The Impact of Drainage Water Management Technology on Corn Yields

The Impact of Drainage Water Management Technology on Corn Yields Crop Economics, Production & Management

Benoit A. Delbecq,* Jason P. Brown, Raymond J. G. M. Florax, Eileen J. Kladivko, Adela P. Nistor, and Jess M. Lowenberg-DeBoer Abstract

Controlled drainage (drainage water management) restricts outflow during periods of the year when equipment operations are not required in the field. This may increase yields as well as reduce the loss of nutrients with negative environmental externalities. An experiment using controlled drainage was investigated and its impact on corn (Zea mays L.) yields was assessed at the field level in Indiana. Specifically, yield monitor data was analyzed across space and time using a geographic information system and spatial panel regression methods. The use of panel data methods controlling simultaneously for spatial and temporal heterogeneity as well as dependence provides precision agriculture researchers with a powerful framework to model crop sensor data across space and time. During the period 2005 to 2009, controlled drainage was found to outperform free-flow systems by an average of 0.57 to 1.00 Mg ha–1 (5.8–9.8% across the effective range of 0–0.61 m above the water control structure) for the experimental field; however, these aggregate results masked substantial year-to-year and within-field variations.

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ontrolled drainage (drainage water management) restricts outflow from tile lines in crop fields during periods of the year when equipment operations are not occurring. This may increase yields as well as reduce the loss of nutrients with negative environmental externalities. The magnitude of the yield gains or losses due to controlled drainage is of key interest to farmers, drainage contractors, and other agribusinesses, but very few studies have attempted to measure these yield changes. This study estimated the impact of controlled drainage on corn yields at the field level in Indiana. Combine yield monitor data were analyzed across space and time using a geographic information system (GIS) and spatial panel regression methods. Although water is a vital component for plant development, both excess and lack of water at critical stages of growth can result in irreversible crop damage and consequently yield losses. There is a direct cause-and-effect relationship between drought and plant stress, which can be managed through irrigation systems. Overly wet soil conditions may affect crop yields through various indirect B.A. Delbecq, Market and Trade Economics Division, USDA Economic Research Service, 355 E St. SW, Washington, DC 20024; J.P. Brown, Resource and Rural Economics Division, USDA Economic Research Service, 355 E St. SW, Washington, DC 20024; R.J.G.M. Florax, Dep. of Agricultural Economics, Purdue Univ., 403 West State St., West Lafayette, IN 479072056, and Dep. of Spatial Economics, VU Univ. Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, the Netherlands, and the Tinbergen Institute, Amsterdam, the Netherlands; E.J. Kladivko, Dep. of Agronomy, Purdue Univ., 915 West State St., West Lafayette, IN 47907-2054; A.P. Nistor, Tutorheight, 5789 Glen Erin Dr., Mississauga, ON, Canada L5M 5J9; and J.M. Lowenberg-DeBoer, Dep. of Agricultural Economics, Purdue Univ., 615 West State St., West Lafayette, IN 47907-1168. The views expressed here are those of the authors and may not be attributed to the Economic Research Service or the USDA. Received 4 Jan. 2012. *Corresponding author ([email protected]). Published in Agron. J. 104:1100–1109 (2012) Posted online 4 June 2012 doi:10.2134/agronj2012.0003 Copyright © 2012 by the American Society of Agronomy, 5585 Guilford Road, Madison, WI 53711. All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

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channels. A review by Evans and Fausey (1999) highlighted the challenges of soil trafficability, timeliness of field operations, growth and development of roots under low soil O2 conditions, and waterlogging effects on both shoot and root growth. In regions or fields with high water table soils, surface and subsurface drainage systems are essential for agricultural production. Conventional drainage targets the water table depth at a specific level all year, regardless of weather conditions. Temperate climates are characterized by seasonal patterns creating alternating periods of wet (during the winter) and dry (during the summer) conditions determined primarily by the offsetting effects of precipitation and evapotranspiration. Although conventional, or free-flow, drainage is well suited to deal with periods of excess water, the maximum drainage intensity is not usually needed during all times of the year. Controlled drainage, or drainage water management, provides the opportunity to conserve water during the growing season while providing maximum drainage during critical field work or crop establishment time periods (Skaggs, 1999). Control structures are placed near the tile drain outlet, and “stop-logs” are inserted or removed to adjust the outlet depth. By giving more flexibility to the farmer in terms of water management, controlled drainage is expected to improve yields over conventional drainage (Evans et al., 1996). The primary objective of this study was to provide empirical evidence supporting, or refuting, the anticipated yield benefits of controlled drainage for a corn field in Indiana. Specifically, we tested the following two hypotheses: (i) controlled drainage increases average yields with time, and (ii) the magnitude of the yield advantage will vary widely from year to year. Policymakers have shown increasing interest in drainage water management systems because of environmental considerations. There have been growing concerns that high concentrations of nutrients in rivers from anthropogenic sources foster algal production in coastal ecosystems, eventually causing eutrophication. Free-flow drainage systems are thought to be responsible Abbreviations: DPAC, Davis Purdue Agricultural Center; GIS, geographic information system; RE, random effects; RE-ERR, spatial error random effects.

