Dynamic Analysis of Policy Options for Mexico’s Sheep Sector’
Charles F. Nicholson
Associate Professor
Department of Agribusiness,
California Polytechnic State University, San Luis Obispo, CA 93407
and
David Parsons
Research Fellow
Tasmanian Institute of Agriculture — School of Agricultural Science, UTAS
March 2012
Abstract
Global demand for livestock products is expected to increase rapidly during the next two
decades, and the global value of livestock products will exceed that of crops by 2020. This so-
called “Livestock Revolution” (Delgado et al., 1999) will challenge policy makers in many
countries to re-examine their objectives and formulate appropriate policies to achieve them.
Most analyses of growing livestock product demand have used global partial equilibrium market
models to explore broader implications, such as impacts on grain markets (e.g., Bruinsma et al.,
2003; Rosegrant et al., 2005; OECD, 2006). Country- and regional-level dynamic models that
focus on livestock can complement these global analyses by assessing a more specific set of
market and technology policy options. An example of the policy challenges in responding to the
Livestock Revolution can be observed in Mexico. The demand for sheep meat in the populous
central region around Mexico City has grown rapidly in recent years, prompting federal and state
governments in sheep-producing regions to provide a variety of investment and feed subsidies as
“regional development” strategies. To assess the impacts of these policy options in the context
of ongoing demand growth, a dynamic model of Mexico’s sheep sector with regional and
producer group disaggregation is developed that incorporates interactions between herd
dynamics, feed dynamics, market inventories of sheep meat and prices for sheep meat and
animals. The model is used to assess the outcomes for commercial and tras patio (backyard,
small-scale) Mexican sheep producers and sheep meat consumers of three growth assumptions
and two intervention alternatives: a variable cost subsidy provided to commercial sheep
producers or the implementation of a stylized health intervention that reduces the mortality rate
' This work was funded in part by a grant from USAID/Mexico through the Higher Education for Development
Program. Emma Stephens provided helpful comments on a previous version of this manuscript.
of young sheep. Model simulations indicate that the dynamics of growth dominate the policy
responses; the principal beneficiaries of producer subsidy and animal health interventions are
Mexican sheep meat consumers, who are often high-income urban residents. Commercial sheep
producers will experience increases in cumulative net margin, but tras patio producers will be
made worse off than they would have been in the absence of interventions. The Mexican sheep
system thus exhibits two characteristics of dynamically complex systems: unintended
consequences (e.g., reduced cumulative net margins for all sheep producers in some cases as a
result of policy) and policy resistance—the ability of the endogenous response of the system to
various incentives to limit the ability of policy to achieve specified objectives. Although the
principal results of this modeling effort are specific to the Mexican sheep case, there are broader
implications related to modeling the evolution of agriculture-based livelihood systems, the
“complex systems” approach to analysis of agricultural systems and the usefulness of
interdisciplinary research collaboration.
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
Dynamic Modeling of Policy Options for Mexico’s Sheep Sector
Introduction
Global demand for livestock products is expected to increase rapidly during the next two
decades, and the global value livestock products will exceed that of crops by 2020. This so-
called “Livestock Revolution” (Delgado et al., 1999) will challenge policy makers in many
countries to re-examine their objectives and formulate appropriate policies to achieve them.
Most analyses of growing livestock product demand have used global partial equilibrium market
models to explore broader implications, such as impacts on grain markets (e.g., Bruinsma et al.,
2003; Rosegrant et al., 2005; OECD, 2006). Country- and regional-level dynamic models that
focus on livestock can complement these global analyses by assessing a more specific set of
market and technology policy options. Of particular concem is how market transformations will
influence the ability of smallholder livestock producers to participate in, and benefit from, rapid
demand growth. Tedeschi et al. (2011), Nicholson et al. (2011) and Parsons et al. (2011) argued
that system dynamics (SD) models of livestock systems can be useful to policy makers in a
variety of ways as the livestock revolution progresses.
