## Abstract

The goal of this paper is to analyze the impacts of climatic variation around current normals on crop yields and explore corresponding adaptation effects in Arizona, using a unique panel data. The empirical results suggest that both fertilizer use and irrigation are important adaptations to climate change in crop production. Fertilizer use has a positive impact on crop yields as expected. When accounting for irrigation and its interaction with temperature, a moderate temperature increase tends to be beneficial to both cotton and hay yields. The empirical model in this paper features with two methodological innovations, identifying the effects of temperature change conditional on adaptations and incorporating potential spatial spillover effects among input use.

- adaptation
- climate change
- crop yield
- fertilizer use
- irrigation
- spatial analysis

## INTRODUCTION

Climate has been the primary determinant of agricultural productivity in human history. The concern for potential negative consequences of climate change has been rising in recent decades, and many believe that the agricultural sector will suffer most given its dependence on the climate. The importance of US agriculture in the global food supply system further suggests that the impacts on US agricultural production could have broad implications for food and nutrition supply worldwide (Schmidhuber & Tubiello 2007). This paper focuses on the impacts of climate change on crop yields, while taking into account the agricultural sector's adaptation efforts in responding to temperature and precipitation change. A key result is that when accounting for irrigation and interactions between irrigation and temperature, a moderate increase in temperature is found to be beneficial to both cotton and hay yields, which is different from most of the existing findings. One implication of the results is that agriculture related climate change policy (e.g. American Clean Energy and Security Act of 2009) should support adaptations through either direct input subsidy or infrastructure investment. For example, the carbon tax collected from the agricultural sector can be used to subsidize irrigation technology improvement. The results from this paper can shed light on policy design of such types.

The paper introduces two methodological innovations, identifying the effect of temperature change conditional on irrigation and accounting for the spatial spillover effects among input use. The role of adaptation has been well identified in the literature (e.g. Mendelsohn & Dinar 2003; Schlenker *et al.* 2005). The relationship between crop yield and temperature is commonly captured through a quadratic function form. In a world without adaptations, the yield–temperature relationship should have larger curvature. In the real world where adaptations mediate climate effects, a yield response with smaller curvature is expected given that adaptations intend to prevent dramatic yield decline. A regression analysis that tries to identify climate change impacts but without accounting for adaptations could have the adaptation effects picked up through the estimated climate effects. Therefore, this paper emphasizes the importance of identifying the effect of climate change conditional on adaptations.

Taking into account the spatial effects in agricultural assessment has gained substantial attention in recent literature. Anselin *et al.* (2004) investigated the crop yield response to the application of nitrogen using spatial econometric models. Their results suggest that the model specification is important when spatial interaction exists among sites. The spatial models consistently indicate profitability of the nitrogen applications, whereas the non-spatial models do not. Schlenker *et al.* (2006) point out that failing to account for the spatial correlation of the error terms can lead to overestimating -value and therefore the wrong inference on the economic impacts of global warming. There are at least two motivations for modeling the spatial effects, as follows. (1) Spatial spillover in production technology and constrained interaction (see Manski (2000) for a discussion on constrained interaction) in resources allocation (e.g. as a result of competition for limited resources), which has important implications for adaptations. Failing to account for this type of spatial effects can lead to biased estimates on the effects of adaptations. (2) Spatial correlation in unobserved effects (e.g. due to policy and other external shocks). Ignorance or wrong assumptions on this type of spatial effects can lead to incorrect standard error estimates and misleading inference results.

This study concerns two major crops in Arizona, hay and upland cotton. They generated about 13% of the state's total farm cash receipts in 2008 and give a good representation of the state's crop production. In terms of field crop value of production, hay production represents 55% out of a total of $801.4 million, and upland cotton represents 14% (Arizona Annual Statistics Bulletin 2008). The particular area holds our interest in two aspects: (1) the agricultural production in the region (featured with arid land) is less dependent on precipitation, which allows us to focus on the impacts of temperature change and its interaction with adaptations; (2) Arizona (especially the south, the major agricultural region of the state) belongs to a warmer, low latitude area of the world agricultural production. According to the literature (e.g. Rosenzweig & Iglesias 1994; Adams *et al.* 1995), areas like these will likely see declines in crop yields even with a CO_{2} fertilization effect incorporated in the context of global warming. It implies that in regions like Arizona temperature increase will result in loss of comparative advantage in crop production unless sufficient adaptation is made. This gives a strong motivation for adaptations in crop production. The main research question of this paper is, what are the impacts of temperature and precipitation change on crop yields in Arizona, and how the consideration of adaptations changes the results.

