” which may refer to either inter-annual or intra-annual
fluctuations in weather conditions depending on the context. Moreover, recent
weather trends should not be conflated with climate change. There are well
known cyclical components in the climate system such as El Niño-Southern
Oscillation (ENSO) which are linked to cyclical changes in weather patterns in
various parts of the world. These multi-year weather patterns do not
constitute climate change, though climate change may alter their intensity.

Climate change can have both natural or human causes. An entire field in
climate science called “detection and attribution” focuses on determining
whether observed historical changes in climate can be attributed to specific
causes. The term “anthropogenic climate change” thus refers to changes in
climate that have been shown to originate from human activities, including
through the emissions of greenhouse gases.

Making the clear distinction between weather and climate is important. Not
only does it help avoid ambiguous terminology and helps convey ideas more
clearly, but it also has economic implications. The reason is that while
economic agents cope directly with weather conditions, they actually form
expectations about climate.

###  2.2 Adaptation

According to the IPCC (2014), adaptation to climate change in human systems is
“the process of adjustment to actual or expected climate and its effects, in
order to moderate harm or exploit beneficial opportunities”. It should be
clear why assessing the potential impacts of climate change on agriculture
should require considering the degree to which farmers would adapt a new
climate. Not accounting for adaptation would naturally overstate potential
damages and under appreciate potential opportunities.

Agricultural economists have mostly focused on adaptation undertaken by
farmers. If you consider weather as a stochastic essential input, then the
adjustments of traditional inputs under the control of the farmer to maximize
profit or utility in response to weather fluctuations are forms of farmer
adaptation. Input decisions are typically sequential in nature (Antle, 1983),
so certain decisions are committed irreversibly early in the season (e.g. crop
and parcel choice, acreage, etc.) before the farmer gets to observe the
weather realization. As a result, some inputs remain fixed throughout the
growing season, constraining the farmer to a limited range of adaptations. In
general, these short-run adaptations to weather fluctuations understate the
range of adaptations undertaken by farmers when considering long run
adjustments in response to a changing climate.

However, certain short run adjustments may not be available to the farmer in
the long run. One example may be irrigation. For instance, a farmer with land
equipped for irrigation may increase the amount of water used in response to
dryer weather conditions. However, if the source of irrigation water is
projected to be depleted or water prices are expected to be much higher in the
future, then adjustments made in the short run may not be indicative of those
available in the long run.

The empirical characterization of future farmer adaptations generally relies
on historical behavior. But past behavior relative to a change in a weather
shock (or small changes in climate) could mischaracterize the degree to which
farmers may adapt in the long run. This is somewhat related to the Lucas
critique applied to the climate change context (see Kahn, 2014).

Accounting for adaptation is critical to the estimation of potential future
climate change impacts on agriculture. This has been a major emphasis in the
literature. Not accounting for adaptation would naturally overstate damages.
Thus researchers typically seek to constrain or characterize their findings
depending on the degree to which farmers can adapt in their modeling approach.

Capturing or measuring long run adaptations to climate change is challenging.
It ultimately requires capturing adjustments to the production process in
response to a long term change in the distribution of weather conditions.
Ideally, characterizing this process requires a long time series of weather
and production decisions. Long longitudinal datasets with detailed information
about production practices are very rare, making detection of adaptation
activities elusive.

Explicitly accounting or modeling all possible farmer adaptation to a changing
climate is intractable. Farmers have numerous potential adjustments to their
production decisions. This could include changes in input use, tilling
practices, planting dates or crop mix for crop production, or the change in
management, feed, animal breeds, equipment or infrastructure for livestock
production. As a result, researchers often rely on indirect evidence to
identify or quantify adaptation (or lack of).

The IPCC (2014) also employs the term “maladaptation” which refers to “actions
that may lead to increased risk of adverse climate-related outcomes, increased
vulnerability to climate change, or diminished welfare, now or in the future”.
However, this term is rarely used in mainstream economic academic discussions.
In the agricultural context, this would mean that agriculture is growing more
vulnerable to climate change, such as becoming increasingly sensitive to
higher temperature (e.g. Lobell et al. 2014; Ortiz-Bobea et al. 2018, 2020).
However, such changes in sensitivity to extreme temperature may result from an
optimal tradeoff so referring to such phenomena as maladaptation which carries
a undesirable connotation may be misleading.

Note that the notion of economic efficiency is absent from the IPCC
characterization of adaptation. Economists bring a unique perspective to
analyze the economic desirability of adaptive investments from a welfare
perspective. This is more often than not absent for the analysis and
discussions surrounding adaptation.

###  2.3 Weather data

Weather data is a fundamental component of conducting empirical analysis of
climate change impacts and adaptation. Here I highlight some key features of
such data without being exhaustive. I encourage readers to consult Auffhammer
et al. (2013) for a complete guide on how to use weather data and climate
model output in economic analysis.

Basic weather variables like air temperature and precipitation are commonly
measured in weather stations. These are commonly (but not always) government-
run facilities with the necessary instrumentation to record information about
atmospheric conditions. In these facilities, temperature has historically been
measured directly via thermometers, whereas precipitation is measured via rain
gauges, which measure the amount of precipitation falling within a time
interval, typically a day. In certain countries like the US and parts of
Western Europe, this instrumental record dates back to the 19th century. Air
temperature varies throughout the day, and it is sometimes possible to obtain
hourly data for certain regions in recent years. But data is more commonly
available at the daily, monthly or annual scales. In such cases summary
statistics are reported including maximum, average and minimum temperature or
total precipitation over the given time period. Note that strict rules and
protocols govern the recording and reporting of official weather data.

Temperature measurements prior to the use of thermometers are based on proxy
variables (e.g. tree rings) and are used to reconstruct past weather
conditions in paleoclimatology. Since the late 1970s, researchers can also
obtain remotely-sensed temperature from satellites which are derived
indirectly from microwave radiation.

Because temperature and precipitation are commonly measured at specific
locations (weather stations) throughout the landscape, such type of weather
data is referred to as “point data” in Geographical Information Systems (GIS).
A point is associated with precise geographical coordinates and is thus said
to be geo-referenced.

Figure 1A provides an overview of the spatial distribution of the more than
100,000 weather stations reporting daily information in the Global Historical
Climatology Network (GHCN) in 2020. The GHCN is the world’s largest database
of climate summaries from land surface stations across the globe and it is
managed by the National Oceanic and Atmospheric Administration (NOAA). The
distribution of weather stations can be very sparse across the world, even
within countries like the US (Fig. 1B). This spatial sparsity raises
challenges for obtaining correct weather information in areas located far from
weather stations, particularly when the landscape has pronounced orography. In
section 4.1 I provide a brief and reproducible introduction on (very) basic
weather station data interpolation.

Figure 1: Spatial distribution of weather stations in the Global Historical
Climatology Network in 2020.

With the goal of providing more complete spatial coverage in a consistent
fashion, climatologists have developed “gridded” weather datasets based on
various interpolation techniques. These interpolation techniques often rely on
elevation and other physical factors that are known to affect both temperature
and precipitation. These procedures are considerably more sophisticated than a
simple spatial interpolation. These geo-referenced datasets come on a regular
grid and are referred to as “raster” data in GIS. They are characterized by a
spatial resolution, often measured in degrees or distance. Raster data is
fundamentally structured as a matrix, where each entry corresponds to a patch
of of the Earth’s surface.

It is important to clarify that some of gridded weather datasets can sometimes
incorporate numerical weather models (similar to those used for weather
forecasts). In that case these gridded weather data are referred to as
“reanalysis”. This is one example of “modeled” data that incorporates both
observations (from weather stations) and information from a mechanistic
weather simulation model. The advantage of such data is that they can provide
a spatially and temporally consistent field of weather information even when
there are gaps in the underlying weather station data. They can also provide
output of variables that are actually not being actually measured in any
consistent way (e.g. temperature or wind speed at high altitudes).

So far I have only discussed weather variables and data relating to
atmospheric conditions. For certain applications the researcher might be
interested in more direct measures of water content or temperature in the
soil. Direct measurement of soil water content and temperature are very rare
and only available over limited areas and time periods in a handful of
nations. Obtaining data on these variables at larger scales generally requires
relying on modeled data, although new satellite sensors are increasingly able
to indirectly measure some of these soil moisture variables.

The evolution of soil water content and temperature is a complex process that
is typically modeled with a Land Surface Model (LSMs). An LSM takes “forcing”
or exogenous variables as inputs (e.g. surface temperature, precipitation,
wind, air humidity, etc.) to characterize the evolution of soil conditions
over time. Some of the key variables of interest include soil water content
but also soil temperature. These models provide a modeled snapshot in time of
these variables at various depths in the soil, often down to a couple meters.
The use of certain highly detailed LSM datasets can be cumbersome as they may
require manipulating terabytes of data. For some applications, the use of
simpler drought indices, such as the Palmer Drought Severity Index (PDSI) or
the Standardized Precipitation Index (SPI), may suffice (see Heim, 2002).
These indices seek to approximate water deficit conditions based on water
supply (precipitation) and demand (evapotranspiration and runoff) with
relatively simple algorithms.

| Spatial | Temporal |
---|---|---|---
Name | Coverage | Resolution | Coverage | Resolution | Source
PRISM | CONUS | 4 km | 1981 – | daily | Daly et al. (1997)
Daymet | North America | 1 km | 1980 – | daily | Thornton et al. (2014)
NARR | North America | 0.3 deg | 1979 – | 3-hourly | Mesinger et al. (2006)
NLDAS | North America | 0.125 deg | 1979 – | hourly | Xia et al. (2012)
GLDAS | Global | 0.25 deg | 1948 – | 3-hourly | Rodell et al. (2004)
GMFD | Global | 0.25 deg | 1948 – 2016 | daily | Sheffield et al. (2006)
Table 1: Commonly used gridded weather datasets.

In table 1 I include a list of commonly used gridded weather and land surface
datasets with at least a daily temporal resolution. This list is by no means
exhaustive but provides the reader with a starting point in their analysis.
Monthly datasets are easier to come by and typically offer longer temporal
coverage. For instance, the widely used monthly version of Oregon State
University’s Parameter-elevation Regressions on Independent Slopes Model
(PRISM) dataset over the contiguous United States (CONUS) is available since
1896.

An important point regarding empirical work in this literature is the common
mismatch in spatial resolution between agricultural and weather data.
Agricultural data is often available to researchers after being aggregated to
administrative units such as counties, states or even countries. This
aggregation is sometimes performed from micro-data from surveys or census to
preserve anonymity of individual farmers. Unless a researcher is dealing with
field or farm-level data, the spatial resolution of agricultural data is
typically coarser than that of gridded weather data. That is, several grid
cells fall within the boundaries of the administrative unit. As a result,
researchers end up aggregating the gridded weather data to the administrative
unit level.