An example of the policy challenges in responding to the Livestock Revolution can be observed
in Mexico. The demand for sheep meat in the populous central region around Mexico City has
grown more than 6% annually in recent years (FAO, 2006). Already there have been structural
changes in the agriculture of some regions of Mexico due to this growth. The Y ucatan region
illustrates many of these changes. Parsons et al. (2006) reported that sheep production had
become a much more important source of household cash income in Y ucatan state between 1989
and 2004. This rapid growth has prompted federal and state governments in sheep-producing
regions to provide a variety of investment and feed subsidies as “regional development”
strategies. In response to the perceived opportunity for sheep production to contribute to the
region’s economic growth, the state government of Yucatan has granted subsidies to sheep
producers, particularly in the form of subsidized loans, cost-sharing grants or input cost
subsidies. This financial assistance has almost always been directed to larger-scale, commercial
producers, and has both lowered the investment cost for entry into larger-scale sheep production
and reduced operating costs. In part, this financial assistance derives from a philosophical legacy
in Mexico of the desirability of self-sufficiency in agricultural production. Although roughly
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
half of sheep meat consumed in Mexico is imported (mostly from New Zealand), policy makers
in Mexico see an opportunity to capitalize on consumer preferences for fresh rather than frozen
sheep meat,” increasing earnings in the agricultural sector and reducing import dependency with
a single set of policies.
At the same time, researchers at a number of Gulf region universities and the Instituto Nacional
de Investigaciones Forestales, A gricolas y Pecuarias (INIFAP; Mexico’s national agricultural
research service, similar to the USDA’s Agricultural Research Service) have been working on
technologies and practices to improve the productivity of the systems (e.g., reduce mortality,
increase both the production and quality of feed for livestock). Given the paucity of agricultural
economists working for INIFAP, ex ante impact assessments are infrequently conducted for
technologies under development, either at the level of the individual production unit or at the
market level. Thus, little is known about the potential market impacts of successful development
and implementation of these technologies. Moreover, relatively little is known to date about the
characteristics of demand growth in Mexico City, although a recent study examined marketing
channels for sheep meat (Fell, 2005). Most policy makers in state governments in Mexico seem
to be operating under the assumption that the current rate of demand growth will continue
indefinitely, and that sheep meat prices will remain at levels profitable for producers regardless
of the actions of policy makers or producers.
In a more general sense, in agriculture and intemational development contexts there are often
significant delays in the development and implementation of technologies and policies, and
agriculture-based livelihood systems are in constant and sometimes rapid evolution. In order to
make technologies and policies better match the future state of these systems, it is necessary to
better understand the likely evolution of agricultural systems. The goal of these efforts should be
to improve understanding about which technologies and policies will be relevant for the state of
future systems so that research can begin on them now. In essence, researchers, policy makers
and donors need an improved understanding of general behavioral tendencies for target systems
five to ten years hence. Although this idea is widely accepted, assessment of systems evolution
appears to have been addressed infrequently and largely in an ad hoc manner in international
2 The majority of mutton consumed in Mexico City is as what is called “barbacoa.” This is grilled sheep meat that is
typically consumed on Sunday afternoons, and for which freshly slaughtered young sheep are the preferred source.
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
agricultural research. Nicholson (2007) noted that analyses of systems evolution will be more
useful if they allow simultaneous treatment of both underlying drivers of the dynamics of
agricultural livelihood systems and the impacts of technological and policy options. He also
proposed that a set of integrated case studies of agricultural systems evolution using alternative
modeling approaches be undertaken to improve our understanding of both systems evolution and
the strength and limitations of various modeling approaches.
Thus, the objectives of this paper are two-fold. The first objective is to assess the likely dynamic
impacts of technological change and state government support policies on the profitability of
Y ucatecan sheep production for different types of producers. One technology (a stylized health
intervention that reduces animal mortality) and one policy option (stylized variable cost
subsidies) are assessed under three different assumptions about future demand growth. The
second objective is to provide one case study of how analyses of systems evolution can
incorporate specific policy and technology options. To achieve these objectives, a system
dynamics model of sheep markets in Mexico is developed and parameterized.
Model Specification
Sterman (2000) and Costanza et al. (1993) argue that most coupled human-natural systems have
the characteristic of dynamic complexity, that is, they can demonstrate unanticipated changes in
behavioral modes as a result of the interaction of factors endogenous to the system (even in the
absence of significant external shocks). As a result, short-term and long-term effects of
interventions may differ, and the outcomes of policy interventions are often offset to a
substantial degree or result in the converse of what was intended. Batty and Torrens (2005) carry
this discussion further, suggesting that “Complex systems generate a dynamic which enables
their elements to transform in ways that are surprising, through adaptation, mutation,
transformation and so on...the hallmark of this kind of complexity is novelty and surprise which
cannot be anticipated through any prior characterization. All that can be said is that such
systems have the potential for generating new behaviors.”
