Sustainable Crop Farm Productivity: Weather Effects, Technology Adoption, and Farm Management

Abstract

The main purpose of this study is to understand the potential determinants of sustainable field crop farm productivity. This paper considers a multi-input, multi-output production technology to estimate the effects of aridity on farm-level productivity using a stochastic input distance function. By isolating the respective weather components of agricultural total factor productivity (TFP), we can better assess the impact on productivity of adopting various technologies and farm practices that might otherwise be masked by changing climate conditions or weather shocks. We make use of data from Phase 3 of the United States Department of Agriculture (USDA) Agricultural Resource Management Survey (ARMS) between 2006 and 2020. We supplement this estimation using field crop farm productivity determinants, including technology adoption and farm practice variables derived from the ARMS Phase 2 data. We identify several factors that affect farm productivity, including many practices that help farmers make more sustainable use of natural resources. The results show that adopting yield monitoring technology, fallowing in previous years, adding or improving tile drainage, and contour farming each improved farm productivity. In particular, during our study period, conservation tillage increased by over 300% across states on average. It is estimated to increase productivity level by approximately 3% for those adopting this practice. Critically, accounting for local weather effects increased the estimated productivity of nearly all farm practices and increased the statistical significance of several variables, indicating that other TFP studies that did not account for climate or weather effects may have underestimated the technical efficiency of farms that adopted these conservation practices. However, the results also show the impacts can be heterogeneous, with effects varying between farms located in the U.S. northern or southern regions.

1. Introduction

The latest United Nations World Population Prospects report projects that the global population will increase by one to two billion over the next 25 years, an increase of approximately 15 to 25 percent [1] that will result in a higher global food demand. Agricultural producers have traditionally increased output by either bringing more land under cultivation or by intensifying input usage; however, this approach also carries a number of undesirable environmental consequences, and it is unlikely to be a viable means to meet the increased food demand of the near future [2]. Instead, many countries’ agricultural sectors have pivoted towards improving productivity, allowing farmers to produce more with reduced inputs, which lessens the burden on natural resources, such as intensive land use [3]. To both meet this new demand and conserve natural resources, it is critical to understand the driving factors behind productivity growth in agriculture and adopt proper farm practices to enhance sustainable productivity growth.

Literature on identifying the factors behind productivity growth usually relies on either crop yield or conventional total factor productivity (TFP) estimates. This study fills the research gap by linking these factors to climatically adjusted TFP estimates, thereby reducing the noise in productivity variation caused by unfavorable weather. Additionally, this study provides a more comprehensive analysis by incorporating more variables that may affect productivity for robustness comparison.

While changes in agricultural productivity are attributed in large part to technological progress, the literature has increasingly tried to determine the direct impact of climate as well. Researchers typically address the impact of climate change on agriculture—as measured through crop yields—by examining changes in precipitation and temperature data [4,5,6,7]. Studies have found that the relationship between weather variables and yield can be nonlinear [8,9,10,11]. The timing and frequency of drought also impact crop production. After witnessing a decline in the growth trend of cereal yields in many European countries, Brisson et al. showed that genetic progress in European wheat yield had not declined but was instead partly counteracted by heat stress during grain filling and drought during stem elongation [12]. More recently, Zhong, Hu, and Jiang used a data envelopment analysis approach to estimate agricultural productivity in China at the provincial level [13]. All of their climate variables—average temperature, evaporation capacity, and, unexpectedly, total precipitation—had significant and negative impacts on productivity. Li and Liu also focus on the Chinese agricultural sector, using a slacks-based measure model to examine the interaction between climate and irrigation facilities [14]. Similar to Zhong et al., they find precipitation has a similarly negative effect, but their results also suggest that higher annual average temperature is actually productivity-improving; however, they did not account for non-linearity in the effects of average temperature.

Using corn yield data in the U.S., Saavoss et al. show that droughts in 2002, 2006, and especially in 2012 have accounted for abnormally low corn yields in those years [15]. Additionally, linking temperature or precipitation data separately to crop yield, Zhang and Carter found that an aridity index (the Oury index—a combination of time, temperature, and precipitation) was an effective climate variable in their econometric model [16]. They stated that “the advantage of using the monthly weather index in a production function (instead of original precipitation and temperature data) is that it reduces the number of variables, increases degrees of freedom, and avoids high multicollinearity”.

Nevertheless, weather variables are not the sole determinant of crop yields. Numerous non-land inputs, such as fertilizer, labor, and machinery, can all enhance agricultural output. In the long-term, technology adoption and improved farm practices–crop rotation, fallowing, or tile drainage, for example–can all promote higher crop yield and overall farm productivity. Critically, many farm practices may simultaneously improve farm resilience to extreme weather events or disruptions in external supply chains; depending on the practice, it may also promote greater sustainability of the farm operation. However, some practices may improve one of these aspects at the cost of the others. Coomes et al. provide a brief but valuable overview of promising sources for productivity growth and agricultural sustainability [2]. Their evaluation suggests that in many cases, practices that enhance either productivity or sustainability will have uncertain effects on the other category. Crop rotation, for example, may improve farm resilience to pest outbreaks and increase biodiversity but may cause logistical challenges; similarly, precision technology can reduce agricultural chemical use but is likely to offset productivity gains with increased use of capital input or purchased services.

It is challenging to promote the adoption of sustainable technologies if they negatively impact farmers’ profits. Consequently, most papers examine the viability of conservation practices by determining their effect on farm productivity. Numerous papers in the agro-economic literature indicate several of these conservation practices may also be economically attractive. Fallowing (and crop rotation more generally) is a common method to mitigate pest outbreaks and improve soil health and structure, and several papers suggest that it might also generate economic returns; Zhang et al. (2024) provide a useful overview of the benefits associated with corn and soy rotation, of particular importance to our study area [17]. Bullock suggested that improvements in soil physical properties and soil organic matter play a beneficial role in rotations [18]. He showed that maize, in a 2-year rotation with soybeans, yields 5 to 20% more than continuous maize cultivation. Critically, no amount of fertilizer or pesticide completely compensated for that difference. Brisson et al. later found that cereal yield decline during the 2000s can be partially attributed to the decline of legumes in rotations [12]. More recently, Zhang et al. (2017) found that farmers in the US Pacific Northwest are increasingly adopting land fallow practices as an adaptation to increasing heat and precipitation [19]. Precision application has become increasingly attractive as a means to mitigate the environmental impacts of fertilizers and pesticides. Schimmelpfennig and McFadden et al. have also shown that the increasing adoption of certain precision-farming technologies (such as yield monitors and maps, variable-rate applicators, and genetically engineered seed application) has contributed to improvements in overall farm performance [20,21]. It is important to note that the impact of specific farm practices may be heterogeneous across geographic regions. For example, previous literature shows that tile drainage is most prevalent in Northern/Midwestern states–regions with a relative abundance of precipitation [22,23].