A g ro n o my J o u r n a l • Vo l u m e 10 4 , I s s u e 4 • 2 012

for facilitating and accelerating the downstream transport of soluble chemicals used in agriculture, primarily nitrates. Numerous studies have investigated the effects of controlled drainage on nutrient losses, starting in the early 1970s. A review by Evans and Skaggs (1996) concluded that nutrient concentrations are, for the most part, unaffected within the tile network but that regulating water outflow successfully reduces downstream pollution (see also Wesström et al., 2001; Ma et al., 2007). Given the well-documented environmental benefits, there is an incentive for public authorities to encourage farmers to invest in drainage water management. The water quality and soil quality effects of the project to which the present study is attached were presented in Adeuya (2009) and Utt (2010). Farmers are economic agents and are hypothesized to maximize profits, among other objectives. Many farmers will not invest in technologies unless the installation costs are outweighed by the discounted stream of expected additional revenues, which are in turn directly linked to the expected change in yields. A full cost–benefit analysis using estimates of the yield premium is needed to make a case in favor of controlled drainage to farmers. Brown (2006) and Nistor (2007) are the only examples of such an analysis in the publicly available literature. As experience with controlled drainage accumulates, it will become possible to estimate yield distributions with the practice and risk-adjusted returns. There are only a few studies of the effect of controlled drainage on crop yields. Yield increases are well documented with subirrigation, but results are less clear-cut when only naturally occurring water is retained by the controlled drainage system (e.g., Sipp et al., 1986; Cooper et al., 1991; Drury et al., 1997; Fisher et al., 1999; Ng et al., 2002). Evans and Skaggs (1996) stated that, in the long run, controlled drainage generated average yield increases of 2 to 5% above yields with a conventional drainage system for a crop such as corn in North Carolina. Tan et al. (1998) presented a study for Ontario, Canada, which showed that controlled drainage increased average soybean [Glycine max (L.) Merr.] yields 12 to 14% above free-flow drainage in a conventional tillage system but decreased yields in no-till systems. Nine out of 15 farmers involved in a central Illinois drainage management project reported higher yields with controlled drainage (Pitts, 2003). Not all studies show yield benefits from controlled drainage, however. Sipp et al. (1986) in Illinois, Grigg et al. (2003) in Louisiana, and Fausey et al. (2004) in Ohio did not find any significant difference in crop yields between controlled and conventional drainage. All of the above studies used small-plot or whole-field data, with the crop transferred from the combine harvester to a weigh wagon and subsequent analysis being based on comparing treatment trials or performing an analysis of variance. Effectively, this implies that it is a priori assumed that the distribution of yields across the field is homogenous and independent of location. Geo-referenced yield monitor data allow relaxation of this assumption by forming a direct tie between a yield measure and a location in the field. Some of the earliest studies using yield monitor data have estimated and compared site-specific crop response functions using multivariate regression analysis (e.g., Malzer et al., 1996; Wendroth et al., 1999; Nielsen et al., 1999). These applications relied on linear regressions estimated with ordinary least squares and therefore implicitly assumed

independent and identically distributed errors (Kessler and Lowenberg-DeBoer, 1999; Bakhsh et al., 2000); however, Kessler and Lowenberg-DeBoer (1999), Lambert et al. (2004), and Anselin et al. (2004), among others, showed that this is an erroneous assumption and that yield monitor data are typically heterogeneous and spatially dependent in nature. Spatial econometric techniques were originally developed in economics and quantitative geography to deal directly with these issues, and a number of studies have estimated such models to investigate crop responses (Bongiovanni and Lowenberg-DeBoer, 2000, 2002; Liu et al., 2006). Likewise, statistical inference from spatially correlated data has a long history in the agronomic literature, starting with the nearest neighbor approach described by Papadakis (1937) and refined by Bartlett (1978). Geostatistical techniques, such as variogram modeling, also have a preponderant place in agronomic analysis (Ruffo et al., 2006). Bullock and Lowenberg-DeBoer (2007) provided a recent review of studies using spatial statistical analysis techniques applied to precision agriculture data. Only two studies have previously explicitly attempted to model the impact of controlled drainage on crop yields, focusing specifically on corn. Brown (2006) applied spatial econometric techniques to cross-section yield monitor data from 2005 for four farms located in White, Montgomery, and Randolph counties in Indiana. Using spatial error regression models for the estimation of yields as a function of linear, quadratic, and interaction terms including elevation, slope, distance to the nearest tile line, and infrared soil color, controlled drainage was found to impact yield in the range of 0.5 to 1.82 Mg ha–1. Nistor (2007) proposed a framework to model crop sensor data with time by using spatial fixed and random effects panel data models. The use of spatial modeling techniques for replicated yield measurements with time is motivated by the fact that precision agriculture data are measured at such a high spatial density that spatial clustering is inherent. In addition, the precision agriculture literature has shown that a yield response can vary substantially from year to year (Cooper et al., 1991; Mejia et al., 2000). Yield response functions are therefore perfectly suited to analysis utilizing spatial panel data sets, allowing for spatially clustered error patterns as well as response variation with time. A panel data set consists of a sequence of observations repeated through time on a set of units (e.g., fields, farms, or countries). Traditional panel data models used in applied research are the fixed effects and random effects (RE) models (Baltagi, 2005). A panel data regression is different from a time-series or crosssection regression in that it considers both the temporal and the cross-sectional dimensions. Panel data offer researchers extended modeling possibilities compared with purely cross-sectional or time-series data because they contain more information, more variability, less collinearity among variables, and more degrees of freedom, and hence the estimators are likely to be more efficient (Baltagi, 2005). Panel data can also reduce the effect of omitted variable bias by controlling for (unobserved) individual heterogeneity through fixed or random effects. Time-series and crosssection studies not controlling for this heterogeneity run the risk of obtaining biased results (Moulton, 1986).

