Weather Fluctuations, Expectation Formation, and Short-Run Behavioral Responses to Climate Change

Abstract

One premise adopted in most previous studies is that weather fluctuations affect economic outcomes contemporaneously. Yet under certain circumstances, the impact of weather fluctuations in the current year can be carried over into the future. Using agricultural production as an example, we empirically investigate how past weather fluctuations affect economic decision-making by shifting agents’ subjective expectations over future climate. We find that agricultural producers do not form expectations on future climate using only long-run normals, and instead engage in a combination of heuristics, including the availability heuristic and the reinforcement strategy. Adopting these learning mechanisms causes farmers to significantly over-react to more recent fluctuations in weather and water availability when making ex ante acreage and crop allocation decisions.

There has been widespread interest in the economic literature on understanding the impacts of climate change on economic outcomes and corresponding adaptation measures. A popular approach to do so is to use random weather fluctuations to identify the effects of climate change on economic outcomes, such as agricultural production (Deschênes and Greenstone 2007; Schlenker and Roberts 2009), gross domestic product (Dell et al. 2012), and long-run adaptation (Deschênes and Greenstone 2011). One premise adopted in most studies is that weather fluctuations affect economic outcomes contemporaneously. For example, extreme heat events decrease crop yields (e.g. Schlenker and Roberts 2009; Lobell et al. 2013), but this negative effect applies only to the particular year in which the extreme heat event occurs. However, under certain circumstances, the impact of weather fluctuations in the current year can be carried over into the future. Studies have shown that extreme weather realizations can affect long-term individual economic well-being (Ebenstein et al. 2016; Deryugina et al. 2018), future macroeconomic output (Dell et al. 2012), and induce and intensify political instability, human conflicts, and wars in the future (Zhang et al. 2008; Hsiang et al. 2013; Zheng et al. 2014; Iyigun et al. 2017).

One particular pathway through which past weather fluctuations can affect future economic outcomes is the process of expectation formation. Not only do weather fluctuations affect contemporaneous outcomes, they also shape what people expect in terms of future climate. Both economists and psychologists have established that recent realizations of an event can disproportionately affect human perceptions on the underlying probability of that event happening (e.g. Tversky and Kahneman 1974; Kahneman et al. 1991; Camerer and Loewenstein 2011). Studies have found that subjective expectations to climate are inconsistent with predictions from rational expectations (Cameron 2005), such that people significantly over-adjust their expectations to climate in response to recent, local, and extreme weather events (Marx et al. 2007; Deryugina 2013; Konisky et al. 2016; Lee et al. 2018). Through expectation formation, economic decisions that require forward-looking inference on climate may be subject to a disproportionately large influence from past weather fluctuations. In that sense, weather fluctuations can cause short-run economic losses due to sub-optimal decision-making based on over-adjusted climate expectations.

Using agricultural production as an example, we empirically investigate how economic agents adjust and adapt present decision-making in response to past shocks, and from which we shed light on how economic agents learn from and act upon those shocks. Agricultural production is uniquely affected by weather fluctuations and the corresponding expectation formation process. Many agricultural production decisions are made before the realization of weather. Examples include decisions on acreage, crop allocation, planting time, seed variety, and tillage method. These ex ante decisions are made based on subjective expectations over climate rather than weather realizations during the growing season. Previous studies have found that climate change induces long-run adaptation in acreage (Cui 2020) and crop-allocation decisions (Seo and Mendelsohn 2008; Ji et al. 2018; Hagerty 2020). This literature usually focuses on farmers’ response to long-run climate normals, which ignores the fact that recent realizations can have a disproportionately large role in driving subjective expectations over climate. Indeed, other studies have found that agricultural production decisions can also be affected by various types of short-run expectation shifters, including monsoon patterns (Miller 2016), spring snowpack forecasts (Manning et al. 2017), and previous realizations of temperature (Miao et al. 2015; Cohn et al. 2016), precipitation (Ding et al. 2009; Kala 2017), and water availability (Buck et al. 2014; Hagerty 2020). However, there is still scant literature that comments on the specific mechanisms by which previous realizations enter the expectation formation process, how they may affect multiple ex ante decisions, and how expectation-induced adaptation can be affected by multiple factor inputs simultaneously.

Our empirical analysis focuses on two ex ante agricultural production decisions: (1) acreage decisions, i.e., how much land to plant, and (2) crop-allocation decisions, i.e., what type(s) of crop to grow on land in production. We estimate fixed-effect models on acreage, crop allocation, and their aggregate effect using farm-level data for an irrigated, multi-crop agricultural system. We use multiple lags of growing degree days (GDD), extreme degree days (EDD), precipitation, and surface water availability (as governed by prior appropriation water rights) as independent variables to identify the effects of past weather realizations on agricultural decision making. A unique feature of our dataset is that irrigation water is distributed by collective water providers, whose water is acquired under prior appropriation water rights. Under appropriative water rights, cross-sectional variation in surface water availability comes from differences in water providers’ water rights attributes. In contrast, time-series variation in surface water availability is governed by the stochastic natural inflows that determine the total water supply available to be allocated across all water users in the region. Our identification strategy relies on time-series variation for individual farmers by differencing out cross-sectional variation using fixed effects. This approach allows us to control for average climate and water right attributes, while simultaneously controlling for other unobserved individual-specific heterogeneity, such as risk attitudes that may drive insurance adoption. This allows us to capture the effect of shifting expectations due to the fluctuations in weather and surface water availability for individual farmers and their subsequent behavioral responses.

Using this identification strategy, we test for three types of expectation formation mechanisms (heuristics). Our starting hypothesis is that farmers form expectations using long-run climate normals, a strategy consistent with the rational Bayesian learning framework. If a farmer follows the Bayesian updating rule and uses long-run normals, then the effect of a recent shock on his/her posterior expectation, and thus ex ante production decisions in subsequent years, will be small, time-independent in magnitude, and long-lasting in duration. We test this long-run-normal strategy against two alternative heuristics identified in the behavioral economics literature. These alternatives are: (1) the availability heuristic, which predicts that the effects on expectations and decisions are larger for more recent shocks, and smaller, or even trending towards zero, for shocks farther away; and (2) the reinforcement strategy, which predicts the effects on expectations and decisions to be cyclical.

Our empirical application is to Water District 1 (WD1) in the Upper Snake River Basin of Idaho, for which we assemble a farm-level, spatially explicit panel dataset spanning 2007–2016. We identify the geographical boundary for each farm, and spatially match the farm with a series of high-resolution geospatial datasets documenting field-level cropland acreage, crop allocation, temperature, and precipitation. We also acquire data on water rights characteristics, water curtailments by day of the growing season, and daily water deliveries for collective water providers in WD1, and match them to the farms to which they supply water.

Our results indicate that previous shocks in weather and surface water availability significantly affect both acreage and crop-allocation decisions. On average, an increase in GDD in past years increases cropland acreage, an increase in EDD in past years reduces cropland acreage, and past precipitation shocks do not have a significant effect on acreage. We do not find significant effects of weather shocks on crop allocation decisions. With respect to surface water availability, we find evidence of cyclical responses to water availability shocks for crop-allocation decisions: an increase in curtailment days, i.e., a negative shock in water availability, decreases expected profitability on planted lands in the first and third years, and increases it in the second and fourth years following the shock. Past increases in curtailment days also decrease cropland acreage, though the cyclical pattern is less prevalent than in the case of crop allocation decisions.

These results provide evidence to reject the hypothesis that farmers only use long-run normals to form expectations on climate and surface water availability. Instead, our results are consistent, to varying degrees, with the alternative expectation–formation heuristics considered. We find evidence to support the recency heuristic, as our results suggest that the effect of endowment shocks dissipates in 4–5 years. We find limited evidence to support the availability heuristic, as there is no clear pattern of gradually decreasing effects over time. Finally, we present evidence consistent with the reinforcement strategy, as responses to previous weather shocks exhibit cyclical behavior in the model on crop allocation, a key characteristic consistent with reinforcement learning.