The literature on the physical and economic impacts of climate change in the agricultural sector has grown substantially since the 1990s. Mendelsohn *et al.* (1994) found that higher temperatures tend to reduce farm values while higher precipitation does the opposite, and they pointed out that the impacts of global warming on agriculture may have been overestimated. Using crop simulation models, Riha *et al.* (1996) found that the average predicted yield decreases with increasing temperature variability where growing-season temperatures are below the optimum specified in the crop model for photosynthesis or biomass accumulation. The influence of changed precipitation variability on yield can be mediated by the nature of the soil. Adams *et al.* (1998) presented a review on the early literature of physical effects of climatic change on agriculture and economic consequences.

Recently, Schlenker *et al.* (2005) found that the economic effects of climate change on agriculture need to be assessed differently in dryland and irrigated areas, and the role of irrigation has to be incorporated into analysis to avoid potential misspecification. Deschênes & Greenstone (2007) predicted that climate change will increase annual profits from US agricultural land by $1.3 billion (in 2002$) or 4% based on the long-run climate change predictions from the Hadley 2 Model. Their analysis also indicates that the predicted increases in temperature and precipitation will have virtually no effect on yields among the most important crops, and previous results in the literature based on a hedonic approach may be unreliable due to its sensitivity to the choice of variables. Ortiz-Bobea & Just's (2013) empirical studies show that plausible adaptation strategies (e.g. change in planting date) with little extra cost could significantly reduce predicted corn yield loss due to climate change in eight rainfed US states.

In the current literature, the region-specific relationship between crop yield and climate variability is not well understood, though the overall relationship between crop yield and long term climate change has been well studied. Among a few intra-regional studies, Deschênes & Kolstad (2011) evaluate the impacts of climate change in California and find a negative effect on aggregate agricultural profits by the end of the century. However, Deschênes & Kolstad's (2011) results are conditional on the lack of statistical precision and other assumptions as well, which suggests that further data collection and alternative estimation procedures are necessary. Reidsma *et al.* (2009) use data from Mediterranean regions and suggest that farm characteristics influencing management and adaptation should be incorporated into analysis given that they alleviate the potential damage of climate change. Roberts *et al.* (2013) investigate the role of vapor pressure deficit (VPD) (found being strongly associated with degree days above 29 °C) and find it significantly improves the corn yield predictions for Illinois. However, all three intra-regional studies need further exploration on the role of adaptations and their effects in responding to climate change in crop production.

The paper is organized as follows. The next section describes the study area, followed by the section which reports model, estimation procedure, and data collection. Results and discussion are presented in the next section followed by the conclusions.

## STUDY AREA

The study area of this paper is Arizona. It is a region where potential climate change impacts have raised great concern regarding future agricultural development and sustainability, and adaptation is likely to play an important role in meeting the goal of sustainable development. The top three agricultural commodities in Arizona are lettuce, hay, and cotton. They represent 10.8%, 7.5%, and 5.4% of the state's total farm cash receipts in 2008, respectively. This study focuses on two main field crops in the state: cotton (upland) and hay (all).

Given that the two field crops are substantially different, the study area of each crop is not the same set of counties. There are 15 counties in the state as of the 2007 US Census of Agriculture (Figure 1). During the time period 1969–2007, almost all of the counties were geographically stable except that La Paz County was established in 1983 after voters approved separating the northern portion of Yuma County. To avoid inconsistency issue, La Paz County and Yuma County are combined into one county for years after 1983. All of the measures are weighted (by the acres of given crop planted in each year) average of original measures from two counties. Counties in northern Arizona and other small counties in the south (e.g. Santa Cruz County) only account for a very small portion of the state receipts, and statistics data are not continuously available for cotton in some of these counties. They are excluded to avoid potential measurement errors. The empirical study includes eight counties (Cochise, Graham, Greenlee, Maricopa, Mohave, Pima, Pinal, Yuma) in the cotton yield model, which accounts for 93% of the upland cotton planted in the state in 2007. In the hay yield model, all 14 counties (Yuma and La Paz are combined) are included.