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MATERIALS AND METHODS Experimental Design This study was designed as a split field experiment (see Frankenberger et al., 2005, for details). The general idea was to compare two areas similar in characteristics and management except for a specific treatment of interest, in this case controlled drainage. This study focused on yield monitor data from the Davis Purdue Agricultural Center (DPAC), Field W, located in Randolph County, Indiana. Corn yield data collected in the pre-experimental period (1996–2003) served as a calibration period. Soybean was grown in 2004 to facilitate drainage system

installation, and thus no yield data were collected. The controlled drainage system was operational for the 2005 growing season and beyond. The panel data approach allowed the calibration data and the experimental data to be analyzed in a common framework and therefore made use of the maximum information available. Through 2003, Field W on the DPAC farm was cultivated under a corn–soybean rotation, but 2005 marked a transition into corn monoculture. Both the east and west sides grew corn in 1996 and 1998 and soybean in 1997 and 1999. In 2000, a fertility experiment was conducted on the field and thus the corn yield data could not be used for calibration of the panel approach. From 2001 through 2003, the corn–soybean rotation was in opposite phases on the east and west sides of the field, while in 2004 the entire field was managed to facilitate drain installation only. Thus corn calibration data were available in 1996, 1998, and 2002 for the east side and 1996, 1998, 2001, and 2003 for the west side of the field. The difference in farming practices and cultivation history motivated the separate analysis of the two sides. Following the split field approach, controlled drainage was installed only on the northern half of the west side and the southern half of the east side of the field. Soil types in the field included naturally poorly drained silt loams and silty clay loams of the Blount, Condit, Glynwood (fine, illitic, mesic Aeric and Typic Epiaqualfs and Aquic Hapludalfs), and Pewamo (fine, mixed, active, mesic Typic Argiaquolls) series. Data Collection and Treatment

Fig. 1. Processing of data from Davis Purdue Agricultural Center, Field W, 2008: (a) raw yield data points as exported from the combine yield monitor; (b) yield data after the cleaning process in Yield Monitor and ArcGIS 9.3; (c) yield data aggregated into a 5- by 5-m grid.

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Yield data were collected “on-the-go” during harvest, with a yield monitor linked to a global positioning system mounted in the combine. The “raw” yield data were exported as a map on which each point, characterized by its coordinates (longitude and latitude), represented the measured yield for a small surface surrounding each point (Anselin et al., 2004; Griffin et al., 2005). The “raw” yield values were computed by an algorithm that combined information on grain flow in the machine, grain moisture, combine speed, and swath width. Measurement errors linked to these “combine dynamics” are frequent and jeopardize subsequent quantitative analysis (for a detailed treatment of combine dynamics and yield monitor data analysis, see Lark and Wheeler, 2003). Questionable observations were removed from the raw yield monitor data using filtering algorithms in Yield Editor (Sudduth and Drummond, 2007) and manual cleaning in ESRI ArcGIS 9.3. Because the points of the raw yield data were closer within the row than between rows, a grid composed of squares of width equal to the average combine pass (approximately 5 m during the experiment) was laid over the yield monitor data. Each cell value represented the average yield of all points contained within that square. In effect, this created a data set that was spatially balanced in all directions. Figure 1 illustrates the main steps of this process for the 2008 harvest on Field W. Previous applications of this methodology can be found in Mamo et al. (2003) and Anselin et al. (2004).


Data aggregation was performed using the same grid each year, thus producing a balanced panel data set that enabled us to compare yields for different years in the “same” location. Because of cleaning the data in this fashion, some grid cells did not intersect with any yield points for some years. These cells were removed from the grid and, as a consequence, some data were lost for the remaining years. The balanced design thus obtained facilitated the use of a spatial regression approach (Anselin et al., 2004). Moreover, because the prediction error for the average values of yields within grids is smaller than the prediction error for any yield point prediction, the precision of the average yield estimator is higher than that of the point estimator (Haining, 2003); however, this procedure also introduced heteroskedasticity because the variance of the mean yield was not constant (see below for more detail on this). Empirical Model

Fig. 2. Relative elevation and controlled water management experimental design for Field W at the Davis Purdue Agricultural Center.

The selection of variables and the specification of the crop yield functional form are always difficult due to the complexity of the yield response (Swanson, 1963; Florax et al., 2002; Anselin et al., 2004). Nistor (2007) reviewed issues specific to the selection of variables and a functional form for drainage response functions. For this application, a simple linear form with interaction variables was chosen because only a limited number of variables were available in the data. For on-farm yield trials, elevation and rainfall are the most commonly available variables. Yearly precipitation data for the DPAC farm were collected but did not vary within the field. Time dummy variables can be interpreted as capturing primarily weather factors, specifically rainfall. Elevation point data with reference to the sea level, collected by topographic surveys performed by contractors for the farm, were interpolated using the inverse distance weighted power 1 method, so that a point data set was obtained with elevation across the whole field. Each grid cell was assigned the average of the elevation points that fell within its boundaries and was converted with reference to the lowest elevation level in each side of the field (elevfld). The resulting relative elevation map is shown

in Fig. 2. Because Field W is relatively flat (around 1% slope) and because controlled drainage affects mainly subsoil water, slope was not a useful explanatory variable. Inspection of this map reveals a general northwest–southeast upward slope for the east side as well as the west side. This is confirmed by Tables 1 and 2, which give summary statistics for the elevfld variable. The southern half is, on average, 0.58 and 0.34 m higher than its northern counterpart for the west and east sides, respectively. All parts of the field needed tile drainage, but installing the controlled drainage system in the southern and lowest part of the field on one side (west) and the northern and slightly higher part of the field on the other side (east) is part of the experimental design. Pivotal characteristics of the specification used in this study were as follows. First, elevfld was allowed to have a nonlinear effect on yields by letting elevation enter the model as a logarithmic term. This was motivated by the idea that low spots in a field are commonly wet and hence detrimental to plant growth in wet years but beneficial to yields in dry years (Kravchenko

Table 1. Corn yield and relative elevation (elevfld) at the Davis Purdue Agricultural Center, Field W, east side. Corn yield Parameter