This study makes several contributions to the economic literature. First, we show that ex ante economic decision-making may be disproportionately affected by past weather fluctuations through cognitive heuristics other than Bayesian updating. This complements the existing literature assessing the economic impact of climate change by demonstrating a mechanism through which past weather fluctuations may affect future economic decisions and outcomes. Second, our study emphasizes the need to incorporate short-run behavioral responses when assessing climate change impacts. We show that weather fluctuations create the potential for an over-adjustment cost as farmers overreact to short-run weather signals. The existing approaches to modeling climate change impacts, such as Ricardian regression, contemporaneous fixed-effect, or long-differences, are not able to identify this short-run response. Our results are particularly relevant given that climate change models project a change in long-run averages as well as increased variability, particularly in temperature. As weather shocks become more frequent and larger in magnitude, this over-adjustment cost may also increase. Third, this study links two important threads in the economic literature, one from the behavioral economics literature on learning mechanisms, the other on agricultural adaptation to climate change. Previous studies in these areas either investigate subjective perceptions over climate change without linking them to behavioral responses or demonstrate adaptive responses to past weather fluctuations without tracing them back to their underlying learning mechanisms.

1 Expectation Formation

In this section, we use a stylized framework to motivate learning mechanisms by which expectations are formed and updated using previous weather and water availability realizations. We start by motivating the case for using the long-run normal as the expectation for weather and water availability, which serves as our baseline learning mechanism. We then discuss how producers may deviate from the long-run normal and use alternative mechanisms to learn from the past.

Imagine a representative farmer who holds a single natural endowment governed by a random variable W, which is independently and identically distributed (i.i.d) with mean $\mu$ and variance $\sigma ^2$. The expectation formation process can be generalized as a process of assigning weights to previous realizations, i.e.,

$$\begin{aligned} E_t(W) = \sum _{s=1}^{T} \beta _s w_{t-s} \end{aligned}$$

(1)

where the expectation of the endowment at time t, $E_t(W)$, is learned from T previous realizations, $w_{t-T}$ to $w_{t-1}$, with a set of weights $\beta _T,\ldots ,\beta _1$. We present three different types of learning mechanisms in this section: long-run normals, the availability heuristic, and the reinforcement strategy. All thrre of them are essentially different sets of weights for previous realizations.

We begin with inference based on long-run normals, i.e., an expectation based on the average of a time series of historical realizations. Long-run normals are widely produced and used by meteorologists and hydrologists as a baseline estimate for long-run climate and water flow conditions.¹ Normals have also been frequently used in the economics literature to approximate farmers’ expectations over climate (Mendelsohn et al. 1994; Schlenker et al. 2005; Burke and Emerick 2016).

The use of long-run normals is appealing because it is consistent with the weights generated from several rational learning frameworks. Not only does it correspond to an unbiased maximum likelihood estimate (MLE) of the underlying climate, it also corresponds to a rational Bayesian learning framework with a non-informative prior.² The Bayesian learning framework builds on the Bayesian updating rule, a standard tool used by economists to model rational probability updating behaviors (Camerer and Loewenstein 2011). While empirical evidence on the validity of the Bayesian updating rule is mixed (e.g. Barberis et al. 1998; Charness and Levin 2005; Rabin 2002; Anwar and Loughran 2011; Chiang et al. 2011), the Bayesian updating framework serves as a common starting point for numerous studies on rational learning and decision-making under risk and uncertainty.

With its links to the Bayesian learning and MLE framework, we argue that if long-run normals provide a rational expectation for the underlying long-run climate (as suggested by their use in climate science), they are thus the best prediction for the realizations in the upcoming season. Following that logic, economic decisions made using expectations formed on Bayesian learning/long-run normals will be optimal. On the other hand, if recent realizations are disproportionately weighted, subjective expectations over climate will deviate from the long-run normal. In that case, we expect that the use of alternative learning mechanisms is likely to generate economic losses by driving sub-optimal decision making.

Two key hypotheses can be drawn from the assumption that the farmer uses long-run normals to define expectations over weather. First, given a lengthy time series of previous realizations, the weather realization for any single year has a relatively small effect on the expectation. This is because each single realization is weighted by $\frac{1}{T}$, which results in a small influence on the posterior expectation if T is sufficiently large. Second, no matter how distant (lagged) the realization, each enters the expectation with the same weight. Thus the effect of each realization on the expectation is independent of its timing.

The literature on cognitive psychology and behavioral economics has pointed out multiple alternative heuristics, i.e., learning mechanisms, that deviate from long-run normals. One such heuristic is the availability heuristic, proposed by Tversky and Kahneman (1974). The availability heuristic describes the phenomenon in which individuals place higher probabilities on events that are foremost in their memory. Often known as the recency bias, the availability heuristic has been documented in multiple empirical settings involving learning and expectation formation, and especially on events with small probabilities, for example, flood risks (Gallagher 2014), climate change (Deryugina 2013), and financial markets (Malmendier and Nagel 2011). In the case of agricultural production, studies have also suggested that farmers often turn to familiar patterns from the past two agricultural seasons, or to those happening at the time of other memorable events (Marx et al. 2007).

In our application, we characterize the availability as a set of unequal weights between different past realizations. This implies that:

$$\begin{aligned} E_t(W) = \sum _{s=1}^{T} \beta _s w_{t-s} = \beta _1 w_{t-1} + \beta _2 w_{t-2} + \cdots + \beta _T w_{t-T} \end{aligned}$$

(2)

where unlike in the case of long-run normals, the weights $\beta _s$ for each realization $w_{t-s}$ under the availability heuristic are unequal, and dependent on how the salience of previous realizations. The qualitative pattern of these weights can take several forms. One possibility that corresponds to the availability heuristic is that producers give higher weights to realizations that are more recent, i.e.,

$$\begin{aligned} \beta _1 \ge \beta _2 \ge \cdots \ge \beta _T \end{aligned}$$

(3)

, because more recent realizations are more salient in one’s memory. Another possibility is that producers draw inference only from experiences in the recent past and ignores the more recent past, i.e.,

$$\begin{aligned}&\beta _s>0 \text{ when } s \le S \nonumber \\&\beta _s=0 \text{ when } S< s < T \end{aligned}$$

(4)

such that any realization more distant than S years receives zero weight. In both cases, producers put larger weight on the more recent shocks and over-react to weather fluctuations, relative to the reactions using long-run normals.

A second learning mechanism we consider here is the reinforcement strategy, sometimes referred to as the “win-stay, lose-shift” heuristic. Under the reinforcement strategy, an individual expects a shock they have personally experienced to recur in the future (Roth and Erev 1995; Camerer and Ho 1999; Chiang et al. 2011). When a previous realization deviates from the individual’s expectation, he/she will expect that positive or negative shock to be carried over to future realizations. Although Bayesian learning exhibits some positive feedback, reinforcement learning amplifies those feedback mechanisms to the degree that is inconsistent with behavior predicted by rational expectation.