This naturally raises the question of how should gridded weather data be
aggregated to administrative levels. Certain administrative units (e.g. US
states) can be fairly large and heterogeneous and contain areas with little to
no agricultural activity (e.g. like high mountains or deserts). In other
words, weather conditions in certain parts of the administrative unit may be
irrelevant for agricultural production within that unit. A common practice is
to rely on fine scale land cover data (e.g. cropland, pastures, or a
combination) to use as an aggregation weight. Land cover data comes in raster
format and with spatial resolutions ranging anywhere from 30m to 1km depending
on the region of the world.

To illustrate this point, Fig. 2A shows maximum temperature in California on
August 16, 2020 when possibly the highest temperature ever recorded on Earth
(54.4 °C) was measured in the Death Valley (darkest shade of red). This daily
gridded data is from PRISM and shows wildly varying weather conditions across
the state on the very same day. However, agriculture is mostly concentrated in
the Central Valley region. This can be seen in Fig. 2B showing the share of
cropland within each PRISM grid cell. A common practice is to aggregate the
weather (panel A) variable within each county (or within the state) based on
weights proportional to the cropland cover (panel B). The large climatic
variations within California illustrate how critical land cover information
can be for representing environmental conditions within administrative units.

Notes: Panel A shows maximum temperature corresponding to August 16 of 2020
over California. This is gridded daily data from PRISM. Panel B shows the
share of cropland contained in each of the PRISM grid cells. The grid cell
share was derived from finer scale 30m land cover data for 2016 from the
National Land Cover Database (NLCD).

Figure 2: Gridded data and cropland land cover in California.

Intuitively, spatial weighting procedures should make little difference if we
are located in a relative small or homogeneous administrative units. However,
potentially substantial differences could arise between different weighting
schemes in the presence of climatically diverse units. Some have suggested
that the weighting should be performed by value (rather than land cover)
although it seems unclear how livestock would be accounted for in such
circumstances. One way to think about issues about spatial aggregation is to
frame it in terms of measurement error. It turns out that implications of
these practices have not been chracterized. Researchers often end up showing
regression results under alternative weighting schemes to assuage concerns
during the peer review process. This practice seems suboptimal and more
systematic analysis of the consequences of various strategies of spatial data
aggregation are needed.

There are also issues regarding temporal aggregation in weather data.
Aggregating weather data over time can also result in measurement error if the
weather conditions are non-additive and if non-linearities in exposure to
various levels of weather conditions are important, which they likely are.

###  2.4 Climate models

Climate scientists have developed Global Circulation Models (GCMs) to simulate
the evolution of the climate system. These models are fundamentally similarly
to numerical weather models used in weather forecasting, but incorporate a
more complete representation of energy exchanges between land, oceans, sea ice
and the many layers of the atmosphere. Central to these models are the Navier-
Stokes equations, partial differential equations that describe the movement of
viscous fluids. Solving these equations to describe moving air masses in three
dimensions requires considerable computational power, which is why running
these models requires super computers. Major countries have research groups
and labs with their own version of these models.

In order to learn more about factors affecting our climate system, modeling
groups have joined a global inter-comparison project called the Coupled Model
Inter-comparison Project (CMIP). Four of such inter-comparisons have been
completed (CMIP Phases 1, 2, 3 and 5) and there is one under way (CMIP Phase 6
or CMIP6). The key feature of CMIP is the parallel implementation of identical
climate experiments across a wide range of GCMs. Some of these experiments are
designed to learn about specific aspects of these models, so that GCMs can be
improved. However, some of these climate experiments are much more policy
relevant and seek to understand how the global climate system is influenced by
anthropogenic influences.

Various experiments seem particularly policy relevant and are commonly used by
economists. Using CMIP6 terminology, these include the Shared Socioeconomic
Pathways (SSPs, see Riahi et al., 2017), including SSP1-2.6, SSP2-2.5,
SSP3-7.0 and SSP5-8.5. The SSPs correspond to different scenarios about the
nature economic development and the pathway of climate forcing (e.g.
emissions) throughout the century. The appended numbers to these scenarios
(i.e. 2.6, 4.5, 7.0 and 8.5) represent the additional radiative forcing on our
climate system in Watts/m2 in the year 2100. The higher the number, the higher
the additional radiative forcing, and the higher global temperatures are
projected to rise. These scenarios are analogous to the Representative
Concentration Pathways (RCPs) scenarios used in CMIP5, and the Special Report
on Emissions Scenarios (SRES) used in CMIP3. Researchers can relate these
projected future states of the atmosphere under various GCMs and SSPs with the
“historical” experiment that seeks to replicate the conditions of our
historical climate system from the nineteen century through 2015 in the case
of CMIP6. The “historical” experiment considers both historical levels of both
natural (e.g. volcanic eruptions from el El Chichón in 1982 and Pinatubo in
1991) and anthropogenic forcing (e.g. greenhouse gas emissions since the
industrial revolution).

Other relevant climate experiments that are relatively underused by economists
are the “historicalNat” in CMIP5 and “hist-nat” in CMIP6. These experiments
run a historical simulation but only with natural forcing. That is, the output
of these experiments provide a counterfactual sequence of modeled weather
trajectories that exclude human influence from the climate system. In climate
science, the comparison of these experiments and the “historical” experiment
is a foundation of attribution studies that seek to establish to what extent
extreme weather events (e.g. heat waves) are likely to arise because of human
influences, and not because of natural variability. Some studies have used
this approach to analyze the historical impact of anthropogenic climate change
on agriculture (See section 3.7).

It should be noted that output from climate models is gridded in nature
(raster format) and can be manipulated in the same way than gridded weather
datasets previously discussed.

Finally, it is worth noting that the CMIPs serve as the basis of the
Assessment Reports (AR) for the first working group (WGI) of the
Intergovernmental Panel of Climate Change (IPCC) charged with describing the
physical basis of the factors affecting our climate system. In fact, the name
of the CMIP and the AR are in phase, so that the lessons from CMIP6 feed into
the the Sixth Assessment Report of AR6. The ARs serve as an input for
international negotiations regarding adaptation and mitigation of
anthropogenic climate change within the United Nations Framework Convention on
Climate Change (UNFCCC).

###  2.5 Degree-days and agriculture

A growing number of studies rely on variables representing “degree days”,
“growing degree days” (GDD), “damaging degree days” (DDD), “extreme degree
days” (EDD) or “killing degree days (KDD) for analyzing the effect of
cumulative temperature exposure on agricultural production. Although the
growing popularity of degree-day measures seems relatively recent in
agricultural economic research, the concept has roots that are centuries-old
(Réaumur, 1735). Here I provide a brief background on the concept and how to
compute these variables.

A degree-day is one of the many units of measurement of thermal time. Thermal
time is a physical quantity measured in units of temperature $\times$ time.
This concept is very familiar to scientists studying phenology, which is the
study of how the periodicity of biological cycles are influenced by their
environment. The concept emerged as an heuristic tool to predict the _length_
of the different phases of plant life cycles (Réaumur, 1735). Some measures of
thermal time are highly correlated with the timing of numerous phenological
events, or cyclical natural phenomena, such as insect or plant development. In
plants, such development phases are typically signaled by the appearance of
new and differentiated organs such as the emergence of subsequent leafs and
flowers or the formation of fruit. French scientist René-Antoine Ferchault de
Réaumur laid the foundations of thermal time in the eighteenth century as
recalled by Wang (1960): _“He summed up the mean daily air temperatures for 91
days during the months of April, May and June in his locality and found the
sum to be a nearly constant value for the development of any plant from year
to year.”_ Thermal time subsequently became a pivotal concept in phenology
(Hudson and Keatley, 2009, ch. 1).

Indeed, the timing of many biological cycles, particularly in plants and
insects, is closely correlated with thermal time accumulation. For this
reason, biologists coined a term that measures thermal time accumulation,
_Growing Degree-Days_ (GDD). This biological thermal time corresponds to
cumulative temperature during a period of time. Intuitively, it is an amount
of accumulated exposure to heat.111Although strictly speaking this is inexact
because “heat”, in thermodynamics, is a form of energy which is measured in
Joules, not in temperature units. There is, however, a direct relationship
between temperature change of a body and the heat it receives. This quantity
is often defined mathematically. As shown in equation 1, thermal time $T$ is
typically expressed as a function of two temperature thresholds,
$\underline{h}$ and $\overline{h}$ and two points in time, $t_{0}$ and
$t_{1}$.

$T(\overline{h},\underline{h},t_{0},t_{1})=\intop_{t_{0}}^{t_{1}}H(t)dt\qquad\qquad\textrm{where
}H(t)=\begin{cases}\overline{h}-\underline{h}&\textrm{if }h(t)>\overline{h}\\\
h(t)-\underline{h}&\textrm{if }h(t)\in\>]\underline{h};\overline{h}]\\\
0&\textrm{if }h(t)\leqslant\underline{h}\end{cases}$ (1)

This definition implies that any measurement of thermal time is a function of
the two temperature thresholds and a duration. In fact, the two temperature
thresholds, $\underline{h}$ and $\overline{h}$, are experimentally determined
to yield a nearly linear relationship between thermal time accumulation and
biological development.222 For instance, for the early-maturing dwarf hybrid
sunflower plant (Pioneer 6150) with $\underline{h}$ defined as 0°C (undefined
$\overline{h}$), the first two true leaves appear after exposure to 249-313
GDD, flowering begins at 935-1077 GDD, and maturity is achieved after
1780-1972 GDD.

The link between temperature and the timing of biological cycles can be
explained at the molecular level within cells. Air temperature, at the most
basic level, affects cellular function, and animals and plants have developed
strategies to take advantage of climatic conditions conducive to their growth
and largely avoid conditions that are harmful. In the case of crops, when air
temperature is below the lower threshold, $\underline{h}$, also referred to as
the crop-specific “base temperature,” or above the higher threshold,
$\overline{h}$, crop development essentially stops (Ritchie et al., 1991;
McMaster and Wilhelm, 1997). Enzymes, which are proteins that accelerate
biochemical reactions within cells, become too rigid at low temperatures and
coagulate at very high temperatures, leading to slow or entirely inhibited
crop growth (Bonhomme, 2000). In other words, because plants cannot regulate
much their own temperature, their metabolism is subject to outside
temperature, which affects the speed of biochemical reactions.333Organisms
unable to actively regulate inner temperature to favorable levels are coined
“ectotherms”. This is not only the case of plants, but also of “cold blooded”
animals such as insects, reptiles, etc.

This relationship is not perfectly linear because the timing of these
development stages are also dependent on adequate light, water, and nutrients
in addition to appropriate temperature. However, temperature remains the major
factor explaining the timing of development stages. This explains why
agronomists and farmers use GDDs to estimate stages of crop development and
weed and pest life cycles.

Note that variables that measure the amount of time exposed to certain
temperature levels are closely related to the concept of degree days. Degree
day are measures of cumulative temperature exposure between two temperature
thresholds. The concept is very general and is used outside of agronomic
sciences. For instance, engineers and energy analysts rely on Cooling Degree
Days (CDD) and Heating Degree Days (HDD) to predict energy consumption for
cooling in the summer, and for heating in the winter, respectively.