To address the potential for dynamically complex behavior in Mexico’s sheep industry, an
integrated dynamic model of sheep markets, sheep flock dynamics and feed resources is
appropriate. This model represents a stock-flow-feedback structure that captures the potential
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
for nonlinear (or counterintuitive) responses to current policy instruments. The model represents
sheep and sheep meat markets in Mexico, but also includes trade linkages because of the
importance of imported sheep meat in Mexican consumption. The production sector is
represented by two different regions (Y ucatan and Other’), each with two different types of
producers. Parsons et al. (2006) categorized producers in Y ucatan state as either commercial or
tras patio. Commercial producers tend to be larger scale, have better access to capital, have
good market access and are often owned by individuals for whom agriculture is not the principal
economic activity. Tras patio, or backyard, producers are smaller scale, often have a limited
investment other than animals, have poorer market access and are owned by individuals who
eam a significant portion of household cash income from agriculture. The differences in
producer characteristics are assumed to influence the costs of production and prices received for
live animals. Demand is assumed to exist at a single central market based in Mexico City.
Inventories of sheep meat are assumed to influence the price of sheep meat, which in tum
influences both sales (quantity demanded) and sheep meat imports. An overview of the various
model sectors and assumptions follows, and a diagrammatic representation of the model (as a
stock-flow structure) are shown in Figure 1. A more detailed and mathematical representation of
the model structure is in the A ppendix.
Animal Numbers
This part of model structure is an adaptation of that in the Meadows (1970) model of the US hog
sector. The model specifies two types of animals: breeding sheep (BS) and young stock (YS).
BS produce Y S with delays for gestation and maturation, and with mortality losses. It is
assumed that Y S are either sold when “mature” or enter into the BS flock. The maximum rate at
which Y S can enter the BS flock is one-half of the maturation rate to account for only females
entering the BS flock. The reproduction rate of the BS flock depends on the lambing interval,
the lambs per lambing, and the fraction of mortality. The model assumes that the lambing
5 Yucatan produces a small proportion of Mexico’s sheep meat; less than 2% of the national sheep flock is found in
Yucatan state. However, Y ucatan is of interest given the policies implemented in response to the growth in demand
for sheep meat.
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
Subsidies
Marketing Costs
Varisble Costs
: Sheep Price
em ee Meat Price
Farm Net
" f
es Inventory
ie]
Meat iy
Inventories| Sales
YS
ie amma
Young by Breeding L
stock PO
Birth Replacements
ss +
Mortality
Health i
Intervention oer
Total Sheep Urbanization
Feed Resources.
PerAnimal
Consumption Per
Rainfall pat
S. Feed
Peat 7 TN Consumption
i iLosses
Land Area
Figure 1. Simplified Stock-Flow Structure of the Dynamic Disequilibrium Model
interval and mortality depend on relative feed availability (i.e., nutrients consumed), and allows
for of technological interventions to decrease Y S mortality.
The number of BS depends on two flows: entrants into the BS flock (the replacement rate) and
culls of BS. The rate of entrants depends on a replacement rate and an adjustment for differences
between the current BS and a desired number of BS. Mean time in BS is increased if the number
of desired BS is greater than the current BS. Maintenance or expansion of the BS takes
precedence over YS sales. Of those maturing, all males are sold, but only those females not
desired for the BS are sold.
The key behavioral assumption for sheep producers relates to the determination of the desired
level of BS, which in turn determines desired replacement animals, adjustments to the current
level of BS, the culling rate and the number of YS sold. The desired BS is based on an
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
anchoring and adjustment heuristic that Sterman (2000) argues is commonly used in capacity-
related decisions. The desired BS depends on the current BS and the expected long-term net
margin of sheep production relative to a reference value of net margin.