We formally express the reinforcement strategy as a case in which the farmer adjusts his/her expectation by reinforcing the most recent shock, i.e., the difference between the most recent realization, $w_{t-1}$, and the expectation prior to that realization, $E_{t-1}(W)$:

$$\begin{aligned} E_t(W) = \sum _{s=1}^{T} \beta _s w_{t-s} + \gamma \big [w_{t-1} - E_{t-1}(W)\big ] \end{aligned}$$

(5)

where $\gamma >0$ measures the magnitude of the reinforcement behavior. Simplifying Eq. 5 by expanding the previous expectation term $E_{t-1}(W)$ yields:

$$\begin{aligned} E_t(W) = \sum _{s=1}^{T} {\tilde{\beta }}_s w_{t-s} \end{aligned}$$

(6)

where ${\tilde{\beta }}_s$ takes the following form:

$$\begin{aligned} {\tilde{\beta }}_1= & {} \beta _1 + \gamma \nonumber \\ {\tilde{\beta }}_s= & {} \beta _s - \gamma {\tilde{\beta }}_{s-1} \quad \text{for any }s\ge 2 \end{aligned}$$

(7)

Equation 7 suggests that the reinforcement strategy generates cyclical weights. The key reason for cyclical weights is that the farmer adjusts his/her expectations based on the shock $w_{t-1} - E_{t-1}(W)$. As such, the farmer relies too heavily on the realization in the year prior t-1, $w_{t-1}$, but puts too little weight on the shock at t-2, $w_{t-2}$, which was the key component in forming the year t-1 expectation, $E_{t-1}(W)$. Expanding the iterated expectations leads us to conclude that the farmer will also over-utilize $w_{t-3}$, under-utilize $w_{t-4}$, etc. If $\gamma$ is sufficiently large, it is even possible that the weights for even years, i.e., ${\tilde{\beta }}_2$, ${\tilde{\beta }}_4$, etc., can become negative.

The mechanism for reinforcement learning can also be understood by linking it with ex ante production decisions through a win-stay-lose-shift strategy. Say a farmer experiences a positive shock in precipitation in year t-1, relative to what he/she expected. He/she could have planted more acres if he/she knew precipitation would exceed the expectation. Using the reinforcement strategy, he/she will over-adjust by planting more acres in year t, in the expectation that this year’s precipitation is going to be more like last year’s. This will lead to a larger-than-optimal planted acreage because, on average, precipitation will not be as good as it was last year. Following the realization in year t, which is a negative precipitation shock relative to year t-1, the farmer over-adjusts to a smaller-than-optimal acreage in year t+1. This pattern implies that a positive shock in year t-1 can lead to a negative adjustment two years later, in year t+1.

We formally write the hypotheses for the four learning mechanisms as follows:

• Hypothesis 1 (Long-run Normal) Given a lengthy time series of previous realizations, the realization from any single year has a relatively small impact on the expectation.

• Hypothesis 2 (Long-run Normal) The timing of a realization is irrelevant to expectation formation.

• Hypothesis 3 (Availability Heuristic) Each realization will have different weights in the expectation, with more recent realizations having larger weights and more distant ones having smaller weights.

• Hypothesis 4 (Availability Heuristic) More recent realizations will have positive weights, whereas more distant realizations will have zero weight.

• Hypothesis 5 (Reinforcement Strategy) Past realizations enter into expectations with cyclical weights.

Figure 1 shows a stylized illustration of learning mechanisms mentioned above, including long-run normals, different representations of the availability heuristic, and the reinforcement strategy with various magnitudes.

Fig. 1

Heuristics and weights on past shocks

For the purpose of illustrating relevant learning mechanisms, we have treated the underlying long-run distributions for climate and surface water flows as stationary over time. It is worth noting that these long-run distributions are potentially trending as a result of global or regional scale environmental change. However, we do not explicitly consider climate trends in this section for two reasons. First, long-run climate trends in temperature and precipitation are much smaller in magnitude than year-to-year fluctuations. Long-run climate trends imply a change of about $0.02^\circ$ Cannually (Intergovernmental Panel on Climate Change 2014), whereas annual temperature realizations have a standard deviation of around $0.7\,^\circ \text{C}$ per year in our sample. Over a relatively short period of time (10 years for our empirical analysis), climate trends are not likely to cause large shifts in the long-run distribution of weather realizations. Second, our empirical analysis is sufficiently flexible to control for trending means of climate or water availability in the data. Trends in mean temperature, precipitation, and surface water availability will be absorbed in the year fixed-effects, such that the weather shocks included in our empirical models are on average stationary over time.

Our analysis does not preclude the possibility that producers interpret weather shocks as signals of a trending climate. In fact, both learning mechanisms we listed above are consistent with some type of over-interpreting weather fluctuations as climate trends. Reinforcement learning is a direct result of interpreting perceived trends in weather fluctuations as actual climate trends. More interestingly, the availability heuristic is consistent with the Bayesian learning framework with a time-variant climate governed by a random walk process. Kala (2017) showed that under such a case, Bayesian learning leads to over-weighing recent shocks relative to more distant ones, and the over-weight is proportional to the variability of the climate trend. However, because the actual climate trend is much smaller in magnitude than year-to-year weather fluctuations, it is not likely for farmers using a Bayesian learning framework to exhibit significant availability bias if the variability of the climate trend is correctly estimated. In fact, one of the possible alternative explanations for the availability heuristic is that farmers use Bayesian learning, but over-estimate the variability of climate trends and underestimate the variability of weather. In such a case, we would expect to see farmers over-weighting more recent weather shocks and under-weighting more distant ones.

2 Data

Our empirical analysis focuses on Water District $\#$1 (WD1) in the State of Idaho, which governs water allocation for the upper Snake River from Minidoka Dam to Milner Dam, as well as tributaries along that segment of the Snake River. WD1 is the largest water district in Idaho, accounting for water deliveries to nine major reservoirs and approximately 350 water users (Olenichak 2015). Among the 350 water users, approximately 200 are individual irrigators, and the rest are collective water management institutions, including public irrigation districts and private irrigation and canal companies. Water is used predominantly for agricultural irrigation in WD1.

We chose WD1 for our analysis because the district operates and keeps the longest and the most accurate information regarding water availability and curtailment decisions in the state. Records on daily water calls for each river segment are available dating back to 1988, including detailed information on how water calls are determined (see Olenichak 2015).³ Using these records as well as the adjudicated water rights database from the Idaho Department of Water Resources (IDWR), we are able to reconstruct daily water availability for every water user within WD1.

We collect data for 1056 unique farms for 2007–2016, with information on farm boundaries, attributes for water rights held by respective water providers, and daily water calls. We spatially match these farms with geo-referenced databases on land use and crop allocation, temperature, and precipitation. Our data assembling strategy is similar to those used in previous studies, including Leonard and Libecap (2016); Browne (2017) and Ji and Cobourn (2018). Table 1 provides summary statistics.

Table 1 Summary statistics of variables

Focusing our analysis on one particular sub-region allows us to address the challenge of measuring irrigation water availability, an essential input and the “most important omitted variable” (Schlenker et al. 2007) in irrigated agriculture in the western U.S. There exist significant hydrological and legal differences in water allocation institutions between and within states, as do efforts and abilities to measure, document, and enforce those institutions. By focusing on a sub-region of which water management institutions are consistent, well-managed, and well-documented, our study addresses the challenges presented by omitted or poorly measure water availability, while simultaneously shedding light on the importance of irrigation water to other semi-arid regions.