Min. Max. Mean SD Min. Max. Mean SD Min. Max. Mean SD

1996 1998 2002 2005 2006 2007 2008 2009 ————————————————————————————— Mg ha–1 ————————————————————————————— Controlled 3.70 7.06 0.63 4.85 6.05 2.07 6.63 6.63 8.23 11.84 6.60 13.93 13.77 9.64 14.93 16.19 6.19 9.05 2.85 10.91 10.82 6.72 12.04 12.13 0.82 0.94 1.22 1.40 1.27 1.41 1.41 1.89 Uncontrolled 2.95 4.78 0.70 4.94 6.64 3.14 6.90 5.80 8.23 12.56 6.16 14.90 13.71 10.22 15.03 16.32 6.10 9.05 3.18 9.65 10.99 6.70 12.02 11.82 0.75 1.07 1.17 1.85 1.23 1.26 1.45 2.13 Whole field 2.95 4.78 0.63 4.85 6.05 2.07 6.63 5.80 8.23 12.56 6.60 14.90 13.77 10.22 15.03 16.32 6.14 9.08 3.01 10.29 10.90 6.71 12.03 11.98 0.79 1.01 1.21 1.76 1.25 1.34 1.43 2.02


elevfld m 0.51 1.97 1.13 0.32 0 1.43 0.79 0.37 0 1.97 0.97 0.38

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et al., 2003). As elevation increases in the field, natural drainage occurs and plant growth is improved up to a point. Beyond a certain elevation level, however, the water table is harder for the roots to reach and yields are expected to decrease because the plant is unable to fulfill its water needs. Such a profile of the effect of elevation on yields would ideally call for a monotonically increasing (or decreasing) function that eventually reaches a plateau. Using such a nonlinear functional form would render estimation unfeasible given the linear regression framework used here. Therefore, a logarithmic transformation of elevation, which behaves in a similar fashion, was used. Second, the controlled drainage treatment was incorporated in the model as a dummy variable that took the value 1 for cells where the control system was in place in a specific year and 0 otherwise. Given this construct, the advantages or disadvantages of drainage water management were measured in comparison to the “benchmark” free-flow drainage. This binary variable was interacted with the time dummy variables to account for probable differential impacts of controlled drainage across years (Nistor and Lowenberg-DeBoer, 2007). In other words, the controlled drainage setup was expected to either benefit, hurt, or have no effect on yields in response to varying environmental conditions. Finally, elevation above the soil surface at the control structure (elevstr) was anticipated to be a critical factor in the impact of drainage water management on yields (Frankenberger et al., 2006). As an illustration, assume that the water table is set 0.3 m (12 in) below the surface in the control box. For field positions located 0.61 m (2 ft) higher in elevation, the water table set point would be 0.91 m (3 ft) below the soil surface, which for this field (and many others in Indiana) is the approximate depth of the tile drain. Thus the control structure will only have the potential to affect yields within approximately a 0.61-m elevation change from the control structure (Frankenberger et al., 2006). The “effective range” of the controlled drainage practice was thus defined as the field area within 0 to 0.61 m above the control structure. This elevation threshold for treatment effects is not fixed but depends on water availability and stop-log height. This is why the response of controlled drainage to this variable was further expected to vary from one year to another. This called for a three-way interaction between the controlled drainage binary variable, the year dummy

variables, and elevstr. The proposed mechanism was that in relatively drier years, controlled drainage would allow the retention of more water than conventional drainage and hence favor plant development at points close to the control structure. This advantage was expected to deteriorate as elevation increased, as described above, until it eventually evened out. Alternatively in comparatively wetter years, controlled drainage might lead to submerging the root system at low elevations above the control structure, in which case free-flow drainage would have more satisfactory results. The full explanation is likely to be more complex than this clear-cut wet–dry distinction because not only the quantity but also the timing of precipitation matters and drainage water management allows the farmer to fine tune the water table level in response to field and weather conditions. The nonlinearity of the relationship between elevstr and the controlled drainage dummy variable was captured by using the logarithm of this variable. With the inclusion of these interaction variables, the model to be estimated was yieldt =a + å b1t yeart + å b2t drain ( yeart ) t

+ g1 log(elevfld)

t

[1]

+ å g 2t drain ( yeart ) log(elevstr) +et t

where yieldt is average yield per grid cell in the tth year, yeart is the time dummy variable for the tth year, drain is the controlled drainage binary variable, elevfld is elevation above the lowest point in Field W, elevstr is the distance between the control structure and the soil surface, and e t is an error term. Given the definition of elevfld and elevstr, each variable has the value 0 at its respective point of reference. To remedy the resulting issue of an undefined logarithmic transform, zero values were replaced at those two points by half the elevation of the next highest point. As a robustness check, the traditional fix consisting in adding arbitrary constants (e.g., 1, 0.1, 0.01, 0.001) was also experimented with but did not qualitatively alter the conclusions of our analysis. The use of dummy variables conveniently led to a three-factor interpretation of this model. The intercept captured the level of corn yield at an elevation 1 m above the lowest point of the focus field [log(elevfld) = 0] in 1996, i.e., under conventional

Table 2. Corn yield and relative elevation (elevfld) at the Davis Purdue Agricultural Center, Field W, west side. Corn yield Parameter