Feed Resources
The model includes a single aggregated “local” feed resource, which assumes that most of the
feed resources used in sheep production are forage or browse and are available locally (i.e., not
traded among regions or producers). This is not quite accurate, because commercial sheep
producers in particular buy feeds, but it may be adequate for a first model because the majority
of feed resources available are those grazed by the animals. The quantity of feed available is
increased by feed production and decreased by feed consumption. Total feed production
depends on the land area, feed production per land area and relative (regional) rainfall. Feed
consumption depends on the number of animals, a base level of per-month feed consumption and
the availability of feed per animal, with consumption increasing nonlinearly with increases in
feed availability. Seasonal differences in feed quality and interactions between quality and
quantity are ignored. The availability of feed per animal is used to modify the reproductive
performance of the sheep flock, with monotonically decreasing functions specified for both the
time required for Y S to mature and the lambing interval.
Sheep Market
A single aggregated sheep market (i.e., in Mexico City) consists of an inventory of sheep meat
(i.e., distinct from sheep numbers), which is assumed to influence price-setting for sheep meat
and therefore sheep meat sales. Although income and population growth will be the key drivers
of sheep meat demand, the model does not include these directly. Rather, it includes structure to
create exogenous growth in demand to test the impact of various demand growth patterns on the
sheep production and marketing system. The assumed own-price demand elasticity is -0.5 based
on estimates for other livestock products in Mexico’ (Stout and Abler, 2004). The sheep meat
price is assumed to translate into a producer sheep price by subtracting the per kg meat
marketing costs and multiplying by the number of kg meat per animal (the carcass yield, which
is set equal to 55% of the mature BS weight of 40 kg and 65% of the mean Y S weight of 25 kg).
* Stout and Abler (2004) report own-price elasticities for beef and veal (-0.334), pork (-0.550) and poultry (-0.620).
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
Meat marketing costs are assumed to vary by region and producer type (to reflect the potential
relative disadvantage to Y ucatecan producers and smaller tras patio producers). This implies
that the net price received by producers, and the aggregated net margin, will differ by region and
producer type. Producer revenues are calculated as animal sales time animal prices. Producer
costs include fixed costs (close to 40% of total costs based on observations made during field
visits in 2004 and 2005) and variable costs (just over 60% of total costs). The latter are based on
costs per BS, assuming that the majority of variable costs are for the breeding flock.
Technology Adoption and Subsidy Policies
As noted above, the model includes two regions (Yucatan and “Other”) and two (aggregated)
types of producers (commercial and tras patio). Commercial producers are assumed to receive
all state government subsidies and to be the only adopters of new technologies. The proportion
of commercial producers that use a technology is time-dependent and is assumed to demonstrate
sigmoidal growth to full adoption over three years.’ The adoption of a stylized health
intervention by commercial producers is assumed to reduce the mortality of Y S, for which
mortality rates average about 20% per year. An investment subsidy percentage variable allows
the variable costs of sheep production to be reduced, to simulate the effects of cost subsidies
provided by state governments. Based on the observation that in practice a preponderance of the
cost subsidies are received by commercial producers, we assume that only commercial producers
are eligible for the subsidy payments. In contrast to the technological intervention, for which a
diffusion and adoption process is required and which only a proportion of the commercial
producers choose to use, the subsidy payments program is assumed to be implementable over a
short time horizon and all eligible (that is, commercial) producers will receive payments. For
clarity, we do not report the results for both policy options implemented simultaneously.
Mathematical Formulation and Solution
Mathematically, the model is formulated in V ensim® (a detailed discussion of the structure is
included in the Appendix). The model includes four key state (stock) variables (BS, YS, feed
resources and sheep meat inventories). The inclusion of inventories that mediate between
5 Thus, this assumes that the technology would be regarded as highly desirable for producers. Sensitivity analyses
were used to assess the importance of this assumption and the outcomes do not change in a qualitative sense.
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
current sheep meat production and current sales implies the possibility for dynamic
disequilibrium in Mexican sheep meat markets. The model time unit of observation is one
month, and the calculation time step is 0.125 months.° The model is initialized in dynamic
equilibrium for time t=0 representing data from 2005,’ and technology or policy changes are
assumed to be initiated at time t=12 months. The model is simulated for a total of 120 months
using the Euler method of numerical integration. The model has been evaluated following the
procedures outlined in Sterman (2000) for dynamic simulation models, and various sensitivity
and extreme conditions tests have been conducted but are not reported herein.