2.1 Surface Water Availability

Irrigation water deliveries in WD1 are administered under the doctrine of prior appropriation, based on the principle of “first in time, first in right.” Available water in the district is prioritized to fulfill senior water rights, or those that are established earliest in time. Junior water rights are curtailed if there is not enough water to fulfill senior water rights on any given day. An individual farmer either possesses his/her own water rights, or receive water deliveries from an irrigation water provider, such as an irrigation district, irrigation company, or canal company. In the latter case, the water provider serves as the ”middle-man” between WD1 and the farmer. The water provider acquires water from WD1 through water rights owned in common by all farmers within that provider’s service area and distributes water to its members (shareholders). Service areas of most surface water providers are determined long before our study period, and remain so since then.⁴ Additionally, in our analysis, we focus on farmers that can only acquire water from the water provider that services the specific plots of land, thus eliminating the possibility that farmers switching water providers/sources during our study period.⁵

We obtain daily curtailment records for each farm in our dataset from 1988 to 2017. Curtailment decisions in WD1 are made using a computerized water accounting model that calculates water availability in each of 36 unique river segments in the district (hereby referred to as “reaches”).⁶ Each day, the district calculates water availability over the entire sub-basin. It then issues a cutoff priority date for each reach following the prior appropriation rule, with the goal of allocating all available water to the most senior water right holders throughout the entire district. For each reach, the cutoff priority date corresponds to the priority date of the last water right fulfilled. All rights with a priority date later than the cutoff priority date are not fulfilled. Depending on the spatial and temporal distribution of water flows in the basin, the cutoff priority date can differ across different reaches and/or on different days.⁷

We also construct a database of water rights portfolios using administrative records from WD1 and the Idaho Department of Water Resources (IDWR). A water portfolio is a combination of one or more water rights owned by the same farm. Water rights in a water portfolio share the same geographical place of use, with each water right having (potentially) different priority dates, diversion points, and diversion rates.⁸ Almost all collective irrigation institutions hold a water portfolio that contains multiple water rights. We then combine water curtailment records with the water portfolio database, from which we are able to determine daily curtailments for each water portfolio. Although curtailment decisions for a single water right are binary on any given day, i.e., either curtailed or filled, water deliveries for a farm with a water portfolio may be partially filled, i.e., some water rights in the portfolio are curtailed, and others are filled. We characterize daily curtailment decisions for a water portfolio as the percentage of diversions curtailed.

Since acreage and crop allocation decisions are made over the entire growing season, we need to aggregate daily curtailments into annual realizations. We count the number of curtailment days annually and create 12 different measures of curtailment days by varying three aggregation methods: (1) total number of days (TND) curtailed versus longest curtailment streak (Streak); (2) Growing Season (April to October) versus Summer Months (June to August); and (3) 100% versus more than 80% versus more than 50% percent of permitted diversions curtailed. Our main empirical models present estimates using the total number of days in summer months where more than 50% percent of the permitted diversion is curtailed (TND.summer.50%), one of the more responsive measures. We conduct robustness checks with other constructed measures, presented in the results section.

Our dataset on water curtailments improves upon previous studies on prior appropriation water rights in both spatial and temporal coverage. In terms of spatial coverage, previous studies usually proxy the underlying distribution of curtailments through direct comparison of priority dates (Lee et al. 2017) or some order-preserving transformation over priority date (Brent 2017; Ji and Cobourn 2018). However, priority date only preserves the order of water seniority within each reach, but can differ widely in the probability distributions of curtailment across reaches and sub-basins. By directly measuring water availability using curtailment records, we eliminate the concern that spatial heterogeneity in water availability for the same priority date across reaches may be correlated with some location-specific unobservables, which can potentially bias statistical inference.

In terms of temporal coverage, most previous studies rely on time-invariant attributes of water rights (e.g. Mukherjee and Schwabe 2015; Brent 2017; Lee et al. 2017; Ji and Cobourn 2018) or some long-run expectations over water delivery (e.g. Schlenker et al. 2007), which cannot capture dynamically evolving expectations over water deliveries. Two exceptions are Buck et al. (2014) and Manning et al. (2017), which measure the amount of water delivered and curtailed, respectively, over a growing season at the county level. Our dataset goes a step farther to quantify variation at the level of the water right and create various measures of water curtailment attributes.

2.2 Farm Boundaries

Farm boundary data were purchased from FarmMarketID, a private firm that collects data on farm characteristics for marketing purposes. We obtain geo-referenced farmland ownership for the year 2016, where each farm in our sample owns one or more common land units (CLU).⁹ For this study, we use farms that are serviced by only one collective water provider, either an irrigation district or an irrigation or canal company.¹⁰ By doing so, we exclude farms that have access to any individual water rights, or those within the service boundaries of more than one water provider. These measures ensure that water availability and farm boundaries are clearly defined for the farms in the analysis. Figure 2 shows the locations of the farms included in our analysis.

Fig. 2

Map of farms in water district 1 of Idaho. Each green dot denotes one farm. Size of the dot indicates relative size of the farm. Blue line denotes the main stem of the Snake River. Lower-right panel denotes the relative location of Water District 1 (Red line denotes the boundary of the district.)

We make several assumptions regarding water rights and farm boundaries. First, we assume that farm boundaries remain constant from 2007 to 2016. Due to data availability constraints, we are unable to obtain farm boundaries earlier than 2016. We do not expect this to jeopardize inference if farmland sales are accompanied by the sale of corresponding right(s) to be serviced by water providers, which is usually the case. Second, we assume that within each irrigation district, water is allocated proportionally to each farm. This assumption is widely adopted by previous studies, including Schlenker et al. (2007) and Buck et al. (2014). Our main inference will not be jeopardized as long as water is not allocated using a seniority-based system within each irrigation district. As Ji and Cobourn (2018) documented, water within irrigation districts is usually allocated to members in proportion to the share(s) owned by each. Similar share systems are widely adopted by irrigation and canal companies in our sample.¹¹

2.3 Acreage and Crop Allocation

Acreage and crop-allocation data are obtained from the USDA Cropland Data Layer (CDL), a field-scale remote sensing product developed for the continental U.S. using satellite imagery and calibrated classification algorithms. For each farm, we identify the percentage of land allocated to six major crops in the region: alfalfa, barley, corn, potato, sugarbeets, and wheat, as well as land in fallow. These six crops and fallow account for over 98% of the total cropland area in WD1 (National Agricultural Statistics Service 2007–2016).¹² Therefore, we do not expect the exclusion of land in other crops to affect our results. Our farm level fixed-effect approach offers additional safeguards against omitted crop types as well as general misclassification in the CDL, as time-invariant misclassifications will be eliminated by the transformation.

2.4 Climate and weather

We obtain daily temperature and precipitation data from the PRISM climate dataset, a medium-scale geo-referenced weather dataset with a spatial resolution of 4km. PRISM has been used extensively in previous studies on climate change, such as Schlenker et al. (2007). Growing degree-days (GDD), extreme degree-days (EDD), and growing season precipitation are derived from PRISM data by accumulating daily temperature and precipitation over the growing season. Following Schlenker et al. (2007), we evaluate GDD by accumulating daily degree days over the growing season, using cutoffs of 8 $^\circ$C and 32 $^\circ$C.¹³ We calculate EDD by accumulating daily degree days‘ exceeding the upper threshold, using a cutoff temperature of 32 $^\circ$C.¹⁴ We calculate growing season precipitation as the cumulative amount precipitation (in mm) between April and September, which reflects the standard duration of the growing season in the region.

3 Empirical Strategy

Our empirical question examines how previous realizations in weather and water availability, transmitted through the expectation formation process, affect agricultural producers’ ex ante decision making. One inherent problem for many agricultural decisions, such as acreage and crop allocation, is the timing mismatch between decision making earlier in the growing season and the realization of key endowments later during the season. In the planting stage of year t, producer i maximizes expected profit by making a production decision, $y_{it}$, based on his/her subjective expectations over a vector of J natural endowments $E_{it}({\mathbf{W}})$, where ${\mathbf{W}}\equiv W_1,\ldots ,W_J$. At harvest, realizations of those endowments, ${\mathbf{W}}_{it}$, are observed, and the producer earns a realized profit. Assuming that the marginal effects of endowments are separable from each other, previous studies have shown theoretically that under certain conditions, the producer’s profit maximization problem yields a series of linear marginal effects between optimal production decisions and the expected level of endowments (Moore and Negri 1992; Ji et al. 2018; Cui 2020).¹⁵ Our conceptual model can be written as:

$$\begin{aligned}&y_{it} = \sum _j \alpha _{j} E_{it}(W_j)\nonumber \\&E_{it}(W_j) = \sum _{s=1}^{T} \beta _{js} w_{i,j,t-s} \end{aligned}$$

(10)

where the producer’s decision, $y_{it}$, is a linear function of expectations over each natural endowment, $E_{it}(W_j)$; and the expectation over each endowment is in turn a linear combination of its historical realization, $w_{i,j,t-s}$. The expectation formation process follows Eq. 6, where each of the previous T shocks, $w_{i,j,t-s}$, contributes to the expectation with a weight of $\beta _{js}$. These unspecified weights nest the three learning mechanisms presented in the previous section.