Possibly the oldest use of degree days was to predict phenology, the timing of
life stages in plants and certain animals (Réaumur, 1735). The modern
incarnation of this concept applied to plants is reflected in the modern use
of Growing Degree-Days (GDD) which are precisely reserved to predict crop
stages (Bonhomme, 2000). Field crops are characterized by their crop maturity
rating which indicates the amount of “cumulative temperature” measured in GDD
to reach maturity. Short-season cultivars require less heat of the growing
season to reach maturity. For this reason such cultivars are used in colder
climate in temperature countries like the US, where the non-freezing period
that is fatal to most crops is relatively short. Thus, farmers choose a crop
maturity rating based on their local climate.

The implication is that once farmers plant a given cultivar, unexpectedly warm
or cold conditions can accelerate or delay the timing to reach crop maturity
and harvest. As a result, changes in GDD can affect yield, because shortening
the time the crop spends on the field shortens the time the crop has to
accumulate biomass. Similarly, lengthening the timing the crop spends on the
field can expose the crop to perilous conditions at the end of the season
(e.g. damaging Fall frost). However, the concept of GDD is not intended to
predict yield, but to predict phenology. Many economic studies rely on “GDD”
measures to predict yield. This is incorrect. A more rigorous use of the term
that does not introduce confusion with its agronomic use is to simply describe
degree day variables in terms of the range of temperature used to defined
them, like “degree days 8-30°C”. Note that degree days capturing exposure to
relatively high thresholds, say 30°C, are commonly referred to as Extreme
Degree Days (EDD), Killing Degree Days (KDD) or Damaging Degrees Days (DDD).
Similarly, describing degree days by their threshold, such as “degree days
over 30°C” seems generally more appropriate.

##  3 Climate change impacts and adaptation

This section provides an overview of the main research questions and the
methods used to evaluate climate change impacts and adaptation in the
agricultural sector. While the discussion will cover developments over the
past 2 decades, I put some emphasis on the evolution of the literature as well
as recent contributions. I also spend some time discussing unresolved or
relatively unexplored research questions. I also invite the reader to consult
several overview articles on methods of assessing climate change impacts on
agriculture and other sectors, including Blanc and Schlenker (2017), Carter et
al. (2018) and Kolstad and Moore (2020), to name just a few.

###  3.1 Biophysical approaches

Most of the early work assessing climate change impacts on agriculture is
fundamentally based on biophysical models (e.g. Adams 1989; Adams et al. 1990;
Rosenzweig and Parry 1994). These plant science models mechanistically
characterize the effect of environmental conditions (e.g. sunlight, water
availability, air and soil temperature, carbon dioxide concentrations, air
humidity, etc.) on the physiological processes that underly crop yield
formation. This type of approach typically assume farmers adopt a series of
more or less sophisticated management practices including choice of cultivar,
fertilization decisions, planting time, etc. These models are subsequently
coupled with climate models and supply-demand economic models to simulate the
effect of climate change on agricultural production and welfare. I revisit the
integration with economic models in subsection 3.11 on market equilibrium and
trade.

One of the main advantages of biophysical approaches is that they can provide
a transparent understanding of the exact channels through which climate change
impacts occur. For instance, these approaches allow unpacking the role of CO2
fertilization as well as which crops and regions of the world would be more
affected. Relying on a supply and demand model also allows to compute welfare
effects of climate change and how they are distributed among consumers and
producers in various regions of the world.

However, these approaches present various limitations. Because these models
are not directly rooted on observational data, it is unclear whether the
assumptions about farmer behavior may be realistic in real-world settings.
These approaches are also deterministic, so they don’t directly provide a
measure of uncertainty regarding the relationship between changes in the
distribution of weather conditions and agricultural outcomes. In general,
these model need to be extensively and carefully calibrated to perform well
within the sample and tend to perform poorly when used out of sample. In fact,
a key criticism of this approach is that results tend to be highly dependent
on the crop model used, which has led some call for an overhaul of modeling
approaches that favor multi-model ensembles (Rötter et al., 2011).

An important development in this literature the Agricultural Model
Intercomparison and Improvement Project (AgMIP, https://agmip.org), which aims
to improve biophysical crop modeling (Rosenzweig et al., 2014). Similarly to
CMIP models, intercomparison projects allow modelers to compare model outputs
based on identical scenarios and to learn about the sources of discrepancies
across individual models. The consensus seems to be that the future of
biophysical crop modeling resides with multi-model ensembles.

Moving to multi-model approaches not only facilitates model improvements, but
also allows researchers to sample from a wider range of crop models when
conducting climate change impact analyses. This helps better characterize
model-driven uncertainty of climate change impact projections.

Although the development to multi-model ensembles seems welcome, it also means
that research projects in this area involves relatively large pre-established
teams which can present a barrier to entry for individual researchers,
especially students. However, there seems to be an important role for
economists to play in the coupling of these multi-model ensembles with supply-
demand and trade models.

Finally, a present limitation of biophysical approaches is the major emphasis
on the major staple field crops such as wheat, corn and rice. Cereal crops
represent about a fifth of the total agricultural value produced so these
approaches have so far overlooked the effects on many other parts of the
global agricultural sector. There is a limited number of models focused on
specialty crops or livestock production, which seem like important directions
of research. But then again, models are likely to do well within the region of
calibration and pose limitations when trying to apply these models to other
regional contexts. See Antle and Stöckle (2017) for a review of the use of
process-based models along with economic models.

###  3.2 The Ricardian approach

The introduction of the Ricardian approach in Mendelsohn et al. (1994) was a
reaction to earlier studies based on biophysical approaches that allowed for
relatively little farmer adaptation to climate change (e.g. Adams, 1989; Adams
et al., 1990; Easterling et al., 1992; Kaiser et al., 1993; Adams et al.,
1995). In retrospect, these studies unsurprisingly tended to point to
relatively large damages primarily driven by losses in crop yields.

The idea behind the Ricardian approach is that one can assess future climate
change impacts capturing for the full range of farmer adaptations without
having to model these adaptive choices explicitly. The key conceptual
assumption is that farmers are already adapted to their local climate. That
is, they would have adopted production practices and choices that are the most
beneficial given the local climate, prices and technology. Because land is a
fixed factor of production, the demand for land generates economic rents. The
discounted stream of these rents are capitalized in the value of land. So if
these rents originate from more beneficial climatic conditions, then climate
would be capitalized in the value of land.

Empirically, the Ricardian approach attempts to recover the marginal value of
climate by exploiting the cross-sectional spatial variation in farmland values
and climate across a large region. This constitutes a hedonic analysis of the
characteristics of land (Rosen, 1974; Palmquist, 1989). The regression can be
expressed as:

$y_{it}=\bar{Z}_{it}\beta+X_{it}\gamma+\alpha_{t}+\epsilon_{it}$ (2)

where $y_{it}$ is farmland value per acre in location $i$ (e.g. county or
district) and year $t$, $\bar{Z}_{it}$ is a vector of climate variables
defined over the previous 30 years
($\bar{Z}_{it}=\sum_{s=t-30}^{t-1}Z_{is}/30$), $X_{it}$ is a vector of control
variables, $\alpha_{t}$ is a year fixed effect and $\epsilon_{it}$ is an error
term. The hope in this analysis is that the inclusion of control variables
will reduce concerns regarding omitted variable bias and lead to unbiased
estimates of $\beta$.

The researcher can then couple these hedonic estimates of the marginal value
of climate on farmland values $\hat{\beta}$ with climate change projections
$\Delta\bar{Z}_{i}$ to derive climate change impacts $\Delta\hat{y}_{i}=\Delta
Z_{i}\hat{\beta}$. In principle, these impacts account for the full range of
farmer adaptations.

The first implementation of the approach (i.e. Mendelsohn et al., 1994) was in
the context of US agriculture and relied on county-level farmland values from
the 1978 and 1982 Census of Agriculture. The main specification estimated
these 2 cross-sections separately and regressed farmland value per acre on
linear and quadratic terms of seasonal (January, April, July, October)
temperature and precipitation along with a series of physical (e.g. average
soil characteristics) and economic controls (e.g. population density and
income per capita).

The most striking finding at the time was that applying a uniform warming of
5°F warming and a 8% increase in precipitation, an approximation of early IPCC
projections, suggested slightly beneficial impacts for US agriculture.
However, the results were substantially different depending on the regression
weights used in the analysis. As indicated by Solon et al. (2015), when
regression coefficients differ dramatically with different regression weights,
it may be a sign of misspecification or un-modeled heterogeneity. The results
were nonetheless in stark contrast to previous work.

The approach and the implementation in Mendelsohn et al. (1994) generated
considerable criticism (see Cline 1996; Kaufmann 1998; Darwin 1999; Quiggin
and Horowitz 1999). As summarized in Schlenker et al. (2005), the main
criticisms included (1) that the Ricardian approach does not account for
adjustments costs, (2) that the regression results were not stable across
regression weighting schemes, and (3) the inappropriate treatment of
irrigation. This last point probably gained the most traction. Farmers in
certain regions can rely on a water supply for irrigation instead of directly
from precipitation. As a result, the shadow value of climate should in
principle differ across irrigated and non-irrigated regions. Econometrically,
that means that the researcher should estimate separate coefficients for
irrigated and non-irrigated areas. A simple dummy for irrigation would not
suffice as that simply alters the intercept.

This precise idea was proposed in Schlenker et al. (2005) which showed that
when the MNS model is restricted to the mostly non-irrigated Eastern half of
the US, the Ricardian model points to large negative damages, rather than
benefits. Results also become stable across regression weights. In a related
study, Schlenker et al. (2006) proposed a new set of climate variables
including degree days variables commonly used for predicting crop phenology
and plant biomass growth. The main results mirrored the findings of Schlenker
et al. (2005). Interestingly, the results in Schlenker et al. (2006) were
robust to the inclusion of state fixed effects. This is striking because it
means that warmer areas within states, tend to exhibit lower farmland values
even after controlling for land quality characteristics and other economic
controls such as population density and income per capita.

Various improvements to the Ricardian approach have been introduced over time.
Timmins (2005) notes that Ricardian estimates may be biased when land is
heterogeneous within locations (e.g. counties) and land owners allocate land
use optimally. This problem arises due to spatial or administrative
aggregation of data of parcels under different land use and with differing
shadow values of climate. Fezzi and Bateman (2015) also point out issues
related to the common issue of spatial aggregation in Ricardian models. Using
a detailed database of land values for Great Britain, they find that
aggregation conceal important interactions between temperature and
precipitation. This results in substantial biases in projection of climate
change impacts. This is particularly problematic for this literature given
that farmland value data is often only available at aggregate scales for
privacy reasons.

Farmland values reflect expectations about future land rents. Severen et al.
(2018) point out that if land market players expect climate change to affect
future rents, then those expectations should be capitalized as well, biasing
Ricardian estimates. They test whether climate change projections (based on
two GCMs) appear to be already capitalized in US farmland markets using a
cross-sectional approach. The paper subsequently proposes a corrected
“forward-looking” Ricardian approach that addresses this potential bias. One
potential shortfall of this implementation is that the test is based on cross-
sectional evidence, so it is unclear if climate change projections are
correlated with unobservable determinants of land values. An alternative
approach would be to track changes in farmland values over time as more
information about climate projections is made public. Another challenge here
is that the US public views regarding the existence and origin of recent
climate change are highly polarized between urban and rural areas across the
US (Leiserowitz et al., 2013). Thus the regional divided in these views could
be correlated with the extent of non-farm pressures on farmland markets.