Min. Max. Mean SD Min. Max. Mean SD Min. Max. Mean SD

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1996 1998 2001 2003 2005 2006 2007 2008 2009 ————————————————————————————— Mg ha–1 ————————————————————————————— Controlled 2.00 6.63 6.53 3.53 4.94 5.39 3.23 6.71 6.96 7.45 12.54 14.25 11.58 12.96 13.83 9.47 14.72 16.75 5.11 9.46 11.11 8.60 9.43 10.50 6.90 12.28 12.17 1.14 1.23 1.23 1.40 1.38 1.37 1.02 1.29 1.70 Uncontrolled 2.20 3.49 7.01 3.23 5.60 5.10 3.24 7.79 6.86 7.56 13.05 14.54 11.83 13.14 13.55 8.83 14.79 16.06 5.60 8.67 11.00 7.73 9.79 9.74 6.54 11.86 11.65 0.82 1.40 1.17 1.77 1.19 1.51 1.16 1.30 1.70 Whole field 2.00 3.49 6.55 3.23 4.94 5.10 3.23 6.71 6.86 7.56 13.05 14.54 11.83 13.14 13.83 9.47 14.79 16.75 5.34 9.09 11.06 8.19 9.60 10.14 6.73 12.09 11.93 1.03 1.37 1.20 1.64 1.30 1.49 1.10 1.31 1.72

elevfld m 0 1.19 0.52 0.26 0.30 2.18 1.10 0.45 0 2.18 0.80 0.46


drainage. Each year dummy variable represented the average yield premium or loss resulting from the conditions in which the crop was cultivated during a particular year. The controlled drainage binary variable and the related interaction terms further refined the yield response decomposition by quantifying the benefits of controlled water management over free-flow drainage. Strictly speaking, this dummy variable captured everything that is specific to the controlled portion of each field during the course of the project. Note that the formulation of Eq. [1] is mathematically equivalent to an expression in which the drainage dummy and the two omitted double interactions drain ´ log(elevstr) and year ´ log(elevstr) would be included. In view of the data aggregation procedure based on calculating average yields for data points contained in each grid cell, the variable on the left-hand side was the average or expected yield rather than the actual yield. This implied that the model in Eq. [1] was inherently heteroskedastic because the variance of the mean varied over grid cells. The left- and right-hand side of Eq. [1] was scaled by the standard error of the mean yield for each grid cell. When only a single data point fell into a grid cell, the standard error of the mean for that cell did not exist. Therefore it was replaced by the average standard error of the mean across all grid cells for the corresponding year. The effect of controlled drainage on corn yields was, however, the result of a combination of factors that was accounted for by adding interaction terms with the elevstr variable. Additional steps were necessary to obtain appropriate marginal yield effects with associated statistical tests. Because the controlled drainage variable is a dummy variable, the marginal effects for the tth year were calculated as

yieldt

drain =1

- yieldt

drain =0

=

b2t + g 2t log (elevstr )

[2]

By averaging the b2t and g 2t coefficients and plugging in each cell’s elevation above the surface of the control structure (elevstr), the mean marginal effects of controlled drainage during the period 2005 to 2009 were obtained. Equation [2] highlights the fact that these marginal effects should not be interpreted as absolute but in comparison with the experimental benchmark, namely free-flow drainage. This is implied in the expression “marginal effects of controlled drainage.” Confidence intervals at the 95% level are reported for each marginal effect (details of the derivations are available on request). Interpretation of these confidence intervals is twofold. First, they indicate whether the marginal effect is statistically different from zero. If insignificant, it can be inferred that controlled drainage did not make a difference over free-flow systems at the specific corresponding time–elevation combination. Second, confidence intervals provide an indication of the margin of error for each marginal effect calculation. Spatial Panel Model Contemporaneous spatial clustering between observations at each point in time and spatial heterogeneity (i.e., parameter variation across space) may arise when panel data include a locational component (Anselin, 1988; Elhorst, 2010). Spatial clustering was controlled for by estimating a spatial version of panel models that

allows for spatially autocorrelated errors. Anselin et al. (2008) and Elhorst (2010) provided overviews of specifications and estimators available for spatial panel data. The most general form of spatial error random effects models allows for spatial autocorrelation of both the individual heterogeneity and residual error components, the magnitudes of which may differ. This model, proposed by Baltagi et al. (2009) and henceforth called BEP after the names of the three authors, is expressed as follows for each time period t:

y t = X t b + ut , u t = u1 + u2t u1 = r1 WN u1 +m ,

t = 1, ,T m ? N (0, sm2 )

[3]

u2t = r2 WN u2t + ut , ut ? N (0, s2u ) where yt is a vector of N observations of the dependent variable and X t is an N ´ K matrix of exogenous variables including an intercept with its corresponding vector of coefficients b. The vector of errors ut is composed of two spatially autocorrelated components, one time-invariant and unit-specific u1, and one time-varying u2t. The BEP model assumes that both spatial processes are subject to the same neighborhood structure, i.e., an N ´ N weight matrix WN, but it allows for different spatial autocorrelation parameters r1 and r2 , respectively. A spatial weight matrix is an exogenously defined mathematical construct that contains information on which locations are treated as neighbors within the spatial system; WN is subject to the standard regularity conditions and is normalized in such a way that its rows sum to one. It is further assumed that the elements of m are independent across i = 1, …, N, the elements of u t are independent across i and t, and they are also independent of each other. Three other random effects models can be obtained by imposing restrictions on the spatial autocorrelation parameters. By setting r1 = r 2 , the strength of the two spatial processes is imposed to be equal, leading to the KKP model (Kapoor et al., 2007). Fixing r1 = 0 yields the simplest form of the spatial error random effects (RE-ERR) model in which only the disturbances are assumed to be correlated across space (Anselin, 1988). Finally, the non-spatial random effects (RE) model is recovered by setting r1 = r 2 = 0. The BEP model can be estimated by maximizing the log-likelihood function derived by Baltagi et al. (2009) (see Appendix). Given the nested nature of the four models and the maximum likelihood estimation framework, likelihood ratio (LR) tests were used to determine the preferred specification for the analysis of each of the panel data sets (Baltagi et al., 2009). Alternatively, Baltagi et al. (2009) derived a set of Lagrange multiplier specification tests, which are asymptotically equivalent to the LR tests. Specifically, the three null hypotheses H0,KKP:r1 = r2 , H0,RE-ERR:r1 = 0, and H0,RE:r1 = r2 = 0 were tested separately against the alternative H1,BEP:r1 ¹ r2 ¹ 0. In practice, all four models were estimated and the likelihood ratio test statistic, LR m, was calculated as