Combining these two steps and adding in different types of natural endowments, our final empirical model becomes:

$$\begin{aligned} y_{it}= & {} \sum _{s=1}^{T} \gamma _{1s} \textit{GDD}_{i,t-s} + \sum _{s=1}^{T} \gamma _{2s} \textit{EDD}_{i,t-s} + \sum _{s=1}^{T} \gamma _{3s} \textit{Precipitation}_{i,t-s} \nonumber \\&+ \sum _{s=1}^{T} \gamma _{4s} \textit{WaterCurtailment}_{i,t-s} + \mu _{i} + v_{t} + \varepsilon _{it} \end{aligned}$$

(11)

where $y_{it}$ is the outcome of interest for producer i at year t; $\textit{GDD}_{i,t-s}$ is the s years’ lag of growing degree days; $\textit{EDD}_{i,t-s}$ is the s years’ lag of extreme degree days; $\textit{Precipitation}_{i,t-s}$ is the s years’ lag of growing season precipitation, and $\textit{WaterCurtailment}_{i,t-s}$ is the s years’ lag of irrigation water availability measured by days of curtailment. The model also includes farm-level fixed effect, $\mu _{i}$, and year fixed-effect, $v_{t}$. Here the coefficient of lag s for endowment j, $\gamma _{js}$, identifies the product of the marginal effect of an endowment on the decision, $\alpha _j$, and the lag-specific weight, $\beta _{js}$, both of which appear in Eq. 9. We are not able to separately identify $\alpha _j$ and $\beta _{js}$ from our empirical model in Eq. 11, but since $\alpha _j$ remains constant for each endowment over time, we are able to identify the relative weights between different lags.

Equation 11 can be used to test for all three learning mechanisms laid out in the previous section. Specifically, if a farmer uses long-run normals to infer the expectation for endowment j, we expect all lagged coefficients on that endowment to be equal, i.e., $\gamma _{j1} = \gamma _{j2} = \cdots = \gamma _{jT}$. If a farmer engages in availability heuristic, we expect two patterns: (1) the coefficients are larger when the shocks happen closer to the current period, i.e. $\gamma _{j1}> \gamma _{j2}> \cdots > \gamma _{jT}$; and (2) the coefficients are different from zero for lags closer to the current period, but to be non-different from zero for lags farther away from the current period, i.e., $|\gamma _{js}|>0 \text{ for some } s\le S$ and $\gamma _s \simeq 0 \text{ for } s > S$. If a farmer engages in reinforcement heuristic, we expect coefficients to be cyclical, as documented in Eqs. 6 and 7 .

We model three outcomes of interest in our empirical models: (1) the crop-allocation effect, summarized as an expected profit from planted land; (2) the acreage effect, i.e., the fraction of planted land; and (3) total expected profit, which summarizes acreage and crop-allocation decisions.

Crop-allocation adjustment is one of the main mechanisms through which farmers adapt to climate conditions and water constraints (Seo and Mendelsohn 2008; Kala et al. 2012; Cobourn et al. 2017; Hagerty 2020). We aggregate crop mixes into a single measure of long-run expected profit, constructed as a function of field-scale crop allocation decisions, state-level crop prices, average state-level crop yields, and region-specific costs of production for the six major crops in the region. This reflects the differences in expected profitability of growing different types of crops: some crops (e.g., corn) have higher expected profits but are sensitive to drought and extreme heat, other crops (e.g., wheat) have lower expected profits but are tolerant to drought.

Acreage adjustment is another mechanism used by farmers to adapt to climate change (Miao et al. 2015; Cohn et al. 2016; Cui 2020). Farmers may decide to adjust crop acreage by fallowing land or by expanding or shrinking production on marginal lands when facing differing climate conditions and water constraints. We define acreage as the fraction of a farm’s land base that is used to produce the six major crops mentioned above.

Finally, we aggregate crop-allocation and acreage margins to construct a measurement of total expected profit, which is the product of the two. This gives us the total extensive margin adjustment when facing climate shocks. All three outcome variables reflect farmers’ ex ante production decisions undertaken early in the growing season.

We employ a panel fixed-effect approach to identify our main effect of interest by exploiting time-series variation in previous weather and water availability shocks for each individual farm. This approach offers two advantages over a cross-sectional or pooled approach. First, by comparing the same individual at different time periods, we are able to simultaneously control for the effect of location-specific average temperature and precipitation, as well as average water curtailments specific to each water right. Although realizations of water availability vary from year to year, the underlying water portfolios for the same farm remain constant, and thus the long-run mean water availability should also remain constant.¹⁶ Second, since weather and water availability shocks are plausibly random, we eliminate concerns about time-invariant omitted variable biases and spatially-correlated measurement errors, which plague empirical studies using cross-sectional regressions (Auffhammer and Schlenker 2014; Blanc and Schlenker 2017).

The effect we capture here differs from those recovered in popular empirical approaches, including the Ricardian approach (e.g. Mendelsohn et al. 1994; Schlenker et al. 2005), the long-difference approach (e.g. Burke and Emerick 2016), and the contemporaneous fixed-effect approach (e.g. Deschênes and Greenstone 2007; Schlenker and Roberts 2009). The Ricardian approach draws inference from cross-sectional variation in climate, which recovers the long-run difference in economic outcomes for different individuals as well as any corresponding adaptation responses. Similarly, the long-difference approach also recovers the long-run impact of climate, but through time-series variations in long-run climate normals for the same individual. Our approach is most similar to the contemporaneous fixed-effect approach, yet there are still subtle differences between the two. The contemporaneous fixed-effect approach recovers the impact of weather shocks on contemporaneous economic outcomes, as well as any short-run adaptation responses that are contemporaneous or ex post to weather realizations. In contrast, our approach captures short-run ex ante adaption responses undertaken prior to weather realizations by using fixed-effect models with lagged dependent variables. In addition, our approach directly tests for the effect of weather fluctuations on resource-allocation decisions, while most contemporaneous fixed-effect studies focus on the combined effect of these decisions and actual weather and water availability, such as crop yield or revenue.

4 Results

4.1 Estimates for Ex Ante Production Decisions

Results from our main model are presented in Table 2. First, we discuss results for acreage decisions, presented in Column (1). We find statistically significant effects of GDD and EDD on cropland acreage. A one degree-day increase in GDD significantly increases planted acreage by 0.034% and 0.055% in the 2nd and 3rd-year lags. The 1st, 4th, and 5th-year lags are not significant. A one degree-day increase in EDD decreases acreage by 0.084%, 0.063%, and 0.153% in the 1st, 2nd and 3rd-year lags. It increases acreage by 0.095% for the 4th-year lag, and is statistically insignificant for the 5th year. We do not find a significant impact of past precipitation on planted acreage. For water availability variables, we find that shocks in water curtailments significantly decreases planted acreage in the 2nd year, but not significant for other lags. The direction of these effects are all as expected: greater GDD increases crop yields, which encourages expansion onto marginal lands for crop production and discourages fallow; greater EDD decreases crop yields, which discourages the use of marginal lands for crop production and encourages fallow; longer curtailments reduce expected supplemental irrigation water supply, leading to decreasing crop yields, and thus agricultural land uses.