The impacts of climate change vary not only by crop, but also substantially by season. For example, Mendelsohn & Dinar (2003) find that higher July temperatures tend to reduce farmland values while April and October temperature increases do the opposite. Given that Arizona has a relatively longer growing season than most parts of the country, this study defines the growing season as the 8-month period from March to October. The entire growing season is further divided into three sub-seasons: March to April, May to August, and September to October. For cotton production, these sub-seasons represent planting, growing, and harvesting season, respectively. In hay production, the seasonality is different. For example, the cutting period of alfalfa hay is 28–30 days, and there are about nine annual cuttings in most areas of Arizona. So the three sub-seasons basically represent the period of increasing yield, stable yield, and decreasing yield, respectively.

## METHOD

Using panel data to assess the impacts of climate change on agriculture has been increasingly adopted in recent literature (Deschênes & Greenstone 2007; Schlenker & Roberts 2009; Baylis *et al.* 2011; Massetti & Mendelsohn 2011). The temporal variation can capture the long-term changes such as climate change and production technology improvements, while the cross-sectional variation can capture farmers’ adaptations to climate change and other exogenous spatial variations. In this paper, spatial panel data models are used to account for the potential spatial interactions among adaptation and unobservable effects. The spatial econometric models represent a wide range of spatial models depending on how the spatial weighting scheme is specified or estimated among endogenous variables, exogenous variables, and unobserved components, respectively. Elhorst (2010a) provides a review on the relationships among different spatial dependence models for cross-section data, which also applies to panel data.

In spatial panel data models, estimation becomes more complicated than in cross-sectional case due to richer error structure (Kapoor *et al.* 2007; Anselin *et al.* 2008; Lee & Yu 2010; Elhorst 2010b). Depending on the context of the problem being studied, three types of spatial effects can explain why observed behavior or outcome associated with a specific location may be dependent on observations at other locations (Manski 1993). Manski (1993) proposes a general model of spatial interaction effects as follows:
1
2where *Y* denotes a vector of one observation on the dependent variable, is a vector of ones associated with the intercept parameter , *X* denotes a matrix of explanatory variables, with the associated parameters and to be estimated. is a vector of disturbance terms which are usually assumed to be with zero mean and variance . , , and denote the endogenous interaction among the dependent variables, the exogenous interaction among the independent variables, and the spatial autocorrelation effects among error components, respectively. , , and represent the spatial weighting matrices of the spatial units in the sample. is defined as the spatial autoregressive parameter, the spatial autocorrelation coefficient. The model in Equations (1) and (2) can fit with either cross-sectional data or panel data. Note that in the case of panel data models, the error components act like fixed effects which absorb the constant terms . Therefore, given a sample of panel data as in this study, allowing for fixed effects, the model in Equations (1) and (2) can be written as:
3

Now *Y* denotes a vector of one observation on the dependent variable for all cross-section units and being stacked over all time periods . Similarly, becomes a vector of disturbance terms. and are all vectors of parameters associated with the matrix of explanatory variables. denotes the identity matrix of *T* dimensions, , , and all weighting matrices to be specified or estimated. , , , and are all parameters to be estimated. If , then we have a spatial Durbin (Durbin error) model. If instead and , then the model in Equation (3) reduces to classical spatial lag (error) model.

