the impact of drainage management technology in agriculture: a

The Impact of Drainage ManagementTechnology in Agriculture:

A Spatial Panel Data Model

Benoıt A. Delbecq, Raymond J.G.M Florax, Jason P. Brown,Adela Nistor and Jess Lowenberg-DeBoer

Purdue Agricultural Economics

August 27, 2009

III World Conference of Spatial EconometricsBarcelona 2009

Benoıt A. Delbecq, Raymond J.G.M Florax, Jason P. Brown, Adela Nistor and Jess Lowenberg-DeBoerThe Impact of Drainage Management Technology in Agriculture: A Spatial Panel Data Model

field water management

A DOUBLE-EDGED SWORD

More is not always better when it comes to water and row-crops.Depending on the stage of growth, lack or excess of watermaybe harmful

Consequences of wet conditions (e.g. corn):field inaccessible for operations such as planting or spraying offertilizer or pesticides

late planting causes yield loss despite fast growing varieties.late application of nitrogen may further delay planting / untimelyspraying of pesticides may increase weed and disease stress onplant

standing water on field may asphyxiate young roots and/or causedevelopment of diseases



DRAINAGE 101

Solutions?dry conditions⇒ irrigation: gravity, sprinkler or dripwet conditions⇒ drainage : conventional or controlled

Drainage:conventional: a network of tiles and ditches which maintain thewater table below a fixed level by evacuating the excess water tothe nearest creekcontrolled: upgrades the conventional with a system of logsallowing for water table to be set at a specified level.



ACTUAL AND EXPECTED BENEFITS

lower level for heavy machinery to enter the field whenoperations are requiredhigher level during off periods (winter and mid-summer)

Expected benefits:technical - yield increase

better control of field operations timingmaximizes water availability at critical stages of growth whilepreventing flooding

environmental - limit chemical runoffpotentially reduces pollution of downstream rivers and water bodies(e.g. Gulf of Mexico)

ä Private and public interestse.g. Environmental Quality Incentives Program for Indiana


a multidisciplinary project

THE DRAINAGE PROJECT

USDA-CSRES Grant #2004-51130-03111“Drainage Water Management Impacts on Watershed Nitrate Load,Soil Quality and Farm Profitability”

Work in the Agricultural Engineering and Agricultural Economicsdepartments at Purdue University

four sites: Davis Purdue Agricultural Center (DPAC) and threeprivately-operated farms in Indianadata collected with yield monitor systems as far back as 1996 forDPACcontrolled water management system functional from 2005 on


a multidisciplinary project

THE AGECON SIDE

Jason P. Brown (2005) (M.S. thesis): site-specific yield responseto controlled drainage - cross-sectionAdela Nistor (2007) (Ph.D. dissertation): yield response andcost-benefit analysis - panel datacurrent: refine the yield response analysis using more advancedspatial panel techniques and updated data

this paper: Field W - DPAC farm - Randolph county, IN, USA


building the grids

COLLECTING YIELD DATA

data collected with AgLeader yieldmonitor linked to a GPS mounted onthe combinecorn was planted in

East: 1996, 1998, (2000), 2002,2005-2008West: 1996, 1998, 2001, 2003,2005-2008

ä Years with controlled drainage in red


building the grids

THE ART OF CLEANING DATA

Measurement errors are numerous.Clean-up is done on the basis of“combine dynamics” criteria:

minimum and maximum yieldminimum and maximum combinespeedgrain flow delaystart- and end-pass delay


building the grids

“GRIDDING” DATA

Why aggregate?need for data spatially balanced in alldirectionsimproves precision of estimator (butinduces heteroskedasticity)

How to aggregate?

cell size: average combine passwidth over years (e.g. 5m)each cell contains the average yield,the standard deviation and the countof the points falling within its limits


the left-hand side

YIELD RESPONSE MODEL REGRESSORS

Left-hand side variables:elevation

interpolated from field measuresusing IDW power 1 method

conventional/controlled drainagedummy variable D

D =

1 if controlled0 if free flow

precipitationtotal rainfall during critical growthperiod (i.e. July 5 to Sept. 5)


crop yield response

A SIMPLE LINEAR MODEL

Heady and Dillon (1961) provide a review of algebraic functionalforms for crop response estimation

ä critical factors - rain, elevation and slope

This paper - linear model with year fixed effects, rainfall, elevation anddrainage dummyInteractions:

D × year - differential response of controlled drainage from oneyear to another?D × elev - ...from one location to another?rain × elev


crop yield response

CORRECTION FOR HETEROSKEDASTICITY

linear crop response model

yield = α + year βββ1 + D × year βββ2

+γ1 elev + γ2 D × elev + δ rain × elev

Because of aggregation method, the LHS variable is actually averageyield whose variance varies over grid cells.