To evaluate the magnitude of producer responses, we calculate the discrete effects of a one-standard-deviation (one-standard-deviation) increase in the independent variables, which suggests that responses to past shocks are economically sizeable. A one-standard-deviation increase in GDD increases acreage by 2.3%, 4.3%, and 7.0%, and a one-standard-deviation increase in EDD decreases acreage by 2.5%, 1.9%, and 4.6% in the 1st, 2nd, and 3rd year. The sizes of the effect are even larger when aggregated over multiple years. Columns (2) and (3) of Table 2 present two models using 3-year and 5-year moving averages as independent variables. A one-standard-deviation increase in GDD for three and five consecutive years will increase planted acreage by 14.6% and 14.0%.¹⁷ A one-standard-deviation increase in EDD for three and five consecutive years will decrease acreage by 8.8% and 9.0%.¹⁸ This suggests that farmers respond to past weather shocks by significantly changing acreage decisions in the short run. The magnitude of the responses is on par with estimates of the long-run acreage responses to temperature in the Eastern United States (Cui 2020). We find a one-standard-deviation increase in curtailment days for the water availability variables decreases planted acreage by 1.0% for the 2nd-year lag, and 1.2% over three years. The 5-year moving average estimate for curtailment is not significant.

Table 2 Parameter estimates of all lags, MA3, and MA5 models

Next, we discuss results on crop-allocation decisions. Our main model, presented in Column 4 of Table 2, suggests that most estimates for the three weather variables are statistically insignificant except for the 5th-year lag of EDD and the 2nd-year lag of precipitation. In contrast, we find strongly significant water availability effects on crop-allocation decisions, and the effects exhibit cyclical patterns. Producers react to a one-standard-deviation increase in curtailment days by planting less profitable crop mixes in the first and third year, which decreases their expected profit by $5.4/acre and $5.7/acre. In contrast, in the 2nd and 4th year, producers plant more profitable crop mixes when seeing an increase in curtailment days, of which a one-standard-deviation increase in curtailment leads to $8.8/acre and $7.5/acre. Estimates for the first four years are highly significant statistically, while the 5th year lag is insignificant.

However, when evaluated over multiple years, the cyclical responses to water availability shocks disappear. Columns (5) and (6) in Table 2 presents models where we use 3-year and 5-year moving averages (MA3 and MA5, respectively) of water shocks instead of year-specific shocks in the fixed-effect model. We find that both MA3 and MA5 of water curtailment do not have a statistically significant impact on crop allocation. This indicates that the short-run cyclical responses to past curtailment shocks would be concealed if either Ricardian regression or the long-difference approaches were adopted, as both approaches smooth yearly shocks into medium to long-run normals.

Finally, we turn to models on total expected profits, presented in Column (7) of Table 2. EDD has the most robust impact on total expected profit among the three variables: the 1st, 2nd, 3rd, and 5th-year lags of EDD are negative and statistically significant. GDD and precipitation both have positive effects on total expected profit. However, most of the estimates are statistically imprecise: only the 2nd lag of GDD and the 2nd and 3rd lags of precipitation are statistically significant, while other lags of GDD and precipitation are statistically insignificant. We do find statistically significant responses to all weather variables when evaluated using multi-year moving averages (presented in Column (8) and (9) of Table 2), and the direction of the responses are as expected. Increases in GDD and precipitation have positive effects on total expected profit, while increases in EDD have negative effects on total expected profit. The magnitudes of effects of moving average estimates are larger than estimates for individual-year estimates.

For the water curtailment variables, we again find evidence of cyclical responses in total expected profit to water availability shocks. Water curtailment days have negative and significant effects on total profit for the 2nd and 4th-year lags, and have positive and significant effects for the 1st and 3rd-year lags. A one-standard-deviation increase in curtailment days significantly decreases total expected profit by $3.76/acre in the first year, increases it by $5.00/acre in the second year, decreases it by $4.63/acre in the third year, and increases it by $10.70/acre in the fourth year. The fifth lag is not statistically significant. We again generate two aggregate measures for the multi-year impacts on total profit, and find that water availability has no significant impact over either the 3-year or the 5-year averages.

Overall, we find that agricultural producers significantly respond to recent shocks in natural endowments by changing ex ante production decisions in the short run. These responses generally differ between different types of endowments. A GDD shock has strong positive effect on cropland acreage, no significant effect on crop allocation, and weak positive effect on total expected profit. An EDD shock has a strong negative impact on cropland acreage, almost no effect on crop allocation, and a strong negative effect on total expected profit. Precipitation has a weak positive effect on crop allocation, and no effect on planted acreages. A water availability shock exhibits cyclical effects on crop-allocation decisions, but this effect is canceled out when evaluated over 3 or 5-years’ time. It also negatively affects planted acreage, though the effect is not as strong as the effects on crop allocation.

4.2 Expectation Formation Mechanisms

Our results suggest that agricultural producers deviate from using long-run normals in several ways. First, we find that ex ante adaptation behaviors significantly respond to previous shocks in endowments. Responses to previous shocks are persistent across different types of endowments, as well as across different adaptation mechanisms. This contradicts the hypothesis that farmers’ expectations are formed through Bayesian updating using a long history of realizations, and the hypothesis that the expectations are drawn from long-run normals. Second, we find that the magnitudes of adaptation responses vary widely between different lags. This further contradicts the long-run normals hypothesis, which predicts that each lagged realization enters the posterior expectation with equal weight.

Instead, we find evidence that, to varying degrees, support alternative heuristics for expectation formation. We find evidence for the availability heuristic, which predicts that more distant lags will not be considered as part of the expectation formation process. We find that a number of endowments have significant effects on ex ante decisions in the first three shocks, for example, water curtailment on crop allocation, GDD, EDD, and water curtailment on planted acreage, and GDD, EDD, precipitation, and water curtailment on total expected profit. Most of these effects die off in 5 years, with the only exception being the effect of EDD on crop allocation and total expected profits. To provide further evidence on potential recency biases, we estimate additional models by including one additional lag (lag 6) into our framework. The extended models suggest that none (0 out of 20) of the coefficient estimates for year 6 are statistically significant at the 10% level (see Appendix Table 10). This lends additional support to our claim on the availability heuristic, such that producers over-utilize more recent realizations when making production decisions.

We find limited evidence to support the hypothesis that that more recent shocks carry greater weight than more distant shocks, another prediction of the availability heuristic. Most effects do not die off gradually, and instead exhibit either cyclical patterns (e.g., the effect of water curtailment variables on all dependent variables) or die off suddenly at the fourth or fifth lag (e.g., the effect of GDD and EDD on acreage).

We find evidence consistent with reinforcement learning, which predicts that previous shocks enter expectations in a cyclical fashion. The cyclical pattern appears strongly in the water curtailment variables the crop allocation responses. In the first year, the farmer reacts to drought by adjusting the crop allocation towards less water-intensive (and lower profit) crops. This is likely an over-reaction since the long-run distribution of water curtailment has not changed significantly. In the second year, the farmer realizes that his/her strategy under-performs by planting too little to water-intensive crops, and over-correct his/her belief and plants more water-intensive crops. In the third year, the farmer under-performs again by planting too much of the water-intensive crop and again over-corrects in the opposite direction. As such, the reinforcement strategy causes the farmer to move back and forth in his/her expectations and the corresponding adjustments in crop mix. The cyclical pattern is also present for the acreage response to water curtailments, and the crop allocation response to GDD, though in both cases, the magnitudes of the response are estimated imprecisely.

Both of the alternative heuristics examined here capture more pronounced reactions to weather and water shocks over the short run, relative to the Bayesian expectation formation process. We argue that using medium or long-run differences to estimate the impact of climate change, such as is common in Ricardian regression or the long-difference method (Burke and Emerick 2016), may fail to capture this effect. This is problematic, especially if reinforcement learning dominates the learning process, as we have found for shocks in water curtailment: a cyclical pattern of water curtailment on crop allocation and overall profit exists, but these effects are entirely masked in the MA3 and MA5 models. This empirical observation is also documented in Buck et al. (2014), which suggests that farmland prices are only significantly affected by water delivery shocks by the first two orders of moving averages, but not by MA3 or higher orders.