Since production decisions on how to allocate on-farm resources into various farm production activities and which farming practices to follow can affect overall production levels and input costs, researchers have come to rely more on TFP measures to assess the impacts of climate, weather, and climate change on farm productivity [11,24,25,26,27,28]. Most TFP and climate studies are linking pre-estimated TFP data to weather variables based on aggregate sector or country data that may be less sensitive to local weather heterogeneity than using farm-level data.

The objectives of this study are twofold: first, to understand climatic effects on farm-level productivity performance over time using local weather data and farm-level survey data; second, to evaluate the determinants–including technology adoption and farm practices–of field crop farm productivity based on weather-adjusted TFP estimates. By doing so, we can separate the noise of weather effects from the TFP estimates and get more insight into the impacts of technology adoption and farm practices on farm productivity. These findings can shed light on the dynamic effects of climate change on farm productivity and advance our knowledge on the determinants of sustainable field crop farm productivity.

2. Methods

2.1. Theoretical Framework

We consider a multi-input, multi-output production technology in our farm-level productivity analysis. We assume that production technology is available to all farms, but that each farm may not have performed optimally; this would result in a lower efficiency score (we set the efficiency score on the frontier to 1). The distance between the best-performing farms (on the frontier) and the individual farm’s productivity is referred to as inefficiency under the stochastic distance function measure. Our hypothesis is that drier weather conditions and unexpected “weather shocks” could drive farmers’ performance further away from the frontier under their normal farm practices. Conversely, less arid weather and reduced weather shocks may make farms appear more efficient than they otherwise would have. We adopt a stochastic input distance function to represent the structural form of farms’ production technology in terms of minimum input use required to produce given output levels. Weather factors are modeled into the stochastic inefficiency term simultaneously using the maximum likelihood approach to avoid two-stage estimation errors [29].

Following Färe and Primont [30], Lovell et al. [31], Kumbhakar and Lovell [32], and Kumbhakar et al. [33], the stochastic input-oriented distance function (D^I) can be expressed as the minimum possible input levels (x) for producing a given output vector (y) under the current technology T while allowing deviation from the frontier:

D^I (x, y) = max {ρ: (x/ρ) ∊ L(y)}

(1)

where L(y) = {x: (x, y) ∊ T} is the input requirement set representing the production technology with the set of all input vectors x that can produce output vector y. The input distance function measures the maximum value of ρ that allows inputs to be reduced radially but is feasible to produce a certain level of output mix. Figure 1 demonstrates an input distance function with two inputs—x₁ and x₂. L(y⁰) is the input isoquant for producing output y⁰. For input sets located on the isoquant, the input distance function is equal to one (points x^A and x^B, for example). For input sets beyond the isoquant are inefficient (less productive), with the input distance function larger than one, x^C, x^D, and x^E for example. Technical efficiency (TE) scores can be measured using the distance function:

TE_I (x, y) = min {θ: D^I (xθ, y) ≥ 1}, θ = 1/ρ, 0 < θ ≤ 1

(2)

TE represents the relative productivity level for each farm under a feasible technology.

To maintain the homogeneity properties of the distance function, we impose linear homogeneity of inputs by normalizing the input variables with land:

$$ln\left({\displaystyle \frac{D_i^I}{X_{1,i}}}\right)={\alpha }_0+\sum _m{\alpha }_{m}ln{x}_{mi}^{*}+\sum _n{\beta }_n{lny}_{ni}+v_i$$

(3)

where x₁ represents land, $x_{mi}^{*}$ represents normalized inputs for farm i, ${\mathit{y}}_{\mathit{n}}$ are outputs, ${\alpha }_0,{\alpha }_m,{\beta }_n$ are parameters to be estimated, $v_i$ is the random error, i.i.d. ~N$(0,{\sigma }_{v,i}^2).$ Land is measured as operated land acreage, and labor is measured as total working hours from hired workers, self-employed workers, and family workers. Capital is measured as depreciated total capital assets. All other inputs are measured in dollar value, due to data availability in the survey. Field crop outputs are measured in their physical quantities. Other crops are measured in values available in the survey. Inputs are normalized using land as the denominator and expressed in logarithmic form. We deflate value variables using the United States Department of Agriculture (USDA) National Agricultural Statistics Service (NASS) paid-by-farmer price index for inputs and the crop price index for other crops.

By rearranging terms in Equation (3)—moving the distance or the inefficiency term to the right-hand side—and adding climate variables to the equation, we estimate:

$$-ln{X}_{1,i}={\alpha }_0+\sum _m{\alpha }_{m}ln{x}_{mi}^{*}+\sum _n{\beta }_n{lny}_{ni}+\sum _k{\gamma }_k{lnz}_{ki}-u_i+v_i$$

(4)

where ${\gamma }_k$ are parameters to be estimated, and${\mathit{z}}_{\mathit{k}}$ are external variables, including climate variables; $u_i$ is the inefficiency error measuring the non-negative distance of the production set of farm i to the frontier [30]. We first test for $u_i=0$. If the “no inefficiency term” hypothesis is rejected, we then model the logged variance of inefficiency,

$$ln{\sigma }_{u_i}=z_i\prime \delta$$

(5)

where δ is a vector of estimated parameters, and $z$ is a vector of external variables, including weather variables. Equations (4) and (5) allow us to estimate both technical inefficiency as a one-sided error term ($u_i$), and its determinants through the stochastic specification. We employ a maximum likelihood method to estimate the error component model using the farm-level data from the USDA Agricultural Resource Management Survey (ARMS) Phase 3 [34]. All econometric analyses conducted in the paper are performed using STATA version 17.