In this study, the dependent variable is crop yield which is a physical measure of outcomes from plant processes. It is clear that these outcomes are conditional on location specifics, but it is unlikely there exist direct interactions among crop yields across different locations. Therefore, we can set . The model in Equation (3) reduces to a spatial Durbin error model: 4

Note that in Equation (4), the exogenous variables matrix *X* in can be different from the *X* in represents the direct exogenous effects from the location where *Y* is observed, while represents the indirect exogenous effects (e.g. spillover) from other neighboring locations through spatial interactions. If an exogenous variable *x* in does not have indirect effects on other regions, then the variable does not show up in . To distinguish between direct and indirect exogenous effects model in Equation (4) can be re-written as:
5where *Z* replaces the *X* in , and *Z* is not necessarily identical to *X*. To estimate the model in Equation (5), we need to determine the spatial weighting matrices and . Specification of spatial weighting matrix depends on the observed spatial pattern and prior knowledge about the sources of spatial interactions in the sample (Pinkse & Slade 2010; Corrado & Fingleton 2012). In the context of crop yields and climate change, there are two major sources of spatial interactions: (1) policies and external shocks; (2) the spillover effects and constraint interactions of input use. The spatial interaction from the first source is usually unobservable and difficult to measure, which can be captured through spatial autocorrelation (i.e. ). Though the basic relationship between crop yields and climatic conditions is independent of policy intervention, as pointed out by Schlenker *et al.* (2006), the unobserved policy impact in agriculture can still lead to strong spatial autocorrelation in regression analysis. The spatial interaction from the second source can be captured via if the exogenous variables matrix *Z* consists of corresponding measures on input use (adaptation channels). Given specifications on and , Equation (5) can be written as:
6where and . The model in Equation (6) becomes a standard spatial error model with panel data which can be estimated by maximum likelihood estimation (MLE). The estimates of may be biased if not accounting for spatial effects properly. The potential bias can be illustrated by deriving the marginal effect of *X* on *Y* in Equation (5). As noted above, *X* and *Z* may share some common variables. Let be a variable in both *X* and *Z*, for a given time period *t*,
7
8where *i* and *k* are the cross-section indices and *j* is the index for independent variables. and are assumed to be time invariant, and represents the row of the matrix. In non-spatial models, the marginal effect of on in Equation (8) is simply the coefficient . In spatial models as in Equations (5) and (6), however, there is an extra term which represents the indirect marginal effect through spatial spillovers. Given the existence of spatial effects, it is clear that spatial models have the advantage of correcting the estimation bias over non-spatial models. The key parameters to estimate in model (6) are: coefficients , spatial autocorrelation coefficient , and parameters in the error structure. The spatial weighting matrix of exogenous variables will be specified based on the planted acreage of a given crop in each county, which basically takes into account the importance of the given crop in each county within the state. The spatial weighting matrix of unobserved effects will be estimated parametrically. , , and parameters in the error structure will be estimated by following the generalized method of moments (GMM) and feasible GLS (FGLS) procedures proposed in Kapoor *et al.* (2007).

### Spatial weighting matrix

In general, the spatial weighting matrix should be a non-negative matrix of known constants (Lee 2004). Since no spatial unit can be considered as its own neighbor, the diagonal elements of *W* are zero (i.e. ). *W* should also satisfy one of the following two conditions: (1) the row and column sums of the matrices, and without row normalizing (standardizing) should be uniformly bounded in absolute value as *N* goes to infinity (Kelejian & Prucha 1999; Kapoor *et al.* 2007); (2) the row and column sums of without row normalizing should not diverge to infinity at a rate equal to or faster than the rate of *N* (Lee 2004). In practice, the condition is satisfied since is usually sparse (i.e. each spatial unit has only a limited number of neighbors) or its elements decline with a distance measure that increases sufficiently fast as the sample size increases.

This paper chooses based on the county level acreage of the given crop planted. That is, we assume that the adaptation to climate change in a county with larger acreage of the given crop planted has more influence on other counties’ practice. Note that physical distance is not considered in specifying to avoid potential measurement errors due to the large county size in the state. Before row normalizing, for county the element of has a value equal to the planted acres of the given crop in county *j*. After row normalizing, for the *i*th row of we have .