4.3 Robustness Checks

4.3.1 Crop Share Models

To further shed light on the mechanism through which agricultural producers react to weather and water shocks, we present regression results explaining the shares of land allocated by crop categories. Specifically, we group our crops into three categories: water-intensive crops, drought-tolerant crops, and the perennial crop, following the agronomic literature and field knowledge of our study region. Water-intensive crops, including potatoes, sugarbeets, and corn, generally have higher expected profit (around $600/acre), but are more sensitive to heat and/or water stress (Yonts et al. 2003; King et al. 2006; FAO 2020). Drought-tolerant crops, including barley and wheat, have lower expected profit (around $100/acre), but are less sensitive to heat and/or water stress. All three crops in the water-intensive category must be produced with irrigation, while field crops like barley and wheat can potentially be produced without irrigation in our study region. We use the only perennial crop, alfalfa, as the baseline category because it lies in the middle of the two above categories in terms of both profitability and drought sensitivity. Alfalfa has a moderate expected profit ($250/acre), and is generally less sensitive to shorter periods of under-irrigation comparing to some of our drought-sensitive crops (Shewmaker et al. 2011; Obidiegwu et al. 2015). In addition, producers can adapt to water stress by targeted irrigation or harvesting at an earlier time (Liu et al. 2018). All these factors make alfalfa the default choice in our study region, with over half of the agricultural lands devoted to it. Overall, these categories capture broad differences between types of crops, which are of greatest importance, whereas the differences within each category, for example, between potato and sugarbeets, are less important because they are both of higher profit and drought-sensitive.

Results from these crop-share models are presented in Figs. 3 and 4, and are generally in line with our main models. In the case of water-intensive crops, we find evidence in support of the availability heuristic, such that all estimates for the last (5th) lag are statistically insignificant. Furthermore, producers’ responses to EDD and precipitation decrease over time, which correspond to one of the key features of the recency heuristic. The signs of the responses are all intuitive: increases in GDD and precipitation support planting of more water-intensive, higher profit crops, while an increase in EDD leads to less water-intensive planting choices.

Fig. 3

Marginal effects on shares of water intensive crops. Black dot denotes the estimated marginal effect, and grey ribbon denotes 90% confidence interval

Fig. 4

Marginal effects on shares of drought tolerant crops. Black dot denotes the estimated marginal effect, and grey ribbon denotes 90% confidence interval

In the case of drought-tolerant crops, we find mixed evidence regarding the availability heuristic. Producers decrease their shares of drought-tolerant crops when they see an increase in GDD. Combining with the model on water-intensive crops, this indicates that producers substitute drought-tolerant crops for the perennial crop when GDD increases. The magnitude of response towards GDD generally decreases over time, which corresponds to the recency hypothesis. On the other hand, crop share responses to EDD and precipitation do not support the availability heuristic, as in both cases, the magnitudes of the coefficients do not decrease or trend over zero over time. Increases in EDD leads to smaller shares of drought-tolerant crops in the 3rd and 4th year, and larger shares of those in the 5th year, which suggest that producers primarily adapt to EDD by substituting between drought-tolerant crops and alfalfa, while keeping the share of water-intensive crops unchanged. An increase in precipitation decrease shares of drought-tolerant crops in the 2nd and 5th year. This is also within our expectation as an increase in water availability shifts the production towards more water-intensive crops.

More interestingly, we find consistent evidence in support of the reinforcement heuristic. In both crop share models, producers exhibit cyclical adjustment patterns when facing a shock in water curtailment. Specifically, when encountering a water curtailment shock, producers increase the share of drought-tolerant crops and decrease the share of water-intensive crops in the 1st and 3rd years. They adjust in the opposite direction in the 2nd and 4th year by decreasing the share of drought-tolerant crops and increasing the share of water-intensive crops. The estimated coefficients are statistically significant and economically sizeable: a one-standard-deviation change (20.3 curtailment days) in water curtailment will lead to cyclical adjustments of up to 2% change in the share of water-intensive and drought-tolerant crops.

4.3.2 Placebo Tests

Since both crop allocation and acreage decisions are made prior to the actual realization, it is expected that the ex post information, i.e., shocks happening after the decisions, will have no effect on ex ante decisions. We check for this hypothesis by augmenting the main models with a series of ex post shocks, which serve as placebos. This includes realizations of GDD, EDD, precipitation, and water curtailment for the current and the immediate next years.

Results for the placebo tests are presented in Table 3. We find that only 3 out of 36 placebo variables are statistically significant: the effect of current year precipitation on crop allocation and on total expected profit, and the effect of GDD on planted acreage. All other placebo variables have statistically insignificant effects on ex ante production decisions. This suggests that our estimate on {textitex ante decisions are not likely to be driven by ex post realizations of weather and water availability.

Table 3 Parameter estimates for placebo tests

4.3.3 Additional Ex Ante Information

We also check if any additional ex ante information, observed by the econometrician and potentially also by farmers, influences our results. To introduce a source of bias, the ex ante information must have both cross-sectional and time-series variation, which rules out common climate and weather prediction models at the regional scale.¹⁹ We run robustness tests using one additional piece of information: reservoir surface water supply index (SWSI Reservoir), which measures the water storage level at the beginning of the growing season.²⁰ We have already included an additional variable on ex ante information, cumulative winter precipitation between November and February, in the main model. Though Both variables are documented to affect acreage decisions by the previous literature (Manning et al. 2017), our empirical results (presented in Table 7) suggest that our main models are robust to the addition of ex ante information, as the parameter estimates in the extended models are very close to the main models.

4.3.4 Stationarity and Predictability of Weather Shocks

Until now, we have assumed that weather and water availability shocks are largely unpredictable events. If the current shocks can actually be predicted using past shocks, then it could be beneficial for farmers to rely more heavily on past realizations when forming expectations. Here we check for two possibilities that may lead to a rational expectation for over-reliance on recent events.

First, we check for whether included weather variables are stationary over time. If there exists time-dependence (which may or may not be caused by climate change), then it could be rational for producers to rely on some sort of alternative learning mechanisms other than the long-run normals. We check this possibility by performing the Im-Pesaran-Shin (IPS) test for unit roots in panel data models (Im et al. 2003), recommended for cases with fixed T and large N (Baltagi Badi 2013). To mimic our main fixed-effect models, we perform the test with demeaned variables but allow for time trends, and present these results in Table 8. We find that for all weather variables (GDD, EDD, and prec) as well as different forms of water curtailment variables, the IPS test strongly rejects the null hypothesis that the panel has unit-roots. This provides suggestive evidence that the weather variables are stationary over our study period.

Second, we specifically check for the predictability of water curtailment shocks, noting that unlike climate variables, water availability is not only governed by stochastic natural processes, but additionally by inter-year storage management that could cause water availability to be serially correlated from year to year. We check this possibility using a leave-one-out validation strategy. For each year from 2007 to 2016, we train a prediction model using data for the past 15 years, leaving out the year in question. The prediction model is constructed using an elastic net algorithm with 10-fold cross-validation (Hastie et al. 2009). We then use the post-elastic-net prediction model to generate predictions for the water curtailment shock, and compare that with the actual shock for the year we have left out. If the predictive model is able to explain some variations for the current shock, then the unpredictability assumption is violated.

We present results from the predictive models in Table 4. Though the models perform well on in-sample predictions, they perform poorly for the omitted year. All prediction models increase the variations for the test sample rather than decreasing it, indicating that these models have no predictive power over future water curtailments. Thus, we rule out the possibility that previous shocks in water curtailment can be used to predict the shock in the upcoming growing season.