LR m =-2 (LLU - LL R ,m ),

with m = KKP, RE-ERR, RE

[4] 1105

where LLU is the unrestricted (BEP) log-likelihood and LLR,m is the log-likelihood of the respective restricted models. Under the null hypotheses, LR m asymptotically follows a cq2 distribution, where q is the number of tested restrictions (two for the KKP model and one for both the RE-ERR and RE models). Estimation and testing were performed with the open-source statistical environment R (R Development Core Team, 2010) using self-programmed scripts. Spatial panel techniques allowed temporal and spatial heterogeneity as well as spatial dependence to be incorporated and hence they permitted isolation of the effect of controlled drainage on yields. RESULTS AND DISCUSSION The mean corn yield was fairly stable with time, except for 1996 (weed problems), 2002 (severe drought), and 2007 (Tables 1 and 2). Examining figures during the calibration period (i.e., before 2005) may give an indication of inherent yield potential differences between the conventional and controlled portions of each side of Field W. With only 3 yr of data for the east side, there was no discernible pattern. For the west side, however, the portion of the field that was set up for drainage water management exhibited higher yields three out of the four calibration years. A comparison of yields under controlled and conventional drainage after 2005 for both sides did not lead to conclusive evidence, although the former seemed to have a tendency to be higher. The results of the LR tests pointed to the BEP model for both sides of the field (Table 3). A quick glance at Table 3 reveals that all but a few coefficients were statistically significant. Although statistical significance of the spatial autocorrelation parameters cannot be tested, both ρ1 and ρ2 were positive and substantial, suggesting the presence of positive spatial autocorrelation in the omitted location characteristics (random effects) as well as other non-location-specific factors. This result revealed how relevant it is to control for spatial autocorrelation in econometric analyses of yield monitor data to obtain accurate statistical inference. With the presence of interaction terms for each of the explanatory variables, interpretation of estimated coefficients as marginal effects is complicated. Regression coefficients, however, are meaningful by themselves. For instance, the coefficient estimates on the yearly binary variables were interpreted as the yield advantage (or disadvantage) for the conventionally drained part of the field due to unobserved parameters specific to each year, using 1996 as a reference. The estimated coefficients corroborated the yield summary statistics presented in Tables 1 and 2. Table 1 shows that 1996 was the worst year for the west side of Field W, which was captured by all yearly dummy variables showing positive coefficients, the largest of all being for 2008. The situation for the east side of the field was identical except for the drought year 2002, which translated into a negative coefficient on the corresponding dummy variable. Table 4 summarizes the marginal effects for all 5 yr, individually as well as for the total period, at four different elevations (minimum and maximum of the effective range and two arbitrarily chosen intermediate values) in the controlled area of each side of the field. By design, notable differences were not anticipated between controlled and free-flow drainage beyond 0.61 m above the control structure. The results presented in Table 4 allowed a test of the two stated hypotheses. First, on average during the period 2005 to 1106

Table 3. Estimation results for Davis Purdue Agricultural Center, Field W, via the BEP model (Baltagi et al., 2009). Regression coefficient Parameter† Intercept Year1998 Year2001 Year2002 Year2003 Year2005 Year2006 Year2007 Year2008 Year2009 Log(elevfld) Year2005 ´ drain Year2006 ´ drain Year2007 ´ drain Year2008 ´ drain Year2009 ´ drain Year2005 ´ drain ´ log(elevstr) Year2006 ´ drain ´ log(elevstr) Year2007 ´ drain ´ log(elevstr) Year2008 ´ drain ´ log(elevstr) Year2009 ´ drain ´ log(elevstr) Spatial autocorrelation parameter r1 Spatial autocorrelation parameter r2 Likelihood ratio test vs. random effects Likelihood ratio test vs. spatial error random effects Likelihood ratio test vs. KKP model

West side (n = 1841) 5.12*** (0.02)‡ 3.76*** (0.02) 5.84*** (0.09)

East side (n = 2034) 6.08*** (0.02) 2.72*** (0.02) –4.42*** (0.03)

3.77*** (0.09) 4.61*** (0.10) 4.68*** (0.16) 2.13*** (0.08) 6.68*** (0.15) 6.23*** (0.25) 0.18*** (0.02) –1.00*** (0.24) 0.32 (0.31) –0.52*** (0.13) 0.77*** (0.19) –0.77 (0.41) –0.50* (0.20) –1.11*** (0.22)

3.42*** (0.08) 4.54*** (0.11) 1.30*** (0.03) 6.33*** (0.11) 4.65*** (0.17) –0.33*** (0.01) 1.53*** (0.16) 0.24 (0.18) –1.04*** (0.08) 1.60*** (0.15) 0.33 (0.28) 0.33*** (0.08) 0.12 (0.19)

–0.51*** (0.10)

–0.73*** (0.12)

–0.07 (0.16)

–0.50*** (0.11)

–1.25*** (0.28)

–1.07*** (0.22)

0.97

0.95

0.53

0.46

3511.4***

2567.6***

99.2***

219.4***

93.1***

180.8***

* Significant at P < 0.05 *** Significant at P < 0.001. † Year t , time dummy variable for the tth year; drain, controlled drainage binary variable; elevfld, elevation above the lowest point in Field W; elevstr, elevation above the soil surface at the control structure. ‡ Standard error in parentheses.