More recently, Ortiz-Bobea (2019) revisited the Ricardian analysis of US
farmland values and found that large damages found in previous studies (e.g.
Schlenker et al., 2005, 2006) appear to be driven by factors outside the
agricultural sector. Essentially, large climate change damage estimates in
recent farmland values cross-section appear driven by non-farm omitted
variables. Using a century of farmland value data, the study finds that
climate change impact estimates are statistically insignificant when relying
on older farmland value cross-sections. The study finds that this result stems
from major changes in the farmland value cross-section over time. A
convergence of evidence suggest such changes in the cross-section are linked
to the rise of non-farm pressures which are correlated with climate within
states (e.g. rise in recreational demand for land in cooler areas of certain
states). These changes in farmland values appear unrelated to technological
change or other forces within the agricultural sector. To circumvent biases
from the capitalization of non-farm pressures, the study proposes a Ricardian
model based on farmland rental prices, rather than farmland asset values. This
approach was employed in Hendricks (2018) that conducts a Ricardian analysis
of cropland rental prices in the central US to assess the potential gains from
innovations that reduce heat and water stress.

The Ricardian approach continues to be used across many contexts. Perhaps its
most attractive features are its simplicity and the conceptual elegance of how
it resolved previous thorny debates about capturing adaptation. The approach
has important drawbacks that seem difficult to overcome. Despite efforts to
make the approach more “structural” (Seo and Mendelsohn, 2008), it still
remains a bit of a “black box” regarding underlying mechanisms that are
important for policy or developing priorities for adaptation.

Perhaps more importantly, empirical economics is well engaged in a
“credibility revolution” (Angrist and Pischke, 2010) where much attention is
given to the quality and credibility of research designs. The Ricardian
approach is based on an empirical strategy that is fundamentally vulnerable to
omitted variables. The identifying variation in the approach comes from the
spatial variation in land values and climate. If unobserved drivers of land
values, of which there are many, are omitted and happen to be correlated with
climate, which is plausible, then estimates are biased. Previously proposed
fixes, like the inclusion of state fixed effects do not fundamentally address
this issue as shown in Ortiz-Bobea (2019). The inclusion of state dummies that
makes the estimation be based on the within-state variation in prices and
climate, could actually amplify omitted-variable bias if those operate more
strongly within states than across states. Current research standards clearly
favor research designs based on longitudinal data in which researchers can
convincingly control for time invariant confounders.

Still, a few attempts have been made to control for unknown omitted variables
in a cross-sectional setting. That includes the introduction of the Spatial
Durbin Error Model (LeSage and Pace, 2009; Elhorst, 2010) in Ortiz-Bobea
(2016) or that of a “Spatial First Differences” estimator in Druckenmiller and
Hsiang (2018). The underlying idea of these approaches is that unobservables
may be spatially dependent in a way that slightly differs from that of
climate. These approach harness this information to control for or subtract
out the influence of these confounders.

###  3.3 Panel profit and productivity approaches

The use of longitudinal data to analyze the effect of weather conditions on
agricultural outcomes has a very long tradition in agricultural economics
(Hodges, 1931; Schickele, 1949; Stallings, 1960; Morgan, 1961; Stallings,
1961; Shaw, 1964; Oury, 1965; Black and Thompson, 1978). This early literature
was not initially concerned with climate change, but with forecasting crop
production to anticipate price swings, and understanding the nature of
agricultural production risk. It was only until the late 1980s (e.g. Adams,
1989) that articles exploring empirically the implications of climate change
on agriculture started to appear in leading agricultural economics journals
like the American Journal of Agricultural Economics (AJAE). However, these
initial studies were fundamentally based on biophysical crop models.

The surge in interest in econometric panel approaches to analyze potential
climate change impacts on the agricultural sector can probably be traced back
to Deschênes and Greenstone (2007), which offered a counter narrative to the
negative findings in Schlenker et al. (2005) based on the Ricardian approach.
See Blanc and Schlenker (2017) for a review on the use of panel models in
assessing climate change impacts on agriculture.

The approach in Deschênes and Greenstone (2007) was to rely on presumably
random year-to-year fluctuations in weather conditions to explain variations
in profits within US counties. This approach allows controlling for time-
invariant omitted variables that may be correlated with climate and may plague
the Ricardian approach. Their model can be expressed as:

$y_{it}=Z_{it}\beta+X_{it}\gamma+\alpha_{i}+\alpha_{st}+\epsilon_{it}$ (3)

where $y_{it}$ is net revenue or “profit” per acre in county $i$ and year $t$,
$Z_{it}$ is a vector of weather variables (e.g. precipitation and
temperature), $X_{it}$ is a vector of time-varying control variables,
$\alpha_{i}$ is a county fixed effect, $\alpha_{st}$ is a state-by-year fixed
effect and $\epsilon_{it}$ is an error term.

Conceptually, the model estimates a short-run effect of climate change on
profits. The idea is that farmers cannot adjust many input decisions to
unanticipated changes in weather. As a result the effect of weather on profits
would be appear more detrimental than it would be if the farmer were able to
fully adjust inputs in the long run. Because the study found very small
effects of climate change on profits in their implementation, their
interpretation is that climate change would have beneficial effects on US
agriculture with the current technology.

As pointed out in Fisher et al. (2012), the implementation in Deschênes and
Greenstone (2007) suffered from a series of shortcomings. Among the main
issues were problems related to weather data quality which tend to attenuate
the magnitude of the $\beta$ coefficients. Another concern is the inclusion of
state-by-year fixed effects $\alpha_{st}$ which arguably “wipe out” a lot of
the weather variation used to identify effects on profits. The main issue is
that with so little variation within state-year, estimates might be imprecise
and potentially more vulnerable to biases associated with measurement error
(see Griliches and Hausman, 1986).

A conceptual limitation of the Deschênes and Greenstone (2007) implementation
is the nature of the outcome variable. The study constructs a “profit”
variable from the US Census of Agriculture by subtracting total county
expenses from total sales divided by the acres of land in farms. Technically
this is a net revenue variable that can be problematic in the analysis. The
potential issue relates to the role of inventories, which farmers use in a
countercyclical manner to smooth the effect of unusual economic and weather
conditions. That is, on a bad year, a farmer may sell more than they produced,
whereas she might sell less than what is produced on a good year. Similarly,
farmers may avoid large purchases (e.g. tractor) in bad years whereas they
might go forward with them in good years. This behavior will tend to bias
contemporaneous weather effects toward zero. One potential fix to this issue
is to estimate a distributed lag model to account for weather shocks in
previous years (see Deschênes and Greenstone, 2012).

When some of the concerns above are addressed (see Fisher et al., 2012 and
Deschênes and Greenstone, 2012), the projected impacts of climate change on
profits are negative. It would seem as if the degree to which these effects
are large or small lies on the eye of the beholder, particularly on how these
short-run effects translate to long-run effects. Indeed, this panel approach
only accounts for farmer adjustments that could happen within the year (or a
couple of years with a distributed lag model).

More recently, a few studies have relied on measures of Total Factor
Productivity (TFP) rather than on net revenue variables. A key advantage is
that TFP data, when well constructed, accounts for changes in inventory. For
instance, the Economic Research Service (ERS) within the US Department of
Agriculture (USDA) develops a high quality US state-level TFP panel dataset
that can be harnessed for climate-related research. While the spatial
resolution is coarser than US Census data (state versus county), the greater
temporal resolution (annual) is particularly useful given that identification
is based on the within-location variation in weather. Examples of such studies
include Liang et al. (2017), Ortiz-Bobea et al. (2018) and Ortiz-Bobea et al.
(2021).

Following the framework proposed in Ortiz-Bobea et al. (2021), consider an
aggregate production function of the form
$Y_{it}=e^{f(Z_{it})}A_{it}X_{it}U_{it}$ where $Y_{it}$ is aggregate
agricultural output in state $i$ and year $t$, $e^{f(Z_{it})}$ is the effect
of weather, $A_{it}$ is a neutral productivity factor, $X_{it}$ is a measured
aggregate input and $U_{it}$ is an unmeasured aggregate input. Taking logs,
first differences and rearranging yields the following expression that
approximate the growth rate of TFP:

$\Delta\ln TFP_{it}\equiv\Delta\ln Y_{it}-\Delta\ln X_{it}=\Delta\ln
A_{it}+\Delta f(Z_{it})\beta+\Delta\ln U_{it}$ (4)

where $\Delta$ denotes change. By definition, TFP growth is the growth in
aggregate output that cannot be explained by growth in measured input. In the
proposed model, that TFP growth is the sum of three factors, a technological
improvement reflected in $\Delta\ln A_{it}$, a weather effect embedded in
$\Delta f(Z_{it})$ and changes in unobserved inputs $\Delta\ln U_{it}$. The
key point is that one can harness fluctuations in TFP to capture and
characterize the effect of weather fluctuations on agricultural production,
net of input responses.

Using this approach, Ortiz-Bobea et al. (2018) analyzes the effect of weather
conditions on US agricultural TFP. The analysis is conducted separately by
Climate Hub regions which are agro-climatically coherent regions proposed by
USDA for adaptation planning. The key finding in the study is that Midwest
agriculture is growing increasingly sensitive to higher temperatures. This is
found by conducting a Wald test of stability of regression coefficients
between the two halves of the sample. The study also provides some ideas of
the drivers. The trend appears related to two compounding factors, the growing
sensitivity of the crop output to higher temperatures, and the increasing
specialization in crop production in Midwest.

The rising sensitivity to high temperature in Midwest agriculture could appear
as a form of “maladaptation” but it remains unclear whether this rising
sensitivity results from a desirable tradeoff with higher productivity. More
research is needed to better understand these trends, especially regarding the
timing of these vulnerability changes over time.

###  3.4 Statistical crop yield models

A statistical crop yield model typically regresses a panel of crop yields on
various weather variables. These models had traditionally been the focus of
agricultural meteorologists. See Decker (1994) for a history of that field.
However, these models have grown increasingly popular among agricultural
economists interested in exploring a specific sub-channel through which
climate could affect agricultural production (e.g. Tack et al., 2015; Ortiz-
Bobea and Tack, 2018; Shew et al., 2020).

The key strength of these models relative to biophysical approaches is that
they are grounded on observational data. This has several advantages. First,
these models account for actual farmer management decisions when the data is
based on crop yields collected from farmers. Because farmers can sometimes
respond to weather fluctuations within the growing season, results can be
interpreted as reflecting short run adaptation to weather fluctuations. This
interpretation is not really correct when crop yield data are based on field
trials in which generally management decision are pre-determined by a
researcher.