To evaluate the relationships between field crop farms’ technical efficiency and farm operators’ actions on precision ag technology adoption and various farm practices, we consider the following variables in our regression analysis, drawing data from the ARMS phase 2: (1) technology adoption--including variable rate technology and yield monitors; (2) farm practices--including use of cover crops, fallowing, irrigation, conservation tillage practices, adding or improving tile drainage, and the presence of soil structures; and (3) we also include farmer experience, replanting rate, rental price of farm acreage, and field insurance as control variables. Given that not all types of crop farms are surveyed in ARMS Phase 2 each year, we impute missing values and use a three-year moving average of the values of each variable in years t − 1, t, and t + 1 to form state-level technology adoption variables in year t.

Since only a small portion of farms simultaneously participate in both ARMS Phase 2 and Phase 3 surveys or participate in consecutive years, we created a pseudo-panel dataset based on state cohorts for the individual farms’ productivity estimates or Phase 2 variables, using respective sample weights for aggregation or mean calculation. By doing so, we are able to get insight into the determinants of crop farm productivity performance based on pseudo-panel data over a longer period of time.

Due to the presence of some zero-valued variables, we adopted an inverse hyperbolic sine specification in place of a logarithmic specification [35]. We conducted a panel regression analysis using efficiency scores as the dependent variable based on the following model specification:

$$sin{h}^{-1}\left({TE}_{it}\right)=c+{\sum }_q{\varnothing }_{q}sin{h}^{-1}\left(F_{qit}\right)+{\delta }_t+{\eta }_i+{\epsilon }_{it}$$

(6)

where ${TE}_{it}$ is the technical efficiency score in state i in year t, $F_{qit}$ is the farm practice or technology adoption variable q in state i and year t. State-level fixed effects and year fixed effects are used when conducting the regression analysis, $c,\varnothing ,{\delta }_t,{\eta }_i$ are parameters to be estimated. We also estimate this model separately for northern states compared to the rest of the country because field practices and crops differ substantially, as well as there being different climate trends.

For the purposes of this paper, the “Northern States” include the states from the following Economic Research Service (ERS) Production Regions: Northern Plains, Lake, Corn Belt, and the Northeast. Each of those regions predominantly grows corn and soybeans, as well as experiencing declining aridity. The remaining regions (Pacific, Mountain, Southern Plains, Delta, Southeast, and Appalachia), which we refer to as the Southern States, are generally more arid than the Northern States and are not experiencing pronounced aridity declines. While the Pacific region may not share the same climate pattern with other states in the Southern region, its geoclimatic status is more like the Southern region than the Northern region, especially since California is the only Pacific region state in our sample. The Southern States are also characterized by large rice and cotton production.

2.2. Potential Endogeneity Issues and Assumptions

The key exogeneity assumptions in productivity analysis are that farmers are profit maximizers and that production choices are predetermined [36]. In keeping with previous literature [37,38], we assume that variation in weather is random, and therefore weather realizations will be exogenous to prespecified farm choices because they occur after those decisions are made. The field practices examined in this paper are similarly prespecified as other farm choices examined in previous productivity analyses, with the exception of replanted field acres. However, replanting acres is a response to acute adverse events, often related to weather, and can be thought of as a proxy variable controlling for adverse events that are more localized than our weather measures. Similarly, prespecified farm choices are considered exogenous to output because they are made prior to the outcome being realized.

2.3. Farm Financial Data

To measure field-crop farm productivity performance with local weather effects, we draw on farm-level data from the USDA ARMS Phase 3 between 2006 and 2020. USDA NASS conducts three types of surveys for different purposes: Phase 1 is a screening survey; Phase 2 is focused on production practices and agricultural chemical use at the field level; Phase 3 collects information on the characteristics and finances of all farm businesses and farm households at the whole-farm level [39]. We based our sample on “commercial-oriented” family farms with gross cash farm income (GCFI) of USD 100,000 or more. To reduce heterogeneity caused by production technology, we focus solely on field crop farms by dropping all other types of farms from the data. Following Wang et al., we define field crop farms as those in which at least 50% of the total farm production value is from field crops [40]. The specialty of a farm is when the production value of one specific commodity exceeds 50% of the total production value on that farm. If no single commodity dominates, but a mix of cash grains accounts for more than 50% of total farm production value, then the farm is defined as a “General cash grain farm”. Otherwise, if the value of all kinds of field crops accounts for more than 50% of total production value, it is defined as a “General crop farm”.

Table 1. Total value of production (in nominal USD 1000) by farm types, 2006 vs. 2020.

Production Specialty	Number of Observations	Mean	Sum (Millions)	Min	Median	Max
2006
General cash grain	911	359	12,148	100	233	7657
Wheat	270	264	2928	100	201	4829
Corn	1040	335	18,183	100	233	8386
Soybean	529	294	4496	100	188	3357
Grain sorghum	14	238	48	105	196	537
Rice	549	408	1579	102	251	3833
Tobacco	84	319	815	101	183	2779
Cotton	574	499	4877	102	295	5756
Peanut	39	284	238	101	183	2378
General crop	547	586	11,496	100	243	37,576
Total	4557
2020
General cash grain	582	700	24,142	102	435	13,751
Wheat	101	418	3170	100	360	2698
Corn	1433	671	60,650	100	383	23,915
Soybean	566	514	20,216	100	280	11,674
Grain sorghum	32	505	1467	101	288	2173
Rice	183	1022	2845	113	753	8936
Tobacco	23	705	747	110	722	2014
Cotton	119	920	3936	104	525	8089
Peanut	18	511	369	130	328	2212
General crop	306	761	15,294	102	358	15,653
Total	3363

Source: Authors’ calculation using United States Department of Agriculture (USDA) Agricultural Resource Management Survey (ARMS) Phase III data.

presents the descriptive statistics of our sample data for 2006 (top panel) and 2020 (bottom panel) by production specialty (i.e., the production value of one specific commodity exceeds 50% of total farm production value). Among these, corn farms have the most producers in both years. In 2006, the mean value of production was highest for general crop farms, while cotton farms had the highest median value of production. In 2020, rice farms had the highest mean and median production values. Despite the mean and median nominal value of tobacco and cotton farm production roughly doubling from 2006 to 2020, the total nominal value of production decreased slightly due to the reduced number of operations. Regarding operated acreage by farm type, grain sorghum farms and wheat farms have the largest farm sizes. Tobacco farms have the lowest mean and median size in both years. In absolute terms, the largest change is the growth of the mean wheat farm, from 3095 acres to 3675 acres from 2006 to 2020. In relative terms, the largest changes were mean tobacco farm sizes increasing from 631 acres to 973 acres and mean peanut farm sizes decreasing from 1396 acres to 984 acres.

