70th SWCS International Annual Conference July 26-29, 2015 Greensboro, NC

1. North Carolina Agricultural and Technical State University
Estimation of Markov transition matrices with
aggregate data:
An application to modeling no-till frequency
Lyubov A. Kurkalova and Dat Quoc Tran

2. North Carolina Agricultural and Technical State University
This presentation
 Motivation for interest in dynamics of tillage choices
 Markov chain model of crop-tillage choice
 Data, estimation, and results
 Conclusions and next steps

3. North Carolina Agricultural and Technical State University
Conservation tillage
 Tillage
»Conventional - leaves less than 30% the soil covered with crop
residue after planting
»Conservation (CT) – 30% or more residue cover
No-till (NT) – only minimal amount of soil disturbed
 CT, and especially NT provides significant environmental
benefits, when compared to conventional till
»Reduction in soil erosion by water and wind
»Reduction in Nitrogen and Phosphorus run-off
»Carbon sequestration (Lal at al., 1999, Lal et al., 2004)

4. North Carolina Agricultural and Technical State University
Dynamics of tillage
 For carbon sequestration benefits to occur, CT needs to
be practiced continuously over several years in a row
» Even a single year of conventional till in between years of CT (NT)
releases most of the accumulated carbon back to atmosphere
(Manley et al., 2005; Conant et al., 2007)
 Theoretical economic studies: dynamic optimization
» McConnell, 1983; Wilman, 2011
 However, most of the empirical economic studies of
tillage choices did not account for the dynamics:
» Binary, single year choice between tillage regimes (e.g.,
Conventional vs. NT), conditional on the crop grown (Rahm and
Huffman, 1984; Soule at al., 2000; Pautsch et al., 2001; Vitale et
al., 2011; Druschke and Secchi, 2014)

5. North Carolina Agricultural and Technical State University
Dynamics of tillage: Limited data
 Nation-wide USDA ARMS (Agricultural Resources
and Management Survey)
» Selected years, crops, states
» Limited attempts to gather information on continuous CT
 Nation-wide CTIC (Conservation Technology
Information Center)
» Tillage systems by county and crop, yearly 1989 –1998, 2000, 2002,
2004
» Survey was not designed to track tillage from one year to another
 Regional, based on surveys of farmers:
» Hill, 2001; Napier and Tucker, 2001

6. North Carolina Agricultural and Technical State University
Data: regional studies: Hill (2001, JSWC)
 Continuous NT
 Corn-soybean, 1994 - 1999
 Randomly selected 230 fields in
each surveyed county
State/
counties
surveyed
% fields in NT continuously for the indicated number
of years
2 3 4 5 6
IL/ 18 44 30 22 19 13
IN/ 11 41 25 18 14 9
MN/ 10 9 7 3 3 n/a

7. North Carolina Agricultural and Technical State University
Rotational tillage
 Anecdotal evidence from Conservation Effects Assessment
Project (USDA CEAP studies):
» Farmers rotate tillage from one year to another
» Tillage rotation is closely associated with crop rotation
 Iowa and central Illinois:
Soybeans: high probability of NT
Corn: lower probability of NT
Corn-after-corn: even lower probability of NT
 Question: can we estimate these probabilities with the yearly
county-level data from CTIC?

8. North Carolina Agricultural and Technical State University
Present study
 Assume that crop-tillage choice could be described as a
stationary 1st order Markov process
 Si, i = 1,2,3,4 is the share of state’s cropland in
1 – NT-corn, 2 – till-corn, 3 – NT-soybeans, 4 – till-soybeans
 Each transition probability pij represents the probability of crop-
tillage category i after crop-tillage category j the year before
   
11 21 31 41
1 12 22 32 42
1 2 3 4 1 2 3 4
13 23
14 24
0 0
0 0
t t
p p p p
p p p p
s s s s s s s s
p p
p p

 
 
 
 
 
 

9. North Carolina Agricultural and Technical State University
NT corn
Till
corn
NT soybeans
Till
soybeans
The 1st order Markov transition diagram

10. North Carolina Agricultural and Technical State University
CTIC data and assumption for the model
No-till crop-tillage share, Source: CTIC

11. North Carolina Agricultural and Technical State University
Estimation of Markov probability matrix
 If the transitions from one crop-tillage category to
another (field-level) are observed, then Maximum
Likelihood can be used (Anderson and Goodman, 1957)
 Time-ordered spatially aggregated data
» Restricted Least Squares (RLS) (MacRae, 1977; Kelton, 1981;
Kelton, 1994 and Jones, 2005)
» Studies of land use (Howitt and Reynaud, 2003; You and Wood,
2006; Chakir, 2009; Papalia, 2010; Aurbacher and Dabbert, 2011)
 We apply RLS to 1992-1997 data
» Transition matrix assumptions: stationary and 1st order

12. North Carolina Agricultural and Technical State University
http://www.csrees.usda.gov/Extension/index.html http://www.icip.iastate.edu/maps/refmaps/crop-districts
State of Iowa: 9 Crop Reporting Districts (CRDs), 99 counties
Iowa

13. North Carolina Agricultural and Technical State University
NT-
corn
Till-
corn
NT-
soyb
Till-
soyb
NT-
corn
0.00 0.00 0.40 0.60
Till-
corn
0.11 0.21 0.14 0.54
NT-
soyb
0.48 0.52 0 0
Till-
soyb
0.00 1.00 0 0
Current year
Previous
year
Estimated transition matrix, state of Iowa

14. North Carolina Agricultural and Technical State University
Observed vs. predicted shares at state level
0
5
10
15
20
25
1993 1994 1995 1996 1997
Adoptionrate(%)
Year
Predicted NT-corn adoption rate Observed NT-corn adoption rate

15. North Carolina Agricultural and Technical State University
Observed vs. predicted shares at state level
0
5
10
15
20
25
30
1993 1994 1995 1996 1997
Adoptionrate(%)
Year
Predicted NT-soybeans Observed NT-soybeans

16. North Carolina Agricultural and Technical State University
IL, Mercer county
Probability of a
field being in NT
2 years in a row
• Hill (2001):
58.1%
• Markov model:
54.1%
0.00 0.06 0.62 0.32
0.25 0.23 0.23 0.29
0.46 0.54 0 0
0.27 0.73 0 0

17. North Carolina Agricultural and Technical State University
Conclusions and next steps
 Conclusions:
»Markov model provides a useful way of describing the dynamics of
crop-tillage choices in Iowa
»Estimates of the probabilities of transition between alternative crop-
tillage categories are consistent with qualitative data on dynamics of
tillage in Iowa
 Next steps:
»Analyze the effect of soil productivity in the estimated Markov
transition matrices
»Analyze the within-state variation in the estimated Markov transition
matrices
»Extend the model to allow the Markov transition matrix to vary across
time
»Apply the Markov process approach to cropping patterns data derived
from USDA/NASS-collected CDL

18. North Carolina Agricultural and Technical State University
Acknowledgements
 Partial support from USDA/ERS/Evans-Allen is
gratefully acknowledged
 The views expressed in this presentation are those
of the authors and do not necessarily reflect the
views or policies of the USDA

19. North Carolina Agricultural and Technical State University
Thank You!
dqtran@aggies.ncat.edu
tranquocdat1506@gmail.com