Statistical crop yield models have also been used to indirectly detect whether
farmer adaptation to climate change has already occurred. Two approaches have
been proposed. The first is to test whether crop yields are growing less
sensitive to extreme weather that are becoming more common under climate
change (e.g. high temperatures). This is typically achieved by testing for
stability of regression coefficients over time, which naturally requires
relatively long panels. But it remains ultimately unclear whether changing
coefficients over time result from changes in crop cultivars, changing inputs
or management techniques, which constitute some form of adaptation, or from a
statistical artifact such as changing weather data quality over time. More
emphasis should be given to teasing out the sources of these changes, ideally
by coupling statistical models with other production information (e.g. crop
cultivars, data on management, etc.).

The second approach of indirectly detecting farmer adaptation is to test for
regional heterogeneity of weather coefficients. For instance, one should
expect that farmers in region with greater exposure to high temperature to
adapt to such environmental conditions over time. Econometrically, this means
that the effect of high temperature should appear to be less detrimental in
warmer places than in cooler places. So this check consists on testing for an
interaction between a weather variable and its climatology. This is the
approach adopted by Butler and Huybers (2013) to analyze adaptation to high
temperature in US corn yields. However, this climate is likely correlated with
other factors that may affect crop yield sensitivity (e.g. soil quality) so
this approach remains vulnerable to time-invariant omitted variables that
interact with weather fluctuations.

One important shortcoming of many studies in this area is that they do not
inform us about the types of adaptations or inputs adjustments farmers may be
engaging. Importantly, the fact that inputs are typically unobserved makes the
interpretation of short run effects more difficult. For instance, when a
farmer increases irrigation intensity in response to higher temperatures or
lack of precipitation means that the effect of these undesirable weather
conditions will appear attenuated. In the other hand, if inputs are
complementary to weather conditions, farmers may cut labor and fertilization
in response to undesirable environmental conditions, which would further
reduce crop yields. Thus, depending on the nature of the input response, the
estimate yield effect may appear either exacerbated or attenuated. It is
critical that researchers acknowledge that farmer input decision are often
times correlated with weather fluctuations, and that results should be
interpreted accordingly.

Another important area of debate in this literature is the nature of the
weather variables and how they are modeled. A fundamental challenge here is
the mixed frequency of the data with high-frequency daily weather predictors
throughout the growing season affecting the ultimate crop yield at harvest
(Ghanem and Smith, 2020). Unlike for the biophysical models, statistical
models cannot directly incorporate daily weather conditions. This would
represent too many regressors which happen to be highly correlated between
neighboring days. As a result, researchers undertake a variable selection more
or less based on first principles (e.g. what conditions are known to be
important for crop yield determination) and data-driven criteria (e.g. in-
sample or out-of-sample measures of model fit or other criteria).

Precipitation and temperature are naturally considered two fundamental
climatic variables affecting crop production. Crops need water to grow so
precipitation is critical in rain-fed systems. Too little or too much
precipitation is presumably detrimental to crop yields, suggesting there is an
optimal level of precipitation. Similarly, very cold condition are detrimental
to crop growth and very hot conditions accelerate evapotranspiration and can
cause heat stress, so extreme temperature are presumed to be detrimental. This
also suggest the existence of an optimal temperature range. As a result,
perhaps the most basic crop yield statistical model takes the following form:

$y_{it}=\beta_{1}T_{it}+\beta_{2}T_{it}^{2}+\beta_{3}P_{it}+\beta_{4}P_{it}^{2}+\phi_{s}(t)+\alpha_{i}+\epsilon_{it}$

where $y_{it}$ is crop yield (or its logarithm) in location $i$ and year $t$,
$T_{it}$ stands for growing-season average temperature, $P_{it}$ represents
growing-season precipitation, $\phi_{s}(t)$ represents a regional time trend
(typically a $year$ variable interacted with a regional dummy), $\alpha_{i}$
is a location fixed effect, and $\epsilon_{it}$ is an error term. The
introduction of the quadratic terms seek to the existence of optimal levels
for temperature and precipitation. However, this imposes symmetry to the
response function.

Note how this model reduces dramatically the dimensionality of the problem by
averaging and aggregating temperature and precipitation over the growing
season. This model boils down the entire growing season to just four variables
in an attempt to make the model tractable.

One drawback of averaging temperature over the growing season, is that is
conceals the distribution of temperature within the growing season. This was a
key contribution in Schlenker and Roberts (2009a), an influential study in
this literature. The study estimated the potential impacts of climate change
on US crop yields later this century by coupling crop yield models for corn,
soybeans and cotton with GCM projections. Its key contribution is the
estimation of non-linear effects using a generalization of the concept of
degree-days that harnesses the intra-daily distribution of temperature over
the growing season. Specifically, the study shows that exposure to temperature
above around 30°C are particularly detrimental for these crops. Because
anthropogenic climate change is projected to increase the frequency of high
temperature, then yields were projected to decline if growing regions and the
crop yield response function remain stable. Analogous studies have found large
damages from higher temperatures in other regions of the world (Hsiang et al.,
2013; Gammans et al., 2017).

Note that the temporal aggregation of temperature conceals its underlying
high-frequency distribution. For instance, two days with the same average
temperature can exhibit different extrema, so averaging conceals the amount of
time exposed to very high or low temperatures. The approach proposed in
Schlenker and Roberts (2009a) is to rely on temperature variables that capture
the amount of time spent at each temperature interval. I cover in greater
detail the technical aspects of how to construct exposure variables as well
how to estimate these models in subsection 4.3.

Perhaps one of the most striking findings in this literature is the dominating
role that temperature plays in explaining historical variations and future
projections of crop yields relative to precipitation. Changes in temperature
typically explain about 80 to 90% of the projected climate change impacts.
Given the fundamental role that water availability plays in the functioning of
plants, this is particularly surprising. To explore this puzzle Lobell et al.
(2013) combines biophysical models to replicate the results obtained using
statistical approaches. The study finds exposure to high temperature, as
measured by degree days above 30°C, are associated higher Vapor Pressure
Deficit (VPD) which contributes to water stress, which negatively affects
yield. In essence, the story is that high temperature affects water
availability. As result, other studies have relied on VPD as a predictor in
statistical crop yields models (e.g. Roberts et al., 2012; Lobell et al.,
2014).

The interpretation that high temperature affects water availability raises the
question about the appropriateness of precipitation as a measure of water
supply. Indeed, season-long precipitation variables are very crude measures of
how much water is effectively available to crops. In the same way that
temporal aggregation in temperature was potentially problematic, a similar
shortcoming affects precipitation. More concretely, it’s not only the amount
of precipitation that matters, but also its timing throughout the growing
season. When precipitation is highly concentrated over short periods of time,
a lot of that water is lost via deep percolation or as runoff. Thus, two
growing seasons can have the exact same total precipitation, but one may be
considerably dryer than the other.

What this highlights is that precipitation, as a measure of water flow, is not
ideal for capturing the yield effect of water availability. In fact, what
matters to crops is how much water is effectively available throughout the
growing season. Water availability is thus a stock rather than a flow.
Unfortunately, there are no widespread network of stations measuring soil
water content, even in countries like the US. However, there are model-
generated raster datasets of soil water availability obtained from Land
Surface Models (LSM). These LSM aim to describe the evolution of soil water
content and other factors given a set of exogenous drivers such as soil
characteristics, land cover, and fine scale atmospheric conditions (e.g.
hourly or sub-daily precipitation, temperature, solar radiation, etc).

To address this concern Ortiz-Bobea et al. (2019) rely on model-generated
measures of soil moisture to unpack the climatic drivers of crop yields for
six major US field crops. The study pointed to three main findings. First, the
adoption of soil moisture variables substantially improves model fit relative
to standard models. Second, climate change impact projections from models
based on soil moisture variables remain similar to those from traditional
models based on precipitation. Finally, the study finds that accounting for
soil moisture reduces the relative role of temperature variables in climate
change impact projections. This means, as hypothesized by previous studies,
that temperature effects were partly reflecting the effects of dry conditions
in previous models. Note that the relationship between high temperature and
drought is not unidirectional. While higher temperature do increase
evapotranspiration and reduce soil water content, droughts can also cause
temperatures to rise (Seneviratne et al., 2010).

The discussion about the importance of the timing of soil moisture
availability raises the question about how to properly account for the timing
of environmental conditions within the season. One basic approach is to adopt
weather variables for various seasons of the year. A more recent approach
introduced in Ortiz-Bobea et al. (2019) relaxes the additive separability
assumption in Schlenker and Roberts (2009a) and allow for the effects of
temperature and soil moisture to have non-linear and time-varying effects on
crop yields. This implementation is based on a tensor product spline or “bi-
dimensional spline” where crop progress within the season and the level of the
variable are the two dimensions. I provide details about how to estimate this
model in subsection 4.4.

Moving forward, work in this area could focus on ways to improve our
understanding of mechanisms through which environmental conditions affect crop
yields including farmer management decisions, crop genetics, soil
characteristics and their interactions.

###  3.5 Mixed statistical and biophysical approaches

Perhaps one of the main methodological divides in the literature assessing
climate change impacts on agriculture is whether the models are biophysical or
statistical in nature. This methodological dichotomy often coincides with
disciplinary boundaries and is thus reflected in publishing outlets. One of
the major issues with this divide is that it could slow down scientific
progress if conclusions from studies based on alternative approaches are
perceived as being biased due to the underlying methods used.

To explore this question, Lobell and Asseng (2017) conducted a systematic
review of the existing literature to compare prediction of climate change
impacts from both biophysical and statistical approaches. The main conclusion
is that when studies follow best practices in their respective literature,
these methods point to impacts that are largely similar. This means that the
previously held perception that statistical model tend to be too “pessimistic”
is not really supported by the existing literature. In a somewhat related
study Moore et al. (2017) find that the differences between biophysical and
empirical studies is small when CO2 fertilization is controlled for.

Recent studies have also started to compare or even combine biophysical and
statistical crop yields models. For instance, Roberts et al. (2017) conduct a
comparison of a statistical model and a process-based model and find that a
combined “hybrid” model tends to outperform individual models in terms of
prediction. In addition, that hybrid model tends to point to projected impacts
of climate change that fall in between those of the individual approaches.

One key advantage of conducting similar analyses based on alternative
approaches within the same study is to better characterize model uncertainty.
For instance, Liu et al. (2016) show that both biophysical and empirical
models point to similar temperature responses on global wheat yield. This
helps address common criticisms from reviewers coming from one specific “camp”
of the methodological divide.

Perhaps a fruitful direction of research in this area is the integration of
statistical analyses within broader inter-comparison projects like AgMIP.
There is indeed a great deal of cross-fertilization that could occur across
these different methods. These efforts help bridge the divide across
disciplines by seeing these approaches as complementary rather than
substitutes.

###  3.6 Joint estimation of short and long run responses

One of the central methodological dilemmas in the literature relates to the
estimation of either short run or long run estimates of climate change
impacts. While the Ricardian approach conceptually captures long-run
adjustments by assuming farmers are already adapted to their local climate,
the approach remains vulnerable to time-invariant omitted variables. On the
other hand, panel approaches control for time-invariant unobservables, but are
generally perceived as only being able to capture within-season short-run
responses to weather fluctuations, and thus unable to capture longer-run
adjustments to a changing climate.