2.4. Farm Management Practices and Technology Adoption Data

To evaluate the relationship between technology adoption/farm management practice changes and farm productivity performance, we draw on USDA’s ARMS Phase 2 data, as ARMS Phase 3 surveys do not contain technology adoption or farm practice questions. The core commodities surveyed in ARMS Phase 2 rotate each year, and the survey questions focus primarily on farm practices and technology adoption rather than financial data. The Phase 2 sample is also smaller relative to Phase 3, and only a portion of the sample can be matched with the Phase 3 observations. Therefore, we measure annual state-level adoption rates for specific technologies or farm practices to put together a pseudo-panel by state and by year so we can conduct a state-level analysis to identify the relationship between field crop farm productivity and technology adoption and adaptation. There are eight main variables under our consideration that we use as proxies of technology adoption/farm practice changes: first, the percentage of farmers that use variable rate applicators for seeding, fertilizers, or pesticides; second, the percentage of farmers that use yield monitors; third, the percentage of farmers that use cover crops for erosion prevention or soil health; fourth, the percentage of farmers who use conservation tillage practices; fifth, the average number of fallow periods per field over the past three years; sixth, the percentage of farmers who improved their tile drainage; seventh, the percentage of irrigated acres; eighth, the percentage of farmers who have established some form of structure to conserve soil. One variable of interest that we would like to have included is use of drought-tolerant corn, but ARMS phase 2 had only gathered that data for 2016, which is not sufficient for this analysis.

Yield monitors and variable rate applicators, together with global positioning system (GPS) mapping, are the primary technologies that comprise “precision agriculture.” Farmers use monitors to collect data on yield variation between plots; they can use this data directly as a general assessment of their management practices or combine it with GPS mapping to increase precision. Variable rate applicators (VRT) calibrate input use–seeds, pesticides, and fertilizers–depending on field conditions. These technologies can also be adopted alongside GPS mapping to increase accuracy [41]. ARMS Phase 2 collects data on GPS mapping, along with yield monitors and VRT; however, we have chosen to focus on the latter technologies due to wording changes in the survey question regarding GPS usage. Like other authors, we find that adoption of yield monitor and variable rate applicator technologies increased substantially over the time period we are studying [41,42]. On average, as seen in

Table 2. Average adoption rate for field practice variables: 2005–2007 vs. 2019–2021.

Variables	2005–2007	2019–2021
Yield Monitor	24.4	40.1
Variable Rate	8.4	19.2
Cover Cropping	0.4	14.7
Fallow Periods	2.9	2.2
Conservation Till	11.3	45.7
Grass Waterways	17.1	13.2
Improved Tile Drainage	2.6	6.2
Irrigated Acreage	17.7	8
Contour Farming	9.7	6.6
Terraces	10.1	6.7

Note: All variables, except for Fallow Periods, are the average adoption rates over our sample, in percentages. Fallow Periods is the average number of fallow periods out of the prior six seasons (3 years). The values in the table are national averages. Source: ARMS Phase II.

, yield monitor usage increased from 24.4% in 2006 to 40.1% in 2020; variable rate applicators had lower usage but rose from 8.4% to 19.2%.

Our variable tile drainage is defined as the proportion of farmers who used results from yield monitors to install tile drainage (or improve existing installations). Unfortunately, ARMS Phase 2 does not have a consistent question regarding the actual use of tile drainage—only whether it was added or improved based on yield monitor information. Tile drainage refers to a network of subsurface pipes that divert excess water out of fields to prevent soil oversaturation. Adequate drainage promotes better root growth in crops and prevents excessively wet conditions that make fields inaccessible for heavy farm machinery. In western states, tile drainage is also used to remove salinity that accumulates due to irrigation. Table 2 shows that the rate of adding or improving tile drainage in the previous year increased from 2.6% in 2005–2007 of farm acres to 6.2% in 2019–2021.

Cover cropping is the practice of planting a crop on a field that is not intended for harvest. There are several purposes for cover cropping, including soil health and erosion control. Table 2 shows that on average cover cropping rises from almost zero in 2005–2007 to 14.7% of planted acres in 2019–2021. Fallowing is the practice of leaving a field uncultivated to crops for a period of time. Farmers were asked about what crops they planted on a given field in previous seasons. If they answered “no crop” or “the field was in the conservation reserve program,” the field was considered to be left in fallow that season. In Table 2, we see that average fallow periods decline from almost half of the planting seasons to slightly over a third. From 2005–2007, 2.9 of the previous 6 seasons were fallowed on average, while that number declined to 2.2 in 2019–2021.

Land rent is the cash rent per acre paid by a farmer and is averaged across farmers within a state. Necessarily, it excludes those farmers that own their land or rent via crop-share. This variable is meant to control for inherent advantages farms in one state may have over farms in another, as we assume that land rent is a reflection of the profitability (via productivity) of that acreage.

Conservation tillage is an umbrella term for the use of specific tilling practices, all of which are less disruptive to the soil than conventional tillage. Our variable is based on farmers’ responses to whether they used conservation tillage as a soil conservation practice in a given year; this may differ from the soil residue calculations that other studies use to estimate tillage intensity. As seen in Table 2, conservation tillage increases dramatically from 11.3% of acres in 2005–2007 to 45.7% in 2019–2021.

Irrigated acreage captures whether or not a farm purchased water. This variable does not detect fields with irrigation capital, just whether it was used. Data on building the capital would be useful, but we’re looking for the productivity impact of using irrigation. Table 2 shows that irrigated acreage declines from 17.7% of acres in 2005–2007 to 8% in 2019–2021.