2009, controlled drainage yields outperformed conventional drainage on both sides of the field. It was estimated that corn yields improved by an average of 0.57 and 1.00 Mg ha–1 across the effective range (0–0.61 m), which corresponds to a 5.8 and 9.8% premium on the west and east sides, respectively, over average free-flow yields. Average yield premiums were as high as 2.96 and 3.43 Mg ha–1, respectively, close to the control structure. These benefits decreased at higher elevations. Note that this was consistently observed across all years except for the east side of the field in 2005 and 2006. Regarding the second hypothesis, the breakdown by year revealed substantial temporal heterogeneity of the impacts of controlled drainage on average yields. The bottom line is, however, that controlled drainage was almost always at least as good as conventional drainage. The relationship between elevstr and the marginal effects of controlled drainage Agronomy Journal • Volume 104, Issue 4 • 2012

Table 4. Marginal effects of controlled drainage on corn yields for Davis Purdue Agricultural Center, Field W, east and west sides. Marginal effect on corn yield Elevstr† m 0.00 0.25 0.50 0.61 Avg.§ 0.00 0.25 0.50 0.61 Avg.§

2005 2006 2007 2008 2009 2005–2009 ————————————————————————————————— Mg ha–1 ————————————————————————————————— West side 1.31 (–0.24,2.86)‡ 5.47* (3.88,7.06) 1.86* (1.08,2.65) 1.10 (–0.19,2.38) 5.06* (3.02,7.10) 2.96* (2.25,3.67) –0.31 (–0.72,0.10) 1.86* (1.49,2.23) 0.19 (–0.03,0.41) 0.87* (0.47,1.27) 0.96* (0.36,1.57) 0.71* (0.51,0.92) –0.65* (–1.01,–0.30) 1.09* (0.69,1.49) –0.17 (–0.36,0.03) 0.82* (0.50,1.14) 0.10 (–0.50,0.69) 0.24* (0.05,0.42) –0.75* (–0.94,–0.56) 0.87* (0.64,1.10) –0.27* (–0.37,–0.16) 0.80* (0.64,0.97) –0.15 (–0.48,0.17) 0.10* (0.00,0.20) –0.42* 1.63* 0.08* 0.85* 0.70* 0.57* East side –1.08* (–2.07,–0.09) –0.72 (–3.48,2.05) 4.67* (2.92,6.41) 5.54* (3.98,7.11) 8.72* (5.64,11.79) 3.43* (2.40,4.46) 1.07* (0.85,1.29) 0.07 (–0.37,0.51) –0.03 (–0.29,0.23) 2.29* (2.05,2.54) 1.81* (1.26,2.37) 1.04* (0.87,1.22) 1.30* (1.05,1.55) 0.15 (–0.14,0.45) –0.53*(–0.67,–0.40) 1.95* (1.72,2.18) 1.07* (0.61,1.54) 0.79* (0.65,0.93) 1.36* (1.23,1.50) 0.18* (0.03,0.33) –0.68* (–0.74,–0.62) 1.85* (1.73,1.97) 0.86* (0.62,1.10) 0.72* (0.64,0.79) 1.11* 0.09* –0.12* 2.23* 1.68* 1.00*

* Statistically significant at the 95% confidence level. † Elevation above the soil surface at the control structure. ‡ Numbers in parentheses are the lower and upper bounds of the 95% interval. § Average of the marginal effects across the effective range of elevstr, i.e., between 0.00 and 0.61 m (or 2 ft).

Fig. 3. Marginal effects of controlled drainage, averaged across the period 2005 to 2009 for the east and west sides of the field, compared with the benchmark of free-flow drainage; elevstr (x axis) is the elevation above the soil surface at the control structure.

Fig. 4. Summer precipitation (Field W, Davis Purdue Agricultural Center) and departure from normal from 2005 to 2009.

is illustrated in Fig. 3, where the marginal effects are plotted as a function of distance from the control structure. It needs to be emphasized that the negative values reported in Table 4 and Fig. 3 resulted from the logarithmic functional form that was imposed on the elevation variable. Note that negative marginal effects were relatively rare. Year-to-year and field-to-field variation in the impact of controlled drainage on yields is the result of many factors, many of which are beyond the scope of this study. It is possible, however, to identify some key elements in the year-to-year variability, including the following: • The amount and timing of precipitation is the key factor in year-to-year variability. If little rain falls after stop-logs are installed, then controlled drainage cannot retain water in the root zone and hence cannot improve yields. For example, in 2005, the first year of the project, corn was planted around 20 April, but the stop-logs were not set into place until 21 June. Little precipitation fell in late June and July, keeping the water level in the tiles low until mid-August and hence during pollination (see Fig. 4). Agronomy Journal • Volume 104, Issue 4 • 2012

This is why controlled drainage made little difference over conventional drainage that year. In 2009, the logs were put in place soon after planting and accumulated sufficient rainfall from the late spring to carry the corn crop through pollination, resulting in a substantial yield benefit for controlled drainage despite the dry summer. • Tile system design affects field-to-field differences. For example, in the controlled part of the west side, the main tile outlet is undersized and causes water to back up and not drain at the design rate. This makes the controlled section of the west side prone to flooding and this tendency is accentuated when the drainage control logs are in place. These tile system design issues are part of the reason why controlled drainage benefits were smaller and more variable on the west side. • Year-to-year differences were also affected by how intensively the water table was managed. The first 3 yr of the trial, the farmer installed the stop-logs in late spring and pulled them out shortly before harvest. In 2008, the stoplogs were managed more intensively. They were inserted and removed several times during the summer in response to field conditions. For instance, in the case of a heavy 1107