However, recent research efforts have sought to combine certain elements of
cross-sectional and panel approaches to jointly estimate short and long run
responses. For instance, Moore and Lobell (2014) introduce a “hybrid” model to
jointly estimate short-run and long-run adaptations to weather fluctuations
and climate variations in European agriculture. The model takes the form:

$y_{ijt}=\beta_{1}\bar{W}_{ijt}+\beta_{2}\bar{W}_{ijt}^{2}+\beta_{3}\left(W_{ijt}-\bar{W}_{ijt}\right)^{2}+\beta_{4}X_{ijt}+\phi_{j}(t)+\alpha_{j}+\epsilon_{ijt}$

where $y_{ijt}$ represents farm profits or yield in region $i$, country $j$
and year $t$, $W$ represents weather variables (temperature and
precipitation), $\bar{W}$ represents climate (average of annual weather over
the preceding 30 years), $X$ are control variables, $\phi_{j}(t)$ is a
country-specific time trend and $\alpha_{j}$ is a country fixed effect. This
specification primarily harnesses the cross-sectional variation in climate
within countries (given there is a country fixed effect and there is
relatively less temporal variation in climate) and the temporal variation in
weather anomalies. According to the authors, combining these estimates allows
depicting an outer “envelope” describing the long run response function, and a
series of short-run response functions that are tangent to the long-run
response function when $W=\bar{W}$. This approach combines both cross-
sectional and time-series variation to estimate different parameters. These
parameters are subsequently combined to assess short and long run responses.
However, note that the cross-sectional estimation is still vulnerable to
omitted variables operating within countries.

A different approach consists in trying to harness slow changes in the within
dimension of a panel model to detect evidence of adaptation to a changing
climate. This is the strategy in Burke and Emerick (2016) which applies a
“long difference” approach to a panel of crop yields to assess the influence
of recent climate trends on changes in the sensitivity of crop yields. The
study first posits a standard panel data generating process of the form:

$y_{it}=\alpha+\beta_{1}z_{it}+\beta_{2}z_{it}^{2}+c_{i}+\epsilon_{it}$

where $y_{it}$ is crop yield in county $i$ and year $t$ and $z_{it}$ is a
weather variable (e.g. temperature). The county fixed effect $c_{i}$ captures
all time-invariant unobserved factors.

The study argues that this model only captures short run changes on yield. The
study then posits that if farmers are adjusting input choices (e.g. crop
cultivars) to adapt to recent changes in climate, then this would be reflected
in a change in the response function over time that would renders extreme
weather less damaging. That, is, the response function would trace out an
“outer envelope” that allows for longer term adjustments.

To explore this hypothesis, the study first proposes averaging the model above
over a multi-year period $a$, to obtain a new model of the form
$\bar{y}_{ia}=\beta_{1}\bar{z}_{ia}+\beta_{2}\bar{z}_{ia}^{2}+c_{i}+\bar{\epsilon}_{ia}$
where $\bar{y}_{ia}$ is average yield over the multi-year period of time $a$
and $\bar{z}_{ia}$ is the multi-year average weather over the same period.
Defining an analogous equation for a more recent period $b$, and taking the
differences between these equations yields what the authors refer to as the
“long difference” model:

$\bar{y}_{ib}-\bar{y}_{ia}=\beta_{1}\left(\bar{z}_{ib}-\bar{z}_{ia}\right)+\beta_{2}\left(\bar{z}_{ib}^{2}-\bar{z}_{ia}^{2}\right)+\left(c_{i}-c_{i}\right)+\left(\bar{\epsilon}_{ib}-\bar{\epsilon}_{ia}\right)$

which simplifies to:

$\Delta\bar{y}_{i}=\beta_{1}\Delta\bar{z}_{i}+\beta_{2}\Delta\bar{z}_{i}^{2}+\epsilon_{i}$

Note that the estimated parameters $\beta_{1}$ and $\beta_{2}$ are the same as
those specified in the original equation. In the absence of any adaptation,
the parameters in this new model would be identical. However, if farmers are
adapting to recent climate trends, then those parameters would shift to make
the response function flatter. Applying this approach to US corn yields, the
study finds that the parameters of the “long difference” model as very similar
to those of the baseline panel model. The study thus concludes that little
adaptation has occurred over several decades.

One should highlight that it is unclear whether farmers perceive recent
changes in weather patterns as a permanent shift in climate. One should not
generally expect agents to make permanent shifts in production practices in
response to transient changes environmental changes. Moreover, note that if
farmers are adapting to a changing climate, then the baseline panel model is
misspecified as we should expect adaptations to be reflected in the short run
response function as well.

It is important to clarify that the idea that panel estimates only capture the
short-run response is not entirely correct. In a panel model with location
fixed effects estimating a non-linear response to weather fluctuations, which
is common practice, the identifying variation stems from within location
deviations from the mean of each variable. In locations with higher average
values of the weather variables (e.g. warmer or wetter climates), the
deviations for the quadratic terms are larger. Effectively, this means that
group means, in this case climate, plays a role in the identification. That
is, cross-sectional variation plays a role in the identification of weather
effects. See McIntosh and Schlenker (2006) for an explanation.

In a key recent study, Mérel and Gammans (2021) show that panel estimates are
a weighted average of the short-run and long-run response functions to weather
and climate. That study also derives the conditions under which the short-run
response approximates the long-run response. Intuitively, the extent to which
the panel estimate represents more or less the short or the long-run response
function depends on the ratio of the within time-series variation to the
cross-sectional variation of the weather variable. If a weather variable
exhibits greater degree of variation in the cross-section than in the within
dimension, then the response function more closely approximates the long run
response function. This means that for small panels with units exhibiting
similar climates, the estimated response function represents primarily the
short run response function. In contrast, estimating global response functions
over a large panel with units with large climatic differences (but relatively
smaller within variations) approximates the long-run response function. In a
similar spirit, Gammans et al. (2020) propose an approach to recover the
global long run response function by harnessing variations across adjacent
climates. A limitation of these models is that they apply to a subclass of
data generating processes.

###  3.7 Retrospective climate change impacts

The literature on climate change impacts on the sector has been mostly
concerned about future projected impacts. Most studies estimate or calibrate a
model based on historical data and make predictions about potential future
outcomes under alternative climate scenarios and assumptions about farmer
adaptation and agricultural markets. However, anthropogenic forces have
already altered the climate system as summarized by the IPCC (Pachauri et al.,
2014). Our climate is about 1°C warmer than during pre-industrial period.
Given that agriculture is highly climate sensitive, it seems natural that
these climate changes may have already affected agricultural production.

The first studies trying to analyze the observed impacts of climate change
have overwhelmingly focused on teasing out the effect of recent climate trends
on yields of major field crops. Lobell and Field (2007) analyze the
relationship between country-level cereal yields and growing season weather.
Specifically, the study computes first differences of yields and weather
variables to control for slowly changing unobservables over time such as
management practices. The study finds that there is a clear negative response
of maize, wheat and barley yields to higher temperatures. The study then
couples these estimates with observed trends in climate variables (1961-2002)
and finds the cumulative impact on crop yield for these 3 crop amounts to 40Mt
or $5 billion per year.

In a related study, Lobell et al. (2011) revisits this question and focuses
maize, wheat, rice, and soybeans, which represent about 75% of calories that
humans consume directly or indirectly. Relative to previous work, the study
does a better job at matching weather conditions to the growing season of each
crop based on the crop calendar complied in Sacks et al. (2010). Other
examples of more regional studies include Nicholls (1997) for Australia,
Lobell and Asner (2003) for the US, Tao et al. (2006, 2008) for China, Lobell
et al. (2005) for Mexico.

As indicated in Porter et al. (2014), these studies have largely focused on
attributing the effect of recent climate trends on crop yields without
unpacking the anthropogenic sources of these climate trends. More recently,
Ortiz-Bobea et al. (2021) coupled an econometric model with counterfactual
climate simulations to conclude that anthropogenic climate change has slowed
global agricultural productivity growth by about 20% over the 1961-2020
period. This loss is equivalent to losing about 7 years of productivity growth
over the same period. The strategy in that study is to first estimate a global
panel model regression country-level agricultural TFP on annual weather
variables. The scope of the study differs from previous ones because the
productivity estimates encompass the entire agricultural sector, and not just
crops. The study then links the econometric estimates with weather
trajectories for 1961-2020 coming out of climate models from CMIP6 from both a
historical run with observed human emissions (the “historical” experiment) and
a historical run without human emissions (the “hist-nat” experiment). This
allows to compute the cumulative TFP growth over the sample period under these
two scenarios. Taking the difference is thus interpreted as the impact of
anthropogenic climate change. One of the caveats in that study is that it does
not recover how agricultural TFP would have responded to weather in the
counterfactual world.

In a related study focusing on global crop yields, Moore (2020) develops an
approach that extends the literature on detection and attribution in climate
science to global crop yields. Rather than relying on multiple climate models,
the paper relies on multiple runs from a single climate model to characterize
the internal variability of the model. The study concludes that the patterns
of yield growth observed on maize, wheat and rice production have less than a
10% chance of having arisen in the absence of anthropogenic climate change.
Specifically, the study finds that anthropogenic climate change has reduced
annual calorie production related to these 3 crops by about 5% per year on
average since 1961.

###  3.8 Statistical crop quality models

The focus on crop yield overlooks the fact that weather conditions can affect
crop quality (Soares et al., 2019). A small but growing number of economic
studies have analyzed the implication of extreme weather conditions and rising
carbon dioxide atmospheric concentrations on crop quality and its potential
implication under climate change. These models also exploit longitudinal
variation in panel model with fixed effects. What typically differs is the
nature of the dependent variable, which can vary greatly across crop quality
classification systems and countries. For instance, wheat quality is typically
captured by its moisture and protein content as well as its milling and baking
qualities. Wheat is graded and classified so aggregate data is typically
obtained as the share of output falling into different grading categories. For
other grains like rice, the quality characteristics vary substantially across
countries reflecting very heterogeneous consumer preferences.

A major obstacle in this area is obtaining comprehensive panel data on crop
quality. Most previous research is either based on process-based models (e.g.
Erda et al., 2005; Asseng et al., 2019) or on the statistical analysis of
quality in relatively small samples (e.g. Rao et al., 1993). The economics
literature in this area is relatively thin but differs from agronomic research
which focuses on direct physical effects on quality. On the other hand,
economic studies tend to focus on tradeoffs between quality and quantity or
seek to quantify the relative contribution of yield and quality changes on
farmer revenues.

For instance, Kawasaki and Uchida (2016) explores the effect of extreme
weather on rice yields and quality in Japan. The study finds that while high
temperature improves yield, it also reduces rice quality, leading to an
overall negative effect on farmer profits. While most economic research has
focused on cereal crops, there is some limited work on fruits and vegetables.
Dalhaus et al. (2020) explores the effect of temperature on apple yields and
quality in Switzerland. The study finds that the detrimental quality effects
of spring frosts can be substantial and can play a larger contribution to
farmer revenue than yield effects. Relatedly, some research has focused on
wine quality (Erda et al., 2005; Ashenfelter and Storchmann, 2010, 2016).