Contour farming, terracing, and grass waterways fall under the larger category of soil structures, which are adopted in order to mitigate erosion. Contour farming is the practice of planting along the “contours” of a sloped field, such that crop rows are ordered “across” a field’s slope, rather than following the slope itself. Contour farming is often adopted alongside terraces, which are a series of embankments in fields to catch water as it flows down a sloped field. Effectively, this turns a longer slope into a series of shorter ones, preventing water from washing away soil by reducing its velocity. Grass waterways are strips bordering fields that have permanent vegetation like grass, which allows water to flow without eroding the soil. As seen in Table 2, usage of all three soil structure variables declines. In 2005–2007, 9.7% of acreage was contoured, whereas only 6.6% was in 2019–2021. Similarly, in 2005–2007, 10.1% of acreage had terraces, while only 6.7% was terraced in 2019–2021. Grass waterway usage declines from 17.1% to 13.2%.

2.5. Weather and Climate Variables

Following Zhang and Carter [16], Paltasingh et al. [43], and Wang et al. [27] (among others), we use the Oury index to construct our weather variables, based on county-level temperature and precipitation data produced by Oregon State University’s PRISM climate group [44,45]. We construct an Oury mean variable for each year using daily weather information in growing season months and two “normal” weather variables—Oury mean and Oury standard deviation—using twenty-years of data prior to the planting year to form the farmer’s expectation on the local climate condition in the coming year. The Oury index (W) is defined as:

$$W_s={\displaystyle \frac{P_s}{{1.07}^{{\tau }_s}}},$$

(7)

where s indicates April–August (months in the main growing season); P is the total precipitation for month S in millimeters (mm); and τ is the mean temperature for month S in degrees centigrade. A lower index, which results from higher temperatures or lower precipitation, indicates drier conditions. Following Wang et al. [27], we also construct an unexpected “weather shock” variable to show the impact of climate change, defined as:

$${\displaystyle \frac{\left(Ourymea{n}_t-Ourymea{n}_H\right)}{{Ourystandarddeviation}_H}}$$

(8)

where t is a time subscript, indicating year, and H is the historical norm of the Oury mean and Oury variation using historical data.

Over time, the historical norm of the Oury mean and Oury standard deviation has gradually changed across regions and has done so unevenly. Between 2006 and 2020 (Figure 2 and Figure 3), the “normal” weather condition (based on 1986–2005 to 2000–2019 historical data) became generally wetter (Figure 2) and increasingly variable (Figure 3). While in the Midwest some states became wetter, given the increased standard deviation, it implies that the wetter condition may emerge in a short period of time rather than be evenly distributed in every month within the growing season. As shown in Figure 3, the annual weather variation became more severe in recent years, covering states mostly in the Mountain, Northern Plains, and Corn Belt regions.

3. Results and Discussion

3.1. Climatic Effects and Field Crop Farm Productivity

We report results based on three model specifications of our multi-output (20 outputs), multi-input (14 inputs), input-oriented stochastic distance function (SDF) in

Table 3. Estimates of alternative model specification for input distance function.

Variables	Specification 1		Specification 2		Specification 3
	Coefficient	t-Ratio	Coefficient	t-Ratio	Coefficient	t-Ratio
Input Variables
Labor input	0.28 ***	6.09	0.26 ***	5.03	0.29 ***	8.77
Capital input	0.01	0.81	0	0.38	0.03 ***	4.12
Intermediate input					−0.66 ***	−24.02
Seed	0.02 *	1.9	0.01	1.27
Contract labor service	0.03 ***	4.59	0.03 ***	4.2
Custom machine work	0.01 ***	2.72	0.01 **	2.59
Fertilizer	−0.02 ***	−2.86	−0.02 ***	−2.64
Chemicals	0.01	1.24	0	1.03
Energy	−0.04 **	−2.3	−0.04 **	−2.39
Water	0.1 ***	4.21	0.13 ***	2.92
Repair	0	−0.6	0	−0.07
Management cost	0	0.1	0	0.48
Capital expense	0.04 ***	5.95	0.03 ***	5.44
Pasture expense	0.23 ***	3.06	0.25 ***	3.39
Output Variables
Barley	0.02	1.42	0.02	1.09	0	−0.15
Canola	−0.02	−1.23	−0.02	−0.6	−0.02 *	−1.92
Corn	−0.03 ***	−3.87	−0.03 ***	−4.14	0	0.17
Corn for silage	−0.02 **	−2.36	−0.02 **	−2.26	0.01 *	1.68
Cotton	−0.02 ***	−6.07	−0.02 ***	−4.33	0	0.77
Hay	−0.02 ***	−3.93	−0.02 ***	−3.38	−0.03 ***	−4.41
Oats	−0.01 **	−1.98	−0.01 *	−1.73	−0.01	−1.24
Other oil seeds	−0.04 **	−2.29	−0.04 *	−1.78	−0.01	−0.53
Peanut	−0.02 ***	−3.26	−0.01 **	−2.31	0	0.01
Potato	0	−0.08	0.01	0.27	0.04	1.4
Rice	−0.04 ***	−6.12	−0.04 ***	−5.75	−0.01	−1.39
Sorghum	−0.02 ***	−3.06	−0.02 ***	−2.78	−0.02 ***	−3.04
Sorghum for silage	−0.13 ***	−4.97	−0.12 ***	−3.94	−0.03	−1.11
Soybean	−0.05 ***	−3.82	−0.05 ***	−4.2	−0.02 ***	−2.67
Sugar beet	−0.06 ***	−4.88	−0.06 ***	−3.79	−0.01	−1.32
Sugar cane	−0.08 ***	−6.83	−0.08 ***	−7.81	0.02 ***	3.22
Tobacco	−0.03 **	−2.5	−0.03 **	−2.28	−0.01 ***	−4.25
Wheat	−0.02 ***	−3.52	−0.01 ***	−3.61	−0.02 ***	−3.85
Other crops	−0.02 ***	−3.84	−0.02 ***	−3.55
Livestock netput	−0.19 ***	−5.26	−0.17 ***	−4.98	−0.08 **	−1.92
Weather Variables
Oury mean			0	−0.68	−0.01 ***	−2.64
Oury shock			0.02	0.65	0.03	0.98
Constant	−3.54 ***	−5.76	−3.09 ***	−3.8	1.33 ***	2.57
lnσY2	−2.79		−3.1		−1.94
σY	0.25		0.21		0.38
lnσu2
Constant	−0.24 ***		0.88 *	1.81	0.52 ***	9.63
Oury mean			−0.04 **	−2.55	−0.14 ***	−3.82
Oury shock			0.11	0.9	0.28 *	1.68
Pseudolikelihood	−2523.7		−2469.84		−1814.49
Observations	3028		3028		3363