Table 4 Dynamic panel estimates

4.3.5 Whether Crop Rotation Drives Cyclical Coefficients

Our main estimation framework suggests that there exist cyclical patterns in the responses to past shocks, which is consistent with reinforcement learning. An alternative explanation for this pattern might be that farmers adjust crop allocation cyclically because of crop rotation rather than responding to weather shocks. Econometrically, this means there is likely negative serial correlation in crop allocation if that is true.

We check for this possibility by estimating an Arellano and Bond (1991)’s dynamic panel estimator. The Arellano–Bond estimator directly includes lagged dependent variables on the right-hand side, and uses a generalized method of moments (GMM) framework to estimate a first-differenced model. Arellano–Bond’s z-test suggests that including two lags of the dependent variable is just sufficient to wipe out serial correlation in the first-differenced error term, and thus we focus our interpretation on the model with two lags, presented in Column (3) of Table 5.

Table 5 Predictive model of TND.Season.100%

We find that the first lag of crop allocation has a negative and significant effect of $-0.116$, while the second lag has a positive and significant effect of 0.104. This suggests that, on average, about 10% of land each year is constrained in crop types because of crop rotations. However, we also find that although the parameter estimates for water curtailment variables are slightly different, the cyclical pattern largely remains. Estimates of water curtailment variables are positive and significant for the 2nd and 4th-year lags. Estimates for the 1st and 3rd-year lags are still negative, but quantitatively smaller and statistically insignificant. Nevertheless, the dynamic panel model presented here still exhibits strong cyclical patterns in the water curtailment variables. As such, we conclude that although there exist crop rotation effects, this explanation is not likely the main driver of the cyclical responses to water shocks.

4.3.6 Choice of Aggregation Methods for the Water Curtailment Variable

In the main specification, we choose to present one specific way to aggregate daily curtailment records to the growing season: the total number of days during summer months that at least 50% of the water is curtailed (TND.Summer.50%).²¹ However, unlike the well-documented non-linear effects of temperature on agricultural production, there is little guidance in the previous literature, theoretically or empirically, documenting which aggregation should be used in the case of irrigation water availability. As such, we conduct robustness checks by running the empirical analysis with different aggregation methods. Results of these alternative specifications are presented in Table 9.

We find that using different aggregation methods leads to similar results qualitatively, although there are subtle differences between different aggregation methods. In the planted acreage model, all models indicate negative effects of curtailment on planted acreage, but the timing of those effects are different. Two other variables, TND.Season.100% and Streak.season.100%, have negative and statistically significant impacts on planted acreage in the farther lags. This is different from the response to the main variable, TND.Summer.50%, which shows a significant and negative effect in the 2nd lag. In the crop allocation model, we find strong cyclical effects in all water curtailment variables. Similar to the main model using TND.Summer.50%, the other three models also show negative estimates for the 1st and 3rd lags, and positive estimates for the 2nd and 4th lag, albeit some estimates are not statistically significant. In the total expected profit model, patterns are similar to those in the crop allocation models, such that all four aggregation methods show cyclical patterns, with the 1st and the 3rd lags negative, and the 2nd and the 4th lags positive. In the TND.season.100% model, the 5th lag is also negative and statistically significant, indicating that the cyclical pattern might span further.

Overall, these results indicate that agricultural producers are more responsive to the total days of curtailments rather than curtailment streaks, and to summer months rather than the entire growing season. On the other hand, while by using the chosen aggregation method we are able to capture most of the producer responses to water curtailment, our chosen model will inevitably omit some of the responsive mechanisms not incorporated in our aggregation method. As such, our main specification represents a lower bound of the actual responses to water shortages.

5 Conclusion

A weather shock is the realization of climate at a certain point in time, but the economic impacts of weather fluctuations have the potential to affect agricultural production for multiple growing seasons in the future. In this study, we show that past weather fluctuations can affect future agricultural decision making through the mechanism of expectation formation. Using a fixed-effect approach, we find significant behavioral responses in acreage and crop-allocation decisions to past shocks in natural endowments, including temperature, precipitation, and water availability. This suggests that instead of using the long-run normals, agricultural producers use alternative learning mechanisms that rely more heavily on recent weather realizations. This over-weighting of recent realizations can result in economic losses if farmers over-react to recent signals by making acreage and crop-allocation decisions that are sub-optimal relative to those made under expectations based on a longer and more representative history of weather observations.

There are several policy implications that follow from this study. First, our results stress the need to incorporate short-run behavioral responses to the assessment of climate change impacts. Economic decisions are made by agents who are prone to various cognitive biases when evaluating future uncertainties. Assuming textbook rational expectations from economic agents overlooks an important behavioral response to weather fluctuations. Second, our study shows that the impact of climate change is caused not only by shifts in the mean, but also by shifts in climate variability. This is in similar essence with Schlenker (2006), who postulated economic losses stemming from the same ex ante decision problem facing weather variability, such that even under the correct set of climate expectations, ex ante crop choice decisions will still be sub-optimal when evaluated ex post because of imperfect foresight. The economic losses we document here are parallel to that in Schlenker (2006)’s, as in our case, the losses come not from the weather uncertainty itself, but from the learning process that agents use to infer weather expectations. As the magnitude of weather fluctuations becomes larger, so do shifts in the subjective expectations over future climate, and thus the resulting economic losses from short-run behavioral responses. Third, our study provides an example of the economic value of information regarding future uncertainty. Reliable forecasts of future climate and water availability, which may in the form of long-run climate normals, spring snowpack forecasts, monsoon or El Niño patterns, as well as extension programs that focus on the proper use of these sets of information, reduce biases when predicting future weather and water realizations. As a result, access to these types of information can alleviate the economic losses induced by cognitive biases from the expectation formation process.

Our study has the potential to provide decision-support to agricultural producers and policymakers. Our results will be directly applicable to places under similar institutional and climatic settings, for example, the Yakima River Basin, the Central Valley of California, or the Murray-Darling Basin. More broadly, our insights on producers’ behavioral response to weather fluctuation can apply to places around the world where heat and water stresses threaten agricultural production, especially in places where irrigation serves as a crucial channel for agriculture to adapt to climate change. Going beyond agriculture, our study can also be used as a foundation to consider other types of ex ante adaptation decisions that require forward-looking inference regarding climate or other types of uncertainty. For example, one could consider the effect of a recent heatwave on the adoption of irrigation, farmland value, or air-conditioner purchases. All of these behaviors require agents to form expectations over future climate, which are subject to the influence of recent shocks. In a broader sense, this study fits into the larger literature on learning and decision-making under uncertainty. Although we study a particular set of uncertainties arising from stochastic climatic and hydrological processes, our study could shed light on other types of uncertainty, for example, flood risk (Atreya et al. 2013), financial markets (Malmendier and Nagel 2011), and energy markets (Fell and Kaffine 2018).

Our study is limited in the sense that we only show behavioral changes due to weather fluctuation, but we do not estimate the associated economic losses. Evaluating the latter question requires field level crop-specific yield data, which we do not have at this time. Future research may quantify these welfare effects through the use of new remote sensing methods to generate data on field-level crop yields (Donaldson and Storeygard 2016; Chance et al. 2017).

Appendix: Additional Figures and Tables

See Fig. 5 and Tables 6, 7, 8, 9 and 10.

Fig. 5

Schematic illustration of relative positions of Snake River and tributary reaches in the Upper Snake River Basin (from Olenichak 2015)

Table 6 Sample water accouting record in WD1

Table 7 Parameter estimates with ex ante information

Table 8 Im-Pesaran-Shin test for unit roots in panel data

Table 9 Parameter estimates with different aggregation methods for water curtailment variables

Table 10 Parameter estimates with extended lags