For in the error component, we do not have strong economic or agronomic knowledge to specify its structure *a priori*. Instead, it is estimated parametrically using a feasible approach. The idea is to use the residuals from a first-stage regression to estimate . The method consists of following steps: (1) use the panel data with all *N* counties and a subset of time series, say time periods, and run a fixed effects panel data model: ; (2) collect the predicted fixed effects from step (1), which gives a vector; (3) fix and choose all possible subsets of time series, repeat steps (1) and (2), which should give a total number of vectors of predicted fixed effects; (4) rearrange the vectors of predicted fixed effects into a matrix with rows corresponding to all combinations and columns corresponding to all *N* counties; (5) compute the correlation coefficients among all columns of the predicted fixed effects matrix from step (4) and take absolute values, which gives all of the elements of associated with any two counties before row normalizing except the diagonal elements. The diagonal elements of are set to zero according to the regularity conditions. The difference between *T* and should be kept small to avoid any significant difference between the behavior of the original time series and the reduced time series. In this study, since we only have nine time periods, is set to 1.

### Coefficient estimation

In small samples, MLE tends to produce biased estimates and incorrect standard errors. The idea of Kapoor *et al.* (2007) method is to use a two-stage procedure: (1) estimate all parameters except the coefficients using GMM while allowing for disturbance terms being correlated over time; (2) estimate the coefficients using FGLS with all parameters estimated in the first stage substituted in. There are two advantages of Kapoor *et al.* (2007) method over MLE. First and empirically, Kapoor *et al.* (2007) method is less demanding in computation than MLE, especially in the case of large scale problems (i.e. large number of parameters to estimate). Another advantage is that Kapoor *et al.* (2007) method efficiently uses structural information in the spatial autocorrelation process with no need for explicit assumptions on the distribution function form of the disturbance terms.

Following Kapoor *et al.* (2007), we assume the following error structure for vector :
9where is an vector of ones and represents the vector of cross-section specific error components, which is different from *u* in the spatial autocorrelation process specified in Equation (2). contains error components that vary over both the cross-sectional units and time periods. In scalar notation, Equation (9) can be written as:
10

The disturbance terms are autocorrelated over time, but not spatially correlated across units (see assumptions in Equations (12) and (13) below). Combining Equations (6) and (9) we have: 11

To estimate Equation (11), the following assumptions are made on : 12 13where and are assumed to be independent processes with mean zero and variance , , respectively. Let be a matrix of ones, then the variance-covariance matrix of is: 14

with some additional assumptions (Kapoor *et al.* 2007) the GMM estimators of , and are derived based on six moment conditions. The estimators take the following form (interesting readers are referred to Kapoor *et al.* (2007) for derivation and consistency proof):
15

Let be a consistent estimator (e.g. OLS estimator under above assumptions) of , and can be defined as: , . ( matrix) and ( vector) are given based on sample moment conditions, and the elements of and are observed. Note that the estimator in Equation (15) can be computed using nonlinear regression methods (Kapoor *et al.* 2007). Given the , and estimated in Equation (15), the corresponding FGLS estimator of , say , can be obtained by replacing , and with the estimated values:
16

The consistency and asymptotic normality of the FGLS estimator are established in Kapoor *et al.* (2007). The estimation procedure in Equations (15) and (16) can be iterated by using from previous iteration as the starting consistent estimates for the next iteration until it converges. In this paper, the estimates are obtained through 10 iterations.

### Data collection

The data used to estimate the proposed spatial panel data model are assembled from three different sources. The crop yields data and county level farm operations data mainly come from the National Agricultural Statistics Service (NASS, USDA). The hay yield data for Yuma County before 1983 come from the Arizona Annual Statistics Bulletin of corresponding years. The farm operations data are extracted from the US Census of Agriculture from 1969 to 2007. The climatic data are derived from the monthly summaries of the GHCN-Daily weather station data from the National Climatic Data Center of NOAA. The third part of the data is the irrigation water use from 1985 to 2005, which comes from the US Geological Survey (USGS). The irrigation water use data were also reported in the 1969 and 1974 US Census of Agriculture. Irrigation water use data from the USGS and US Census of Agriculture are combined to derive all irrigation related measures. The definition and descriptive statistics of variables are summarized in Table 1.

The US Census of Agriculture reports economic and demographic measures on farm operations at county aggregate level. This study is interested in the measures capturing productivity change and farmers’ potential adaptation channels in the agricultural sector. In this study capital to labor ratio is used as an approximate measure for productivity level. The labor input is measured by per acre expense on hired labor and contract labor, and the capital input is measured by per acre value of the machinery and equipment on place, both at county level.