Policy Options Analyzed
Nine alternative scenarios are analyzed with the dynamic model (Table 1). These scenarios are
1) a base case that assumes no changes in Y S mortality over time due to technology adoption and
no variable cost subsidy, 2) a scenario in which Y S mortality is reduced from 20% to 10% per
year due to a stylized health intervention (assumed to be developed by Mexican university and
INIFAP researchers)*® for commercial producers in both regions, and 3) a scenario in which
governments provide variable cost subsidies that lower by 20% the unit costs of sheep
production for commercial producers in both regions. Each of these scenarios is assessed under
three different demand growth scenarios: No growth (which serves as a dynamic equilibrium
baseline in the absence of technological change or subsidies), growth of 6% per year throughout
the simulation and 6% growth over four years, slowing to 2.5% growth over the remaining years
of the simulation. This latter scenario is designed to test the importance of the assumption on the
part of state-level policy makers concerning continuous rapid growth in the Mexico City market.
The key outcomes of interest to policy makers from these simulations are sheep meat prices, net
margins for each type of producer in both regions, total consumer expenditures on sheep meat
and government expenditures on variable cost subsidies.
5 Alternative values of the time step were used to evaluate the degree of integration error. The value of 0.125 was
determined to be adequate as a compromise between computational requirements and the likely degree of
computational error due to the assumption of dS/dt is constant for the interval At, as assumed for Euler integration.
t Principal data sources include FAO (2006), Parsons et al. (2006), field visits in 2004 and 2005 and G. Rios Arjona
(personal communication).
5'In most ex ante impact assessments, the costs of research investments would be included. Due to the stylized
nature of the intervention modeled, no research or implementation costs are included, and it is assumed that the
“technology” involves changes in management practices for which no additional costs are incurred by producers.
10
Nicholson and Parsons
Dynamic Modeling of Sheep Sector Policy Options in Mexico
Table 1 Policy Options Analyzed
Technology or Policy Growth Assumption
Altemative No Growth Constant Growth Slowing Growth
6% growth for 4 years,
0% growth; 6% annual growth; 2.5% growth
Baseline (No Change) No changes in No changes in subsequently;
technology or policy technology or policy No changes in
technology or policy
6% growth for 4 years,
0% growth; 6% annual growth; 2.5% growth
Subsid 20% variable cost 20% variable cost subsequently;
y subsidy for commercial | subsidy for commercial 20% variable cost
producers producers subsidy for commercial
producers
6% growth for 4 years,
0% growth; 6% annual growth; 2.5% growth
. Reduction of YS Reduction of YS subsequently;
Reduced Mortality mortality from 20% to | mortality from 20% to Reduction of Y S
10% 10% mortality from 20% to
10%
Results
The results are presented using two approaches. First, a graphical representation of key variables
over the model time horizon is provided for selected variables. The graphical approach
facilitates discussion of the dynamic effects of the interventions because their short-term and
long-term effects often differ. Second, as a means of summarizing the overall policy or
technology effects over a ten-year period, tabular summaries of relevant variables are reported
and compared to a baseline dynamic equilibrium without growth. Although the scenarios with
no demand growth are not realistic, they provide insights that are relevant for latter consideration
of the two scenarios with growth. As noted above, the key variables of likely interest to policy
makers and agricultural researchers are the sheep meat price, net margins for different types of
sheep producers in the two regions, and government expenditures on variable cost subsidies.
No Growth Scenarios
The effects of the subsidy policy and the intervention to reduce mortality have differing initial
effects on Mexican sheep markets. The subsidy reduces commercial producers’ costs of
production, increasing net margin. As a result of this immediate increase in profitability,
11
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
commercial producers seek to expand sheep numbers (that is, the desired number of BS
increases). In the short-term, this results in an inverse supply response, because a larger number
of female Y S are retained for inclusion in the breeding flock (Figure 2). The sheep meat price
increases for a period of about 18 months as commercial producers adjust their BS holdings, but
as the gap between desired and current BS holdings is closed and more Y S are being produced,
prices fall below the level observed in the dynamic equilibrium simulation (Figure 3). The
subsidy policy also results in oscillatory behavior of prices over a period of about seven years.
Initially, commercial producers experience a rapid increase in net margin (Figure 4), but this is
eroded by increasing costs (associated with larger BS holdings) and eventual decrease in animal
prices due to increased meat inventories. Net margins for commercial producers are increased
overall, but not by as much as the amount of the subsidy. Tras patio producers, in contrast,
benefit from the policy in the short-term when sheep prices are above the dynamic equilibrium
baseline level, but ultimately see net margins eroded by increased supplies resulting primarily
from commercial producers (Figure 5).