Note: 1. ‘*” indicates 10% significance level, ‘**’ indicates 5% significance level, ‘***’ indicates 1% significance level. In all specifications, state fixed effects are used in the frontier equation, and state cluster variance is used in the inefficiency equation. 2. To maintain the homogeneity properties of the distance function, we impose linear homogeneity of inputs by normalizing the input variables with land (measured as operated land acreage). 3. Labor is measured as total working hours from hired workers, self-employed workers, and family workers; capital is measured as depreciation for all capital assets, such as farm buildings, machinery, tractors, trucks, etc.; intermediate input is the sum of all input expenditures other than labor, capital, and land; all other inputs are measured as expenditures reported in ARMS; outputs are measured in their physical quantities except for “other crops” and “livestock netput”, which are measured in cash values; Oury mean and Oury shock are weather variables (see the weather data section for more details regarding their calculation). Source: Authors’ estimation.

, for the year 2020. We first estimate the results without weather variables in Specification 1. Specification 2 adds weather variables–Oury mean and weather shock–in both the frontier and inefficiency equations. In Specification 3, we aggregate the expenses of all variable inputs into one category of intermediate goods. All equations include state fixed effects in the frontier equation and state cluster variance in the inefficiency equation.

According to Table 3, labor, capital, most of the variable inputs, and all outputs are expressed in the proper sign; in Specification 3, labor, capital, and most of the outputs are expressed in the proper sign with the exception of the intermediate inputs and a few of the outputs. This implies that the monotonicity condition may hold locally but not globally. Weather variables are not robust in the frontier equation, as they are not significant in Specification 2. In the inefficiency equation, both weather variables demonstrate consistent signs and significance for three out of four coefficient estimates. The negative sign of the Oury mean variable in the inefficiency equation indicates that drier weather conditions will drive farm performance away from the production frontier, and a larger scale of unexpected weather shock will do the same thing. These results are consistent with those found in Wang et al. [40], although they differ somewhat from Zhong et al. [13] as well as Li and Liu [14].

To further understand if farm productivity performance has changed over time in response to changing weather conditions, we estimate stochastic distance functions from 2006 to 2020 based on Specification 3. Since fewer than half of the coefficient estimates are significant for weather variables in the frontier equation, and nearly 90 percent of the coefficients of weather variables are significant in the inefficiency equation, we only report the results in the inefficiency equation for weather variables in

Table 4. Estimates of weather variables in inefficiency equation.

Year.	Inefficiency Equation Based on Specification 3
	Oury Mean Coefficient	std. err.	t-Ratio		Oury Shock Coefficient	std. err.	t-Ratio
2006	−0.149	0.057	−2.63	***	0.280	0.441	0.63
2007	−0.143	0.041	−3.51	***	0.512	0.217	2.35	***
2008	−0.090	0.017	−5.32	***	0.324	0.180	1.81	*
2009	−0.197	0.145	−1.36		−0.225	0.567	−0.40
2010	−0.066	0.025	−2.65	***	0.512	0.279	1.84	*
2011	−0.099	0.015	−6.59	***	1.167	0.246	4.74	***
2012	−0.076	0.021	−3.59	***	0.448	0.198	2.26	**
2013	−0.083	0.017	−4.96	***	0.336	0.185	1.82	*
2014	−0.089	0.012	−7.40	***	0.224	0.172	1.31
2015	−0.120	0.016	−7.68	***	0.154	0.064	2.41	***
2016	−0.092	0.013	−7.16	***	0.387	0.094	4.12	***
2017	−0.077	0.019	−4.03	***	0.416	0.159	2.61	***
2018	−0.113	0.013	−8.47	***	0.738	0.101	7.32	***
2019	−0.086	0.014	−6.23	***	0.224	0.110	2.04	**
2020	−0.135	0.035	−3.82	***	0.284	0.170	1.68	*

Note: ‘*’ indicates 10% significance level, ‘**’ indicates 5% significance level, ‘***’ indicates 1% significance level. Source: Authors’ estimation.

. In Figure 4, we show the 95% confidence intervals of weather variable coefficient estimates to provide insight into farmers’ reactions to changing weather conditions over time. As shown in panel a of Figure 4, it appears as though average moisture conditions have had roughly similar impacts on field crop farms’ relative performances toward their best practices since 2010. Farms’ reactions to unexpected weather shocks seem to oscillate from year to year, although the scale of variation is diminishing. This may imply that farmers have taken actions to mitigate the impacts of unexpected weather shocks over time.

3.2. Impacts of Technology Adoption and Farm Management Practices on Field Crop Farm Productivity

Accounting for local weather conditions is also necessary to evaluate the productivity of farm practices.

Table 5. Effects of farm practices and technology adoption on technical efficiency (TE).