Moving forward, there is much to be learned regarding the impact of
anthropogenic climate change on crop quality. One of the main obstacles seems
the availability of reliable longitudinal datasets. This will require new
efforts of data collection or partnerships to track quality to better
understand the ongoing processes. There is also limited understanding of how
climate change may affect micro-nutrient availability, which are critical for
small scale farmers who primarily rely on their own production for
subsistence. Greater emphasis on how post-harvest management and climatic
conditions affect quality is also needed.

###  3.9 Modeling planting and harvesting decisions

A growing season for annual crops is essentially determined by the time
ranging from planting to maturation or harvest. The decision of which crop or
cultivar to plant, and when, is critical for agricultural production. For
instance, in moisture-limited regions with highly seasonal rainfall, planting
prior to the arrival of the first rainfall events could lead to plant death
which would require new planting. A similar constraint exists in temperature
areas when planting too early in the spring, when the increased risk of frost
can jeopardize crop emergence.

In addition, the timing of planting and the choice of the crop cultivar
largely determines the timing of when specific stages of plant growth occur
during the calendar year. Planting a long-season cultivar in a region with a
short season could mean that the crop would not reach maturity during the
usual harvest period, which can be problematic. For instance, fall frost can
damage the crop in temperature regions. Importantly, the flowering period
which tends to occur around the middle of the growing season for annual crop
can be particularly vulnerable to heat and moisture stress (Fageria et al.,
2006).

Farmers have formed expectations about climate which guides the choices about
planting (crop and cultivar choice as well as timing) before the weather
conditions unfold throughout the growing season. This is well known but there
is relatively little research in economics regarding how farmers form
expectations that guide the nature and timing of planting decisions. Changes
in the length of the growing season are likely important channels through
which climate change will affect farmers. For instance, the expansion of the
frost-free period in temperate regions may expand growing seasons allowing
farmers to grow longer season crops and cultivars of giving farmers more
flexibility with their planting dates (Ortiz-Bobea and Just, 2013).

While the the current spatial distribution and drivers of planting dates for
major crops has been characterized (Sacks et al., 2010), less is known about
how farmers are adjusting their practices in response to a changing climate.
There is evidence of a multi-decadal trend toward earlier planting in US
Midwest that appears beneficial to crop yields (Kucharik, 2006, 2008).
However, it is still unclear whether these trends are primarily driven by new
cold-resistant varieties or by climate trends.

In addition, climate change is also increasing the intensive and variability
of rainfall events, which could lead to excessive moisture during parts of
this could be detrimental. For instance, excessive rain in the Spring reduces
the ability of heavy farming equipment to enter fields without causing severe
soil compaction, which is detrimental to root development and causes long term
damage to crop yields (Hamza and Anderson, 2005). These events can be
extremely disruptive as the US floods in the Spring of 1993 and 2019
exemplified.

More generally, the influence of weather shocks and climate on the decision of
what and when to plant remains under-explored. We still need a more systematic
understanding of the potential barriers precluding farmers from making optimal
decisions in a changing climate. This is particularly critical in the context
of perennial crops such as fruits trees and vineyards where planting is
extremely costly and affects farming performance for many years or decades.
For instance, it is still unclear whether farmers have begun to shift crops or
varieties in specifically in response to climate change and what types of
information they rely upon for making these decisions. For instance, would
farmers presented with information about recent and projected trends in their
locale chose different cultivars of a perennial crop?

The discussion so far has primarily focused on planting. However, the decision
of whether to even harvest is also important. Crop abandonment occurs when
farmers decide not to harvest a crop they previously planted. Conceptually,
this occurs when the cost of harvesting exceeds its expected benefits.
Expected benefits depend on yield and output price (as well as any form of
production-based government subsidy). Harvesting cost depends on input prices
such as fuel and are not necessarily proportional to yield in the case of
field crops. One can also factor in the cost of post-harvest management and
storage as part of this harvest cost. There are numerous reasons why expected
benefits might be lower than harvesting costs. It could be that either yield
or output prices are considerably lower at harvest time than the farmer
anticipated at planting. It is also possible that harvesting costs become
unexpectedly high, which might happen in the presence of an unexpected
disruption to labor necessary for harvest (e.g. sudden immigration policy or
shock that restricts access to the labor supply).

When these crop abandonment decisions are driven by unexpected drops in yield,
say from unusual weather, it is not uncommon to refer to the situation as
“crop failure”. Note that crop failure is the result of an economic decision
and not a physiological or agronomic condition. The decision not to harvest a
crop is inherently economic in nature. One could easily envision a farmer
deciding to harvest a crop with extremely low yields if there is a
sufficiently high output price.

The literature on climate-induced crop abandonment or failure is relatively
thin. The first economics study on this question seems to be Mendelsohn
(2007), where a Ricardian-style cross-sectional model is estimated to predict
average crop failure rates in the US context. The study relies on reported
crop failure rates at the county level based on 5 years of data from the US
Census of Agriculture collected from 1978 to 1997. The study finds that about
39% of the cross-sectional variation in crop failure can be explained by soils
and climate.

More recently, and using longitudinal variation in a panel, Cui (2020)
explores how weather shocks not only influences US crop yields but also the
fraction of planted acres farmers end up harvesting. As with other panel
studies, it is unclear to what extent these historical relationships can be
extrapolated in the long run under climate change. More research is certainly
needed to understand the heterogeneity in crop abandonment decisions and how
it is influenced by other sources of risk (e.g. crop and storage prices) and
risk management strategies (e.g. crop insurance).

So far the discussion has focused on planting and harvesting decisions
surrounding a single season. However, many regions of the world have one or
more seasons for the same or different annual crops (Siebert et al., 2010).
The number of harvest per year is also referred to as cropping frequency or
intensity. Areas with more than one harvest per year tend to be located in
warmer regions with sufficient precipitation to sustain multiple seasons.

This is an area that has received considerably more attention by natural
scientists than economists. Crop intensity has received growing attention
because of its potential to increase global crop production without expanding
croplands (Ray and Foley, 2013; Wu et al., 2018) although recent work
indicates limited room for increasing cropping intensity (Waha et al., 2020).
A particular focus is how climate change could affect the cropping intensity.
Using a biophysical modeling approach, Seifert and Lobell (2015) find that the
area suitable for the most common form of double cropping in the US (winter
wheat followed by soybeans) rose by 28% from 1988 to 2012. The study also
finds that the suitable area could double or triple depending on the future
climate scenario.

Naturally, a rise in suitable area doe snot imply that actual area under
double cropping will increase given that changes in cropping intensity affects
yields (Challinor et al., 2015). Moreover, there is a large discrepancy
between the area suitable for double cropping and the area currently under
double cropping suggesting that there are other constraints farmers faced that
have not yet been well documented. Gammans et al. (2019) develop an empirical
model based on observed double cropping area in the US to assess potential
expansion of agricultural production under a warming climate. Climate change
is likely to play a key role in driving changes in cropping intensity (Iizumi
and Ramankutty, 2015; Cohn et al., 2016).

###  3.10 Irrigation and other input adjustments

Water is an essential input in crop production. Farmers can obtain water via
precipitation, but also from irrigation water coming surface or underground
sources such as rivers, lakes or underground aquifers. Irrigation has played a
fundamental role in the development of agriculture of many nations, including
the US (Edwards and Smith, 2018). The main emphasis in the economics
literature on climate change and agriculture relate to 1- the role of
irrigation in explaining how farmers cope with environmental change, and 2-
understanding the sources, consequences and solutions to irrigation water
misallocation.

Irrigation consists in 1- moving water from a source (e.g. river, lake,
aquifer) on or close to an agricultural field, and then 2- applying that water
throughout the field where it can reach the root system of crops. The first
point relates to the water source (surface or groundwater). The second point
relates to the irrigation technology (flood, sprinkler, drip, etc.). Surface
irrigation typically requires major infrastructure to manage water flow from
the source to the field. That includes canals and water holding infrastructure
like dams or reservoirs. This infrastructure investments are substantial so
they can require collection action from an association or government.
Groundwater irrigation from an aquifer requires drilling and using a pump. It
does not require the type of common infrastructure to transport water over
potentially long distances like surface water irrigation.

A fundamental point is that having access to water via irrigation
fundamentally changes how farmers cope with changing climatic conditions. For
instance, Ortiz-Bobea et al. (2018) shows that agriculture is much more
sensitive to weather fluctuations in the Eastern parts of the US than in the
mostly irrigated Western regions of the country. This points relates to an
early debate regarding the role of irrigation in the Ricardian literature. In
Mendelsohn et al. (1994), the hedonic model did not include an irrigation
variable in the cross-sectional regression. Darwin (1999) pointed this out and
proposed an alternative model with irrigation as an additional variable.
However, water from irrigation is not separable from other climatic inputs.
Empirically, this means that irrigation and climatic variables interact, so
that the marginal effect of weather on agricultural outcomes depends on
irrigation. In addition, and as pointed out in Schlenker et al. (2005),
irrigation water is often subsidized in the US and its long term availability
is uncertain, so performing a Ricardian model over irrigated areas to make
long term inferences about climate change impacts can be misleading. As a
result, Schlenker and Roberts (2006) propose a Ricardian model focused on the
mostly rainfed Eastern parts of the country. Focusing on the Eastern US and
non-irrigated areas has become a common sample restriction in order to avoid
the complex issues surrounding irrigation.

There seems to be three major factors that complicate the long term analysis
of irrigation in a changing climate. First, irrigation infrastructure (e.g.
canals, dams, etc.) is often subsidized and water is typically supplied to
agricultural users below its cost of provision. Understanding the long term
implication of irrigation for the agricultural sector requires understanding
these true costs, but obtaining that data is difficult. One of the
implications is that farmers may treat water as an abundant resource, and
therefore not invest in irrigation technologies that conserve water.

The second complicating factor are water rights. The rules surrounding how
water is allocated between agricultural users and between agricultural and
non-agricultural users can be highly complex and vary considerably by region.
In the US context, water in the Western US is governed by a prior
appropriation doctrine (first users to claim water have priority) whereas
water rights in the Eastern US follow riparian rights (users close to the
water source have priority). There are also important issues regarding the
common pool nature of groundwater resources and the potentially perverse
incentives that arise that may lead to more rapid water depletion.

The third complicating factor is the the future availability of water,
especially in a changing climate (Elliott et al., 2014). In the case of
aquifers with slow natural recharge (e.g. Central Plains aquifer in the US),
the use of water is akin to mining a non-renewable resource. But in other
aquifers the dynamics of recharge and the interactions with surface water
systems make projections future water availability highly uncertain. A warming
climate will also increase evaporative demand, placing new constraints on
water availability for irrigation (Fischer et al., 2007). Also, surface water
supply is linked to precipitation in a watershed, so the future availability
of water for irrigation at a given location may depend on the water cycle in
potentially distant locations. This is particularly the case in agricultural
regions that depend on water from recurrent glacier melt such as in the Indus,
Ganges and Brahmaputra river basins. But these complicating factors do not
preclude to research documenting the nature of farmer adjustments to changing
environmental conditions over historical periods.