Var(yield i ) =σ2

ini

i = 1, · · · ,N (1)

ä inherent heteroskedasticity Correction: divide LHS and RHS of equation (??) by σi√ni

, thestandard error.


spatial panel

THE WHYS AND THE PROS

Why panel?control for (unobserved) individual heterogeneity,

hereby reducing omitted variable bias

Why random effects?yield monitor data is a sample rather than a

population (Griffin et al., 2005)

Why spatial?contemporaneous spatial dependence between

observations at each point in time and spatial heterogeneity mayarise when panel data include a location component (Anselin, 1988;Elhorst, 2009)

Why autoregressive error?spatial autocorrelation is due to omitted

variables rather than to the effect of corn yield grid cells on each other(Anselin et al., 2004; Lowenberg-DeBoer et al., 2006)


spatial panel

NOT SO SIMPLE ANYMORE...

Following Baltagi et al. (2007), the random effects model withspatially autocorrelated error components can be formulated for eachtime period t as:

yt = Xtβββ + ut , t = 1, . . . ,Tut = u1 + u2t

u1 = ρ1WNu1 +µµµ, µµµiid∼ N (0, σ2

µ)

u2t = ρ2WNu2t + ννν t , ννν tiid∼ N (0, σ2

ν) (2)

The vector of errors ut is composed of two spatially autocorrelatedcomponents, one time-invariant and unit-specific u1, and onetime-varying u2t , with two separate autocorrelation parameters.


spatial panel

Stacking the model for each time period so that the slower index istime and rearranging equation (??) into a single equation yield thefollowing reduced form:

y = Xβββ + (INT − ρ1WNT )µµµ+ (INT − ρ2WNT )ννν (3) Note:Because of the time invariance, µµµ = ιιιT ⊗µµµ where ιιιT is a vectorof ones of dimension T .WNT = IT ⊗WN is block diagonal

calculations of (INT − ρr WNT )−1 and |INT − ρr WNT | involve N × Nmatrix instead of NT × NT (r = 1, 2)renders estimation more computationally manageable


spatial panel

MAXIMUM LIKELIHOOD ESTIMATION

Concentrated likelihood function:

LLc(ρ1, ρ2, φ) = −C − NT2

ln σ2ν(ρ1, ρ2, φ)− 1

2ln detΣΣΣu(ρ1, ρ2, φ)

where

φ =σ2

µ

σ2ν

σ2ν =

u(βββ)′ΣΣΣ−1u u(βββ)

NTβββ = (X′ΣΣΣ−1

u X)−1X′ΣΣΣ−1u y

ΣΣΣ−1u = σ2

νΩΩΩ−1u

ln detΣΣΣu = ln det[Tφ(A′A)−1 + (B′B)−1] + (T − 1) ln det(B′B)−1


exploratory spatial analysis

SUMMARY STATISTICS

N/S 1996 1998 2002 2005 2006 2007 2008Minimum 47/59 76/113 11/10 79/77 106/96 50/33 110/106Maximum 131/131 200/189 98/105 237/221 218/219 163/154 239/238Mean 97/99 145/144 51/45 154/174 175/172 107/107 192/192SD 12/13 17/15 19/19 30/22 20/20 20/22 23/22(Whole field)Minimum 47 76 10 77 96 33 106Maximum 131 200 105 237 219 163 239Mean 98 145 48 164 174 107 192SD 13 16 19 28 20 21 23rain (in) 3.60 4.03 2.53 5.67 3.78 8.24 5.38

Table: Corn yield (bu.a−1) and precipitation - Davis, Field W, EAST

N/S 1996 1998 2001 2003 2005 2006 2007 2008Minimum 32/35 106/56 104/112 56/52 79/89 86/81 51/52 107/124Maximum 119/121 200/208 227/232 184/188 206/209 220/216 151/141 239/236Mean 81/89 151/138 177/175 137/123 150/156 167/155 110/104 196/189SD 18/13 20/22 20/19 22/28 22/19 22/24 16/18 21/21Whole fieldMinimum 32 56 104 52 79 81 51 107Maximum 121 208 232 188 209 220 151 239Mean 85 145 176 130 153 162 107 193SD 16 22 19 26 21 24 18 21rain (in) 3.60 4.03 4.96 7.33 5.67 3.78 8.24 5.38

Table: Corn yield (bu.a−1) and precipitation - Davis, Field W, WEST


exploratory spatial analysis

SPATIAL AUTOCORRELATION?