	(1)	(2)	(3)	(4)	(5)	(6)
Variables	TE	CTE	TE North	CTE North	TE South	CTE South
Yield Monitors	0.0046	0.014 ***	−0.029 ***	−0.0033	0.0093 *	0.016 ***
	(0.91)	(2.74)	(−3.04)	(−0.46)	(1.65)	(2.81)
Variable Rate Technology	−0.0025	0.0013	−0.013 **	−0.0048	−0.0036	−0.0073
	(−0.46)	(0.28)	(−2.37)	(−1.04)	(−0.43)	(−1.05)
Field Insurance	−0.0033	0.0025	0.014	−0.0019	−0.012	−0.0075
	(−0.50)	(0.40)	(1.23)	(−0.25)	(−1.61)	(−1.06)
Farmer Experience	−0.029 **	−0.013	−0.021	0.0012	−0.026 *	−0.019
	(−2.09)	(−0.94)	(−0.80)	(0.058)	(−1.80)	(−1.28)
Cover Cropping	0.0012	0.0023	−0.00074	−0.0012	0.0011	0.0060 **
	(0.66)	(1.32)	(−0.30)	(−0.60)	(0.43)	(2.53)
Fallow Periods	0.013 *	0.034 ***	0.0082	0.014 *	0.013	0.064 ***
	(1.95)	(3.89)	(0.88)	(1.68)	(0.91)	(4.76)
Conservation Tillage	0.0034	0.011 ***	0.0011	0.010 ***	0.0073 **	0.012 ***
	(1.60)	(5.47)	(0.29)	(2.72)	(2.36)	(5.01)
Replanted Acreage	−0.0040 *	−0.017 ***	0.0027	−0.0070 ***	−0.012 ***	−0.025 ***
	(−1.71)	(−6.94)	(0.81)	(−2.95)	(−2.90)	(−7.40)
Land Rent	0.0052	0.0074	−0.0099	0.013 *	0.031 ***	0.028 ***
	(0.85)	(1.41)	(−1.05)	(1.91)	(3.23)	(3.43)
Improved Tile Drainage	−0.0030	0.0069 ***	0.0050	0.0088 ***	−0.0088 *	0.0052
	(−1.28)	(2.75)	(1.55)	(4.04)	(−1.75)	(1.05)
Irrigated Acreage	−0.0047 ***	0.00037	0.0011	0.0033 ***	−0.010 ***	−0.0080 ***
	(−3.72)	(0.27)	(0.63)	(2.68)	(−3.79)	(−2.95)
Grass Waterways	0.00015	0.0027	0.0078 *	0.00089	−0.00074	−0.0040
	(0.065)	(1.21)	(1.75)	(0.28)	(−0.25)	(−1.25)
Contour Farming	−0.0039 **	0.0049 ***	−0.0045 *	0.0076 ***	−0.0016	0.0077 ***
	(−2.46)	(3.03)	(−1.85)	(3.33)	(−0.75)	(3.43)
Terraces	0.0016	2.69 × 10−6	−0.0042 **	−0.0056 ***	−0.00047	−0.0020
	(0.95)	(0.0018)	(−1.98)	(−2.60)	(−0.17)	(−0.91)
Constant	0.67	0.53	0.80	0.63	0.57	0.49
	(9.43)	(7.00)	(6.35)	(8.26)	(6.09)	(5.06)
Observations	481	481	195	195	286	286
R2	0.593	0.875	0.758	0.893	0.541	0.872

Notes: Variable names starting with “C” indicate that the dependent variables are based on climatic-effects-adjusted technical efficiency estimates. All specifications use region and year fixed effects with heteroskedasticity robust standard errors. The numbers in the parenthesis are t-ratios. ‘*” indicates 10% significance level, ‘**’ indicates 5% significance level, ‘***’ indicates 1% significance level. Source: Authors’ estimation of Equation (6).

presents the regression results for Equation (6), which links farm practices and technology adoption to technical efficiency. Several variables, such as yield monitoring adoption, fallow periods, farmer’s field experience, tile drainage, and the use of certain soil structures, all appear to have either negative or insignificant impacts on technical efficiency until we adjust for climatic effects. For the coefficient on conservation tillage in particular, we see a marked increase in both magnitude and significance after adjustment. An interesting note is that the R² value is noticeably higher on the weather-adjusted specification, particularly in southern states. This indicates that after accounting for the random weather effects, these farm practices and technology variables can better explain farm productivity performance.

As mentioned earlier, yield monitors are adopted to improve farmers’ input efficiency and improve management practices, and we would expect their adoption to improve overall farm efficiency. However, the magnitude of this impact will depend on the variability of field conditions. It may also be influenced by perception; one 2013 study of cotton growers suggested that respondents tended to underestimate field variability prior to yield monitor adoption [42]. According to our results, yield monitors appear to have no impact on farm efficiency before adjusting efficiency measures for local weather conditions. However, after adjusting for weather, yield monitors have a statistically significant positive effect at the national level and for the southern region. In the northern region, yield monitors have a negative relationship with efficiency before adjusting for weather and a statistically insignificant one after. In the southern region, the relationship is marginally positive before adjusting for climate and more positive after, while also becoming highly statistically significant. These results are generally in line with what we expect from the literature. Schimmelpfennig found a statistically significant reduction in farmers’ input production costs as a result of adopting yield monitors; he also noted that farm size was an important determinant of the adoption of precision agricultural technologies as a whole [20]. McFadden et al. also found yield maps—generated from the data collected by yield monitors—increase agricultural efficiency from 6 to 12 percent, though the impact depended on both farmer demographics and field characteristics (such as land tenure and insurance). They also found substantial heterogeneity in where yield monitors were adopted [46]. Our results appear to conform to these findings and may also suggest an indirect linkage between weather variability and field variability. The adoption of different farm management practices in response to climate change could generate sufficient uncertainty such that feedback from yield monitors would prove valuable.

We have specific data on whether farmers relied on yield monitor results to add or improve their tile drainage in the survey year. In our unadjusted regressions, the impact of adding or improving tile drainage (installation or improvement) on productivity is mixed. Northern states appear to benefit from tile drainage, while southern states become less technically efficient. The overall impact is negative, and only the coefficient for southern states is statistically significant. After controlling for weather, the relationship becomes positive across all three regressions. The significance of the coefficient changes—northern states (and the country) become highly statistically significant, while the South becomes insignificant. The benefits of tile drainage should increase as precipitation becomes heavier (exceeding the natural drainage rate of soil) or if the timing becomes unfavorable (i.e., it impedes machinery operation). As we can see in our Oury index maps, Northern states have a generally higher Oury index (and variation in the index) than Southern states. Prior to weather-adjusting our TE estimates, southern farms that adopt tile drainage appear to be less efficient—possibly because farms that need to adopt tile drainage are at a relative climatic disadvantage in the region. However, when we control for weather and compare between farms with similar climates, tile drainage becomes a technical improvement to farm efficiency. In the north, farms without tile drainage may be the ones at a disadvantage instead.