Indeed, an important direction of research documents how farmers adapt to
changing water scarcity. For instance, Hornbeck and Keskin (2014) explore the
advent of groundwater irrigation in US Central Plains following the Second
World War. A key characteristic of this region is the presence of one of the
largest groundwater aquifers in the world, which was previously inaccessible
to farmers with pre-war technology. The study analyzes how agricultural
production evolved on either side of the aquifer boundary. The study shows how
counties with access to the aquifer first became more resilient to droughts,
but then progressively specialized in more water-intensive crops which in turn
increased drought sensitivity. Counties without access to the aquifer
maintained drought-resilient agricultural systems. In a related study,
Hornbeck (2012) explores the long term impact of the American Dust Bowl and
analyzes, among other things, the role of irrigation in helping farmers cope
with an unprecedented environmental disaster and drought.

A more recent example includes Hagerty (2020), which relies on high-resolution
land cover data in California to derive short and long run changes in farmer
cropping choices over time in response to changes in water availability. The
paper exploits changes in institutional settings that lead certain farmers to
have more water than others. This type of work requires detailed institutional
knowledge of water allocation arrangements and regulations. In a related
study, Arellano-Gonzalez and Moore (2020) show that access to a groundwater
banking project decreased drought risk, which in turn increased the farming
transition from lower-value annual crops to higher-value perennial nut crops
in California.

Research has also focused on credibly teasing out the value of irrigation
water to farmers. These valuation models consist in hedonic models where
access to irrigation water is one of the features of the land. The rising
availability of repeated sales data now allows the estimation of panel models
with parcel or location fixed effects which allows the more credible
identification of these values relative to cross-sectional designs (Buck et
al., 2014; Mukherjee and Schwabe, 2015).

There is also a growing literature exploring the role of irrigation in helping
stabilize agricultural production and thus prevent conflict. For instance,
Gatti et al. (2021) find that irrigation infrastructure can help mitigate the
effect of growing-season rainfall shocks on conflict in Indonesia.

The rise of smart technologies are also providing access to new datasets to
track farmer behavior in ways that were impossible before. For instance,
Christian et al. (2021) track high frequency data on water use in Mozambique
and find what appear like inefficiencies in farmer decisions. The study then
introduces a randomized control trial providing information aimed at improving
farmer water management. Field studies like appear promising in helping
enhance farmers decisions about water allocations in a changing climate.

###  3.11 Market equilibrium and trade

Most of the discussion so far has focused on direct impacts of extreme weather
or climate change on agricultural production without any particular
consideration to market equilibrium and price formation. Climate change is not
a localized idiosyncratic shock, but a shift that affects virtually every
economic agent in the world. As a result, domestic and international trade and
markets are likely going to play a central role in modulating how climate
change impacts are distributed within and across nations.

One of the earliest studies to endogenize prices in a country-level context is
Adams et al. (1990). In that study, the authors linked biophysical process-
based crop models with a partial equilibrium market model. While the goal of
the crop model is to translate changes in climate into changes in agricultural
productivity, the role of the economic model is endogenously determine prices
and quantities produced in the agricultural sector. However, these are partial
equilibrium models where some features of the global economy are considered
exogenous (e.g. demand for food, incomes, etc). Other examples based on
partial equilibrium models include Adams et al. (1995), Reilly et al. (2003)
and Janssens et al. (2020).

It was perhaps Rosenzweig and Parry (1994) that first introduced a general
equilibrium framework to the analysis of climate change impacts on world food
production. In that study, the authors linked biophysical crop models with
national agricultural sector models in an overall framework representing all
economic sectors with endogenous supply and demand. More recent work in this
area relies on the Global Trade Analysis Project or GTAP (e.g. Randhir and
Hertel, 2000; Hertel et al., 2010;Baldos and Hertel, 2014 and Moore et al.,
2017). For a guide to general equilibrium modeling in agriculture see Hertel
(2013).

In a large comparative study, Nelson et al. (2014) contrast how nine global
economic models influence estimates of climate change impacts when subjected
to standardized yield impacts. Among the economic models, they consider both
partial and general equilibrium models. They find that the largest differences
coming out across these economic models are in terms of responses in
agricultural production, cropland area, trade, and prices. They find that
these differences originate from model structure and specification. In
particular they find that the ability to convert land to agriculture, to
intensify agricultural production and the propensity to trade are some of the
most critical factors in these models. It appears that there are still
important uncertainties related to the role of these market forces in
modulating climate change impacts.

In a recent study, Costinot et al. (2016) propose a general equilibrium
framework based on micro level data from 1.7 million agricultural fields to
explore the role of trade and within country reallocations in modulating the
effects of climate change on global agricultural welfare. A key contribution
is the ability to consider a large number of fields within countries that
allows analyzing adjustments both within and across countries. The study finds
that changing comparative advantage will drive crop substitution within
countries which will greatly reduce climate change impacts. They find that
climate change would reduce global GDP by about 0.26 percent, which is about
one sixth of total crop value. Perhaps surprisingly, they find trade
adjustments would play a very little role in explaining the magnitude of this
result.

More recently, Gouel and Laborde (2021) revisit this work and find drastically
different results. They find that international trade plays a comparable role
to within-country crop reallocation. It appears that the main critical factor
explaining the differences is the choice of the counterfactual. In Costinot et
al. (2016), the authors appear to constrain the export shares to remain
unchanged under climate change. Instead, constraining bilateral import shares
to remain the same yields a much larger role for trade. Interestingly, this
new study finds large regional heterogeneities in impacts with large losses
for net-food-importing countries and benefits for agricultural-exporting
countries due to more favorable terms of trade.

I should highlight that the trade literature has most closely developed in
tandem with biophysical crop process-based models. The interactions with the
empirical literature based on statistical and econometric models remains
limited. It seems like greater collaboration and integration accompanied by
systematic model comparisons are needed to resolve ongoing debates.

###  3.12 Understudied problems and unsettled questions

Here I discuss problems in the literature that seem understudied or that
remain unsettled. This list is by no means exhaustive and reflects my own
preferences as a researcher.

One of our roles as researchers is to identify mechanisms and policies that
could enhance adaptation to a changing climate. This includes identifying
institutional barriers to adaptation. For instance, governments pay billions
of dollars in subsidies every year to farmers. Some governments have also
implemented major policies that create sizable non-food markets for
agricultural products, such as the Renewable Fuel Standard in the US. However,
the effect of farm policies in enhancing or hampering adaptation to climate
change remains largely unexplored. Ortiz-Bobea et al. (2018) finds that
certain US agricultural regions are growing increasingly sensitive to rising
temperatures and this is partly due to regional specialization. The role that
policies and trade have played in this remains unclear but seems plausible.
There may also be unintended consequences to large government programs. For
instance, Annan and Schlenker (2015) find some indications that crop insurance
could provide a disincentive to adapt to extreme temperatures.

Perhaps one of the most understudied issues pertaining to agriculture and
climate change is climate justice. A lot of the global work has emphasized
inequities in terms of cross-country impacts. But more research is needed to
understand inequities within countries and how these are potentially
exacerbated by existing socio-political systems that perpetuate social
exclusion.

Another area that has received little attention is the economics of research
and development (R&D) and innovation in a changing climate. The literatures on
R&D and climate change have evolved mostly separately and the time is ripe for
integration and collaborations between these fields. This is critical, because
agricultural innovations are for the most part developed outside the farm and
they are not easily transferable across bio-climatic zones. In addition, the
returns to R&D take years if not decades to materialize and climate is rapidly
changing. Are current global and regional investments and infrastructure
adequate under a changing climate? There is also no research on the potential
role of the private sector in the R&D ecosystem under climate change.

An environmental challenge that is likely to become more prevalent in a
warming climate is soil salinity. Soil salinity arises from salt water
intrusion in low-lying agricultural coastal areas (e.g. Bengal region) or from
the evaporation of large quantities of irrigation water. Soil salinity is
toxic for many cultivated plants which negatively affect yields. Breeding or
planting salinity-tolerant crops likely imposes a cost to farmers in these
areas. For instance, Finkelshtain et al. (2020) recently analyzed the
substitutability between freshwater and non-freshwater sources in irrigation
in Israel. More research on these matters under climate change are needed and
will likely require inter-disciplinary collaboration with non-economists to
better characterize the process of water salinization in the future.

Researchers have allocated considerable effort to understanding a few things
very well. However, we still have a rudimentary understanding on very
important matters. For instance, we know relatively little about the impacts
of climate change on agricultural labor. There are a few studies analyzing how
weather shocks affect the labor supply. For instance, Branco and Féres (2020)
find that droughts tend to increase the labor supply of rural households in
non-agricultural sector in Brazil. Some studies are also exploring how heat is
affecting human capital accumulation and the role that agriculture plays (Garg
et al., 2020). But more research is needed in this under-explored area.

Overall, there is much more emphasis on agricultural production and in
agricultural fields, and less on what happens afterwards or beforehand. For
instance, there is less research on how weather can affect food quality and
post harvesting processing and associated crop losses. Similarly, there is
little understanding of the robustness of food and agricultural supply chains.

We also have a limited understanding of how changing pest pressures linked to
changing biodiversity would affect agriculture. This is particularly
challenging because observational studies based on panel data might not be
necessarily well suited for such analysis. For instance, a warm year does not
lead to the same pest pressure than an equally warmer climate would induce.
There are not only farmer adaptations to consider, but also ecological
adjustments that remain largely unknown. This invites a greater degree of
collaboration and integration with ecologists and other natural scientists.

Finally, economists have for the most part favored working on observational
empirical studies in isolation. However, there are fruitful collaborations
that can arise from closer integration with crop scientists, particularly in
the context or large inter-comparison projects such as AgMIP. These
collaboration can lead to major publications in interdisciplinary outlets that
could have greater impact on policy than what economists can do on their own.

##  4 Coding and other empirical matters

The analysis of climate change impacts and adaptation in agriculture involves
specialized knowledge and training that is generally not offered in graduate
programs in economics, agricultural and resource economics or other related
fields. For instance, conducting empirical research in this area requires
manipulating large geospatial datasets (e.g. weather data) which are more
common currency in environmental sciences than in economics. Unfortunately,
this deficit in training means that new researchers to this field often face
substantial barriers to entry.

This section provides a hands-on introduction to common tasks in this area of
research in an attempt to cover this “hidden curriculum”. Increasingly, these
tasks are carried out in open-source programming languages like R, which
allows the flexible integration of workflow from the manipulation of
geospatial data to the regression analysis with the ability to produce high-
quality visualizations. This integration also facilitates the reproducibility
and replicability of research projects. This is critical as a growing number
of academic journals require that papers be fully reproducible.

The section provides a rationale behind how to code these tasks, but also
provides code and data to fully carry out these tasks, including the ability
to reproduce the figures in the chapter. The reproduction code and data are