Using USGS data and US Census of Agriculture data, a measure for average per acre irrigation water use is derived. One issue with the USGS data is that the survey year does not match with the US Census of Agriculture survey year. Following Mendelsohn & Dinar (2003), we believe the 2 year gap between two data will not bias the results given that we focus on the long run relationship between crop yields and climate change rather than annual effects. Note that the irrigation water use in 1978 and 1982 were not reported in either sources, which is filled in through a linear interpolation and extrapolation based on the total number of days with maximum temperature greater than or equal to 90.0 °F (32.22 °C) in growing seasons (March–October). Another adaptation variable per acre expense on fertilizers is measured at county level as well. Irrigation water use and fertilizer use variables comprise the matrix *Z* in model (5).

Based on the agronomic facts, all climatic measures are computed with data from the growing season only. The measures that sum over each sub-season are: cooling degree days using a 65 °F (18.3 °C) base (CLDD); number of days with maximum temperature greater than or equal 90.0 °F (32.22 °C) (DT90); total precipitation amount (TPCP). The measures that average over months within each sub-season are: monthly mean minimum temperature (MMNT, the mean minimum temperature is only used in the cotton yield model); monthly mean maximum temperature (MMXT); monthly mean temperature (MNTM). This study uses three alternative temperature measures (CLDD, DT90, MMXT) other than mean temperature to capture the impacts of temperature change on crop yields. If the temperature change does not involve distributional changes in the temperature range (i.e. only causes the range to shift), then using extreme temperature measures (e.g. CLDD, DT90, MMXT) is equivalent to using mean temperature measures (e.g. MNTM). However, if the temperature change does involve distributional changes of the temperature range, then extreme temperature measures are better variables to predict the impacts of temperature change because the mean temperature may not change when the temperature range has already expanded in both extremes (minimum and maximum) significantly.

## RESULTS AND DISCUSSION

### Estimation results

Table 2 reports the results from non-spatial fixed effects panel data models with mean temperatures. Fertilizer use and irrigation variables tend to have the expected positive signs, but the effects are not significantly different from zero except irrigation on hay yield at 10% confidence level. The planting season and growing season mean temperatures do not explain the yield variation well, which is consistent with the consideration with using alternative temperature measures. Table 3 presents the estimation results from fixed effects panel data models with alternative temperature measures. The fixed effects models are chosen based on the Hausman Tests. Three general observations come from the results, as follows. (1) There is virtually no significant productivity change in crop production during the study period. This is further confirmed with spatial models. (2) Among three alternative temperature measures, mean maximum temperature (MMXT) has better explanatory power to the crop yield variation. (3) Cotton yield is more sensitive to the planting season precipitation, and hay yield is sensitive to temperature changes across all seasons.

Table 4 reports GMM–FGLS estimation results of spatial models with alternative temperature measures. Note that following the comments received from extension specialists in Arizona, MMNT is introduced into the cotton yield model to see if cotton yield is vulnerable to extreme low temperature. The coefficient estimates of MMNT, however, are not statistically significant at 10% level. This suggests that extreme low temperatures through the growing season do not significantly affect cotton yield in the study region. Similar to the results with non-spatial panel data models, a general observation from the GMM–FGLS results is that models with mean maximum temperature (MMXT) have better explanatory power.

The estimate of the spatial autocorrelation parameter is expected to be positive in the models, because the spatially correlated unobserved effects (e.g. policy) are expected to cause simultaneous change of crop yields statewide. However, the estimates of spatial autocorrelation parameter have a negative sign in the models with MMXT, which is not consistent with other models. One possible reason for this unusual result is the multicollinearity among MMXT measures from three different seasons (with correlation coefficients larger than 0.9). To solve the issue, three different models are estimated with three MMXT measures separately. The results are reported in Table 5. In the new results, the estimates of are as expected and consistent with other models. The discussion regarding specific effects of adaptations and climate change is given based on the estimates in Table 5.