rain on already saturated soil, stop-logs may be lowered to accelerate tile outflow. The yield improvement linked to controlled drainage was positive and statistically significant up to 0.61-m elevation above the control structure on both the east and west sides in 2008. SUMMARY AND CONCLUSIONS Controlled drainage systems are designed to provide farmers with better water management possibilities than conventional free-flow drainage. Because of the ability to raise the level of the water table during periods requiring no machine operations, controlled drainage may boost corn yields. With yield monitor data collected from a split field experiment at the DPAC from 1996 to 2009, this study used spatial panel data techniques to determine whether controlled drainage outperformed conventional drainage in terms of yield. The use of spatial panel data methods provides precision agriculture researchers with a powerful framework to model crop sensor data across space and time. The findings are summarized as follows: • Hypothesis 1 was supported. On average during the period 2005 to 2009, it was estimated that controlled drainage improved corn yields compared with conventional drainage at all relevant elevations above the control structure. The estimated corn yield improvement was as high as 3.43 Mg ha–1, and benefits decreased as elevation above the surface at the control structure increased. On average across the effective range of 0 to 0.61 m above the control structure, yields were found to have improved by 5.8% (0.57 Mg ha–1) to 9.8% (1 Mg ha–1). Furthermore, it was determined that controlled water management always did at least as well as free-flow drainage near the control structure. • Hypothesis 2 was also supported. The impact of controlled drainage varied greatly across space and time. In the model, variation across space was closely tied to elevation. Differences in rainfall and drainage management appear to be responsible for year-to-year variations. The data suggest that more intensive management of the stop-logs leads to the best performance. In addition to facilitating machinery access to the fields for planting and harvesting, controlled drainage provides farmers with the means to react to unpredictable weather events. Such a system could play an important role in ensuring that enough moisture is available to crops during critical growth periods. In addition to specific yield estimates for controlled drainage, this study provides an example of how farmers, agribusinesses, and agronomists can make use of the data from combine yield monitors to statistically test the impact of production practices like drainage that are difficult to test in a small-plot situation. Spatial panel regression methods explicitly model the spatial autocorrelation inherent in combine yield monitor data and allow unbiased inferential statistics. Spatial panel methods also provide a robust methodology for summarizing yield monitor data with time, eliminating the need for “normalizing” or other ad hoc methods used by some analysts with multiple years of yield maps. APPENDIX The likelihood function to be maximized when estimating the BEP model (Baltagi et al., 2009) is given by 1108

LL (b , s2m , s2u , r1 , r2 ) = -1 -1 1 NT log 2p- log T sm2 ( A ¢A ) +s2u (B ¢B ) 2 2 -1 1 T -1 log s2u (B ¢B ) - u ¢Wu-1u 2 2

-

[5a]

ˆ , A = (I – where | | is the determinant operator, u = y – X b N –1 r1WN), B = (I N – r2WN), and W u can be expressed as -1 -1 Wu-1 = JT Ä éêT s2m ( A ¢A ) +s2u (B ¢B ) ùú ë û 1 é + 2 êë ET Ä (B ¢B )ùúû s

-1

[5b]

u

where the elements of the T ´ T matrix JT are all equal to 1/T and ET = IT – JT. Note that even though W u–1 is the inverse of an NT ´ NT matrix, its computation involves only the inverse of N ´ N matrices, making the maximum likelihood estimation computationally more manageable. The log-likelihood function can be further concentrated, as shown by Baltagi et al. (2009), before being maximized by quasi-Newton optimization, restricting r1 and r2 to be between –1 and 1. The KKP (Kapoor et al., 2007), RE-ERR (Anselin, 1988), and nonspatial RE models can be estimated by setting r1 = r2 , r1 = 0, and r1 = r2 = 0, respectively. ACKNOWLEDGMENTS This research was supported by the USDA CSREES National Integrated Water Quality Program, Grant 2004-04674 entitled “Drainage Water Management Impacts on Watershed Nitrate Load, Soil Quality and Farm Profitability”. Thanks to Nathan Utt and Roxanne Adeuya for their help with data collection and formatting. References Adeuya, R.K. 2009. The impacts of drainage water management on water table depth, drain flow and yield. Ph.D. diss. Purdue Univ., West Lafayette, IN. Anselin, L. 1988. Spatial econometrics: Methods and models. Kluwer Acad. Publ., Dordrecht, the Netherlands. Anselin, L., R. Bongiovanni, and J. Lowenberg-DeBoer. 2004. A spatial econometric approach to the economics of site-specific nitrogen management in corn production. Am. J. Agric. Econ. 86:675–687. doi:10.1111/j.0002-9092.2004.00610.x Anselin, L., J. Le Gallo, and H. Jayet. 2008. Spatial panel econometrics. In: L. Matyas and P. Sevestre, editors, The econometrics of panel data. Adv. Stud. Theor. Appl. Econ. 46. 3rd ed. Springer-Verlag, Berlin. p. 625–660. Bakhsh, A., T. Colvin, D. Jaynes, R. Kanwar, and U. Tim. 2000. Using soil attributes and GIS for interpretation of spatial variability in yield. Trans. ASAE 43:819–828. Baltagi, B. 2005. Econometric analysis of panel data. John Wiley & Sons, Chichester, UK. Baltagi, B., P. Egger, and M. Pfaffermayr. 2009. A generalized spatial panel data model with random effects. CPR Work. Pap. 113. Ctr. for Policy Res., Syracuse Univ., Syracuse, NY. http://www.maxwell.syr.edu/uploadedFiles/ cpr/publications/working_papers/wp113.pdf. Bartlett, M.S. 1978. Nearest neighbor analysis models in the analysis of field experiments. J. R. Stat. Soc., Ser. B 40(2):147–174. Bongiovanni, R., and J. Lowenberg-DeBoer. 2000. Nitrogen management in corn using site-specific crop response estimates from a spatial regression model. In: P.C. Robert et al., editors, Proceedings of the 5th International Precision Agriculture Conference, Bloomington, MN [CD-ROM]. 16–19 July 2000. ASA, CSSA, and SSSA, Madison, WI.


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