1996 1998 2002 2005 2006 2007 2008EAST 0.48*** 0.68*** 0.62*** 0.63*** 0.56*** 0.73*** 0.62***

1996 1998 2001 2003 2005 2006 2007 2008WEST 0.71*** 0.83*** 0.37*** 0.62*** 0.58*** 0.62*** 0.67*** 0.61***

Table: Moran’s I (yields), Davis, Field W

ä Evidence of strong within year positive spatial autocorrelation


reports

yield RE SEM-RE KKP BEP

intercept 104.30 *** 104.21 *** 104.23 *** 104.33 ***( 0.407 ) ( 0.434 ) ( 0.434 ) ( 0.438 )

years *** *** *** ***

elev 13.12 *** 14.10 *** 14.05 *** 13.76 ***( 0.963 ) ( 0.961 ) ( 0.959 ) ( 0.958 )

year05× D 15.62 *** 12.23 *** 12.22 *** 12.17 ***( 1.744 ) ( 1.842 ) ( 1.837 ) ( 1.828 )

year06× D 0.89 2.19 1.96 1.62( 2.066 ) ( 2.420 ) ( 2.409 ) ( 2.386 )

year07× D 1.35 0.90 0.89 0.84( 1.096 ) ( 1.123 ) ( 1.12 ) ( 1.114 )

year08× D 33.70 *** 32.57 *** 32.60 *** 32.72 ***( 1.694 ) ( 1.856 ) ( 1.850 ) ( 1.834 )

elev× D 1.69 *** 1.72 *** 1.72 *** 1.74 ***( 0.250 ) ( 0.233 ) ( 0.232 ) ( 0.234 )

elev× rain -5.71 *** -5.97 *** -5.96 *** -5.93 ***( 0.209 ) ( 0.202 ) ( 0.202 ) ( 0.201 )

ρµ — — 0.527 0.949ρν — 0.538 0.527 0.477φ — — — 0.0146Log Likelihood -63747.6 *** -62644.0 -62631.6 -62565.0LR vs BEP 2364.1 *** 157.4 *** 132.0 *** —

Table: Estimation results for Davis field W - East

ä BEP model stands implying both time-variant and time-invariantspillovers


reports

yield RE SEM-RE KKP BEP

intercept 76.80 *** 76.45 *** — 76.45 ***( 0.417 ) ( 0.462 ) ( 0.462 )

years *** *** ***

elev 30.36 *** 28.97 *** — 29.00 ***( 1.890 ) ( 1.973 ) ( 1.974 )

year05× D 1.89 1.41 — 1.37( 3.056 ) ( 3.344 ) ( 3.346 )

year06× D 35.94 *** 37.46 *** — 37.46 ***( 2.864 ) ( 3.190 ) ( 3.191 )

year07× D 2.31 1.77 — 1.75( 2.417 ) ( 2.446 ) ( 2.446 )

year08× D 13.766 *** 14.52 *** — 14.51 ***( 0.964 ) ( 0.963 ) ( 0.963 )

elev× D -33.76 *** -33.90 *** — -33.87 ***( 2.288 ) ( 2.278 ) ( 2.278 )

elev× rain -7.02 *** -6.69 *** — -6.69 ***( 0.469 ) ( 0.486 ) ( 0.486 )

ρµ — — — -0.562ρν — 0.568 — 0.57Log Likelihood -70651.1 -69101.7 — -69100.7LR vs BEP 3100.8 *** 1.91 — —

Table: Estimation results for Davis field W - West

ä SEM-RE model is the final specification implying only transitoryspillovers


reports

MARGINAL EFFECTS

The marginal effect of the watermanagement system in year t(t = 2005, . . . , 2008) depends directlyon elevation:

(∂yield∂D

)t= β2t · yeart + γ2 · elev

∆yield 2005 2006 2007 2008EASTbu.ac−1 14.1 2.0 2.0 34.7% 8.1 1.2 1.9 18.1WESTbu.ac−1 -17.7 19.8 -17.7 -3.2% -11.8 11.9 -16.1 -1.6

Table: Average effect of controlleddrainage on yields


IN A FEW WORDS

impact of controlled drainage varies:from year to year: positive or negative, with large variancefrom field to field:

predominantly negative for the West sidepositive across all years for East side

within field (direct function of elevation)

year to year difference explained by significance of year × Dinteraction

when significant, positive effect on yieldsinsignificant in 2006 and 2007 for East and 2005 and 2007 for West

presence of spatial autocorrelation in the error termhowever, autocorrelation of the ramdom effects relevant for East


FUTURE DIRECTIONS

1 fine tune and improve the agronomic model specification inparticular on the inclusion of precipitations

take into account not only quantity but variation of rainfall overcritical growth period or yearuse precipitation data after logs are installed in the spring afterplanting. hypothesis: if rainfall is low, there is nothing to hold back and

controlled drainage would have no impact

2 estimate similar models for the three other sites in the project3 discuss results with agricultural engineers and agronomists for

interpretation


the impact of drainage management technology in agriculture: a

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