The specification of empirical models in this paper involves interaction terms, quadratic terms, and spatial interaction terms. The coefficient estimates do not necessarily reflect the true marginal effects. To interpret the effects of marginal changes, it is necessary to compute marginal effects and corresponding standard errors. Table 6 reports the marginal effects computed using the delta method based on the crop yields in 2007. The left and right panels show the marginal effects for models with logarithm of cotton yield and hay yield as dependent variable, respectively. In each panel, three different columns represent models with MMXT measures for different seasons.

### Extreme temperature

One of the main concerns regarding climate change is global warming and the damage to crop production. After partially accounting for adaptations (only fertilization and irrigation), however, empirical results show that a moderate increase (1 °C) in mean maximum temperature is beneficial to crop yields holding irrigation at the mean level. For cotton, given a 1 °C temperature increase there will be a slight increase (10–20 lbs/acre, or 5–10 kg/acre) in yield, but it is not significantly different from zero.

For hay, the adaptation effect through irrigation is more noteworthy. Given a moderate increase (1 °C) in mean maximum temperature in the early season, there will be an 0.1542 ton/acre increase in yield. The yield increase will be 0.1152 ton/acre and 0.1324 ton/acre for the same temperature increase in the summer and autumn, respectively. Notice that the benefit from warming is relatively higher in non-summer seasons, and one possible explanation is that high temperature during the summer growing season can cause over-flowering which reduces both the quality and quantity of hay. Warmer spring and autumn seasons can extend the growing period of plants, therefore hay yield is increased due to potentially more cutting cycles.

### Precipitation

Precipitation change is usually less of a concern compared to temperature change. However, precipitation change does not simply mean change of water supply from rainfall. It also implies change of precipitation pattern, which can be very harmful to certain crops. In the autumn, for example, the drying rate of hay becomes lower with declining temperature. When the drying conditions get poor (e.g. due to rainfall) the respiration period of plants after cutting is extended, which leads to losses in both quality and dry matter. Increasing amounts of rainfall can also cause quantity loss by leaching and knocking off the leaves. Fonnesbeck *et al.* (1986) found that substantial quantities of the available carbohydrate (18.8%) in hay are lost by 20 mm of rainfall. This amounts to a 5% loss of the yield given 28% of the dry matter is available carbohydrate. This paper finds that a 10 mm increase in precipitation in the autumn can lead to a loss up to 0.1 ton/acre in hay yield. For cotton, the yield loss due to the same precipitation change can be much more severe. A 10 mm increase in precipitation in either the spring or the autumn can cause a loss up to 13.6 kg/acre in cotton yield, which is significantly different from zero. In general, the relationship between crop yields and precipitation is complicated and often being confounded with other factors. Therefore interpretation of results should always consider the particular crop's characteristics.

Another interesting result to note is that, during the summer growing season, precipitation change has no significant impacts on the yields of either crops. A possible explanation is that most of the crops in Arizona receive a water supply from irrigation during the summer. In other words, precipitation may not be a good measure of water supply for crops in regions like Arizona where most of the cropland is not rainfed.

### Adaptations

This paper considers two adaptation measures: fertilization and irrigation. The marginal effects (after accounting for the interaction between irrigation and temperatures) reported in Table 6 reveal that both fertilization and irrigation tend to have positive impacts on crop yields. On average, a $10/acre increase in fertilizer use can lead to a yield increase around 9 kg/acre for cotton, and about 0.12 ton/acre for hay. The 0.12 ton/acre increase is more than enough to compensate the loss to hay yield due to an 1 cm increase in autumn precipitation. Fertilizer use also has strong spatial spillover effects, which is discussed later.

Both cotton and hay (e.g. alfalfa hay, one of the main hay crops in Arizona) are water-needy crops. However, from the results we do not see a significant effect on crop yields by increasing irrigation water. One possible answer to the puzzle is that the irrigation variable may not be measured accurately. It is possible that the effect of irrigation on crop yields could have been underestimated. Over the four decades study period, the irrigation technology has been gradually switching from gravity/flood irrigation to more efficient sprinkling irrigation and micro irrigation systems. The irrigation efficiency improvement leads to less water demand in irrigating the same amount of land. Though the current model does not capture the effect of irrigation efficiency improvement, this points to an interesting direction for future research. Another reason for the lack of statistical significance is the small sample size. The chance of a significant difference (compared to the null hypothesis of no effects) is small if the samples are small. Therefore, future research should also focus on data collection.