Fallowing serves several purposes: it can disrupt pest habitats, it will gradually replenish soil nutrients, and it can increase the accumulation of soil moisture prior to the next planted crop. Longer periods of fallowing can also improve soil structure and aggregation. We may expect greater levels of fallowing under certain climate conditions; specifically, farmers that face higher temperatures or greater variation in precipitation may leave fields fallow to stockpile soil moisture for next season. In our unadjusted regressions, the coefficient on fallowing is positive across all regressions but statistically insignificant in the regional specifications. This aligns with our expectations, as fallowed soil should indeed be more productive, holding other attributes constant. In addition, the “cost” in this case is foregone profits in the previous year rather than purchased inputs in the current one. When we control for weather effects in our productivity estimates, the coefficient on fallowing becomes statistically significant and increases across all regions, particularly in the south. As our Oury index map indicates, Southern states have lower precipitation relative to temperature as compared to the North and thus would likely see larger benefits.

We expect productivity to increase with quality of land; this may include better soil fertility, access to markets, or local climate, and we would therefore expect the regression coefficient to be positive. It is not immediately clear what effect we might expect our weather adjustment to have on this coefficient. It is also possible that an individual farmer’s rent may reflect their proximity to urban areas, which could introduce a biasing issue. A priori, we have no reason to assume urban proximity would have either a positive or negative effect on farm productivity; however, if there is some correlation between proximity and productivity, it may attenuate or exaggerate our results. Our unadjusted results indicate that the linkage between rent and productivity is mixed. The South has, as expected, a positive, statistically significant relationship, while the North is both negative and insignificant; the result for the country as a whole lies close to zero (and, like the North, is also insignificant). When we run this regression using our adjusted productivity estimates, the relationship reverses in the North and becomes statistically significant, conforming to our expectations. The coefficient on Southern states decreases, but only slightly. If rental price reflects the quality of land—and assuming there is no proximity effect—then this may suggest higher-quality land is disproportionately impacted, either in the incidence of adverse weather effects or their financial magnitude.

Conservation tillage is positive across all regression specifications and statistically significant in all but one; additionally, when we use the weather-adjusted estimates, the magnitude of our coefficient increases. We note that existing literature is primarily concerned with how conservation tillage affects crop yields directly; studies indicate that whether conservation tillage improves yields depends primarily on soil compaction and weather conditions (heat and drought) [47]. However, as our results address productivity, they are not directly comparable. No-till and conservation tillage practices reduce fuel expenditure and wear and tear on machines; as long as this is sufficient to offset potential yield loss, then these results are consistent with what we would expect. In the weather-adjusted scenario, they may also mitigate some of the impact of water- or wind-driven soil erosion. It is also important to note that there are also programs that offer financial incentives to farmers that adopt conservation tillage practices, which may bias our regression results.

Replanted acreage measures the amount of acreage in a state that had to be replanted for any reason; multiple replantings on the same field are added together. Replanting acreage typically occurs when there is early-season plant damage, such as freezing conditions in late spring. The coefficients of this variable are significantly negative across almost all regression specifications and cross regions. This result is expected given that more inputs were used, which resulted in lower productivity performance.

As contour farming and terracing are means of maintaining soil quality on erosion-susceptible land, returns on these practices are likely to be positive but potentially delayed, and the magnitude will depend on land and climate characteristics. Returns will be largest on fields with high-quality soil, steeper gradients, and heavier precipitation. Based on this, it is not immediately clear what relationship these variables will have with TE in our unadjusted regression, but we expect them to increase after adjusting for weather [48,49,50]. Prior to adjusting for weather, contour farming is of mixed statistical significance but is negative in both regions (and overall). However, our post-adjustment coefficients are all positive and statistically significant. This pattern seems to support our initial expectations regarding their post-adjustment shift and possibly suggests that contour farming is adopted by farmers that are subject to heavier precipitation events (and thus greater risk of soil erosion). In contrast, our terracing coefficient is only significant in the northern states, both pre- and post-adjustment. Curiously, the downward shift in all coefficients after controlling for weather effects suggests farms that adopt terracing are systematically disadvantaged in comparison to other farms, and that climate heterogeneity somehow masks this effect. On the other hand, given that contour farming and terracing are both adopted for similar purposes, it is possible this result is simply an artifact of multicollinearity.

4. Conclusions

The main purpose of this paper is to understand the potential determinants of sustainable field crop farm productivity. We assume a multi-input, multi-output production technology in this study and evaluate the effects of arid climate on farm-level productivity using a stochastic input distance function. We then assess the impact of various technologies and farm practices on field crop farm productivity based on TFP measures with and without weather-effect adjustment. Our data are drawn from both Phase 2 and Phase 3 of the USDA Agricultural and Resource Management Survey between 2006 and 2020. Results show that an increase in average moisture condition has the consistent effect of reducing the distance between crop farms’ productivity performance and their best practices since 2010; however, their reaction to unexpected weather shocks appears to be oscillating from year to year (though the scale of variation is converging).

With regard to the impacts of technology adoption and farm practices, we find that adjusting efficiency measures for local weather conditions generally makes the estimated impacts on efficiency more statistically significant and the signs of the coefficients are more reasonable (more aligned with expectations). It implies that adjusting for weather effects in productivity estimates is relevant. For example, a 100% increase in contour farming is estimated to reduce technical efficiency by about 0.4% before accounting for weather effects, but that flips to increasing technical efficiency by about 0.5% when weather conditions are accounted for. Based on the weather-adjusted productivity regression results, yield monitoring technology adoption can promote farm productivity, especially in the Southern region, while variable rate technology does not have a significant impact on crop farm productivity. Some farm practices, such as cover cropping, fallowing, conservation tillage, tile drainage, and contour farming, show positive impacts on crop farm productivity. However, the results vary between the Northern and the Southern regions given their distinct weather conditions, climate trends, and crops grown. Land rent seems to be a good proxy for land quality, as higher land rent has a positive impact on farm productivity. The major driver of long-run productivity growth is innovation, including technological and managerial improvement, and accurately accounting for environmental conditions like weather is necessary when evaluating the productivity of sustainable agriculture practices.