### Spatial spillover effects

The model incorporates two types of spatial effects: spatial spillover effects among exogenous adaptation variables and the spatial correlation among unobserved effects. The empirical results show that there is a strong spatial spillover in fertilizer use. A $10/acre increase in fertilizer use in all neighboring counties can boost the crop yield by about 45 kg/acre for cotton and 0.35 ton/acre for hay. In percentage terms, that is about a 10% and 7% yield increase, respectively. Since we do not have variables to measure factors like technology investment and innovation, it is possible the fertilizer use variable actually picks up effects of those unobserved factors. If ignoring such a spatial spillover effect, then we are likely to underestimate the effect of fertilizer use as shown in Tables 2 and 3.

For irrigation water use, we expect there is a constrained interaction – different locations compete for water resources, which works in a way like negative spillover. The empirical results show that there is a negative impact associated with irrigation water use in neighboring counties, but it is not significantly different from zero. This implies there is not a strong competition effect among irrigation water use as we expected. A possible explanation is that farmers usually pay a very low price for water in Arizona, and the water supply budget is relatively soft until recently. According to Wilson & Gibson (2000), for example, the Maricopa-Stanfield Irrigation and Drainage District (MSIDD) who recovers its non-water variable costs through a volumetric water charge set the price at about $16 per 1,000 m^{3} (about $19.7/acre-feet) in the early 1990s.

The spatial autocorrelation in the error structure is generated when unobserved spatially correlated factors drive the dependent variable. The error terms for observations in any given location contain times the average error found in neighboring locations. is expected to be positive in the models, as mentioned before, because the spatially correlated unobserved effects are expected to affect crop yields statewide simultaneously. This is empirically confirmed in the paper. If otherwise failing to account for the spatial autocorrelation, we are likely to have incorrect standard error estimates and therefore wrong inferences on the effects of adaptations and climate change.

## CONCLUSIONS

This paper conducted an intra-regional analysis of impacts of climatic variations on crop yields in Arizona. It finds that it is necessary to incorporate adaptation measures in the crop yield model, otherwise climate variables may pick up the adaptation effects and lead to biased results. Through counterfactual analysis, the empirical results suggest that both fertilizer use and irrigation are important adaptations to climatic variation. Fertilizer use has a positive impact on crop yields as we expected. When accounting for irrigation and interactions between irrigation and temperature, a moderate increase in mean maximum temperature tends to be beneficial to both cotton and hay yields, which is different from most of the existing studies.

The spatial effects among input use need to be explicitly incorporated, especially when there are spillover effects or constraint interactions associated with these adaptation practices between different counties. Otherwise we may underestimate or overestimate the effects of adaptations. The empirical results show that there is a strong spatial spillover associated with fertilizer use. It also shows evidence of a negative impact on crop yields associated with irrigation water use in neighboring counties. Note that adaptations to climate change are region and crop specific, and these effects may not show up in analysis with nationwide or global data due to aggregation.

The analysis in this paper can be further developed in several ways. First, the estimation is confined with limited data and potential measurement errors in adaptation variables. More data work should be done in future research, especially for the crop specific adaptation measures. Though being subject to data availability, the results and proposed approach can be found useful in practices like precision agriculture, and risk analysis in support of decision-making in crop production management. Second, the current model ignores micro behavior of farmers in responding to climate change. For example, farmers can reduce yield variation by changing planting date and crop mix. There is also a complex system of government programs that have impacts on agricultural profits and land values by affecting farmers’ decisions about which crops to plant, the amount of land to use, and the level of production. Modeling farmers’ strategic behavior in responding to climate change is another interesting direction for future research.

A methodological caveat to note is that the approach used in this paper can be categorized as a spatial-analogue approach, which assumes a long-run equilibrium that ignores short-run adjustment cost in responding to climatic variation (Adams *et al.* 1998). An implication is that the predicted marginal effects of adaptations and climatic variation are only reliable within a certain range, effects of any large or structural change can only be validated upon new model specification and estimation.

- First received 19 April 2015.
- Accepted in revised form 20 July 2015.

- © IWA Publishing 2016

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