3000
2500
2000 ha
1500
Sales/month
0 12 24 #36 48 60 72 84 96 108 12
— Equilbrium — Subsidy — Reduce Mortality
Figure 2. Y oung Stock Sales, Y ucatan Region, for Initial Equilibrium
and Two Intervention Alternatives
12
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
0 12 24 36 48 ~~ 60 72 84 96 108 120
— Equilbrium — Subsidy — Reduce Mortality
Figure 3. Sheep Meat Price (Pesos/kg) for Initial Equilibrium and Two Intervention Alternatives
300
100
() 12. 24 #36 #48 60 72 8&4 96 108 120
— Equilbrium — Subsidy — Reduce Mortality
Figure 4. Commercial Producer Net Margin, Y ucatan, for Initial Equilibrium
and Two Intervention Alternatives
13
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
300
250
g 200
: [nN
150 — —
100
0 12 24 36 48 60 72 8&4 96 108 120
— Equilbrium — Subsidy — Reduce Mortality
Figure 5. Tras Patio Producer Net Margin, Y ucatan, for Initial Equilibrium
and Two Intervention Alternatives
The impact of the technology to reduce Y S mortality, in contrast to the subsidy, produces a
gradual increase in Y S supplied to the market (Figure 3) and a gradual reduction in sheep meat
prices (Figure 2), albeit with low-amplitude oscillations. These patterns of behavior are driven in
part by the gradual process of adoption assumed for use of the technology by commercial
producers, and by the less direct effect of the intervention on net margin and desired BS.
Adoption of the technology increases net margin for commercial producers over time (Figure 4),
but also demonstrates oscillatory behavior.’ Ultimately, the net margins become similar to those
under a subsidy: commercial producers see increases in net margin and tras patio producers, a
reduction. The ultimate outcomes with regard to sheep meat prices derive in part from the
assumption of inelastic demand. The subsidy and mortality reductions both increase the supply
of animals, and markets respond by reducing prices (which must fall to a larger degree due to
inelastic demand). However, it is worth noting that the initial and subsequent outcomes often
differ, the ultimate outcomes differ by type of producer (and presumably the impact on tras patio
producers would be considered undesirable) and that this system demonstrates considerable
° Oscillations arise from a system structure that includes at least one negative feedback loop with a significant delay
process. In this case, the negative feedback loop involves the response of sheep numbers to higher margins, and the
delays are those associated with acquisition of additional BS (i.e., the maturation delay).
14
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
policy resistance: the integrated market system responds in a way that offsets the magnitude and
sometimes the intended direction of the interventions.
The cumulative outcomes for the health intervention and the subsidy policy under no demand
growth are lower mean sheep meat prices, reductions in consumer expenditures (but increased
sheep meat consumption), increased cumulative net margin for commercial producers and
reduced cumulative net margin for tras patio producers (Table 2; first three data columns).
Changes in the overall cumulative net margin in the Y ucatan are small (less than 0.5% for the
subsidy policy and 1.1% for the health intervention), but the direction of change differs for these
two interventions. The increase in cumulative net margin for both types of producers in Y ucatan
due to the cost subsidy constitutes only about 2% of the government expenditures (the increase
in cumulative net margin for commercial producers is only 13% of subsidy expenditures),
indicating the extent to which policy resistance processes undermine intended outcomes. The
principal beneficiaries of both of the interventions are Mexican sheep meat consumers, for whom
the change in cumulative expenditures amounts to about $35 to $50 million US dollars over ten
years. Thus, the interventions have the (perhaps unintended) consequence of benefiting higher-
income sheep meat consumers and larger (and wealthier) commercial sheep producers at the
expense of tras patio producers (and the government in the case of the subsidies).
Constant Growth Scenarios
In the context of constant growth in sheep meat demand, prices for sheep meat increase
continuously over model simulation time regardless of the type of intervention assumed (Figure
6). This rate of increase is not constant over time, however, and differs depending on the
intervention. Analogous to the behavior observed in the no growth case, price initially increases
most rapidly under the subsidy policy, but after two years remains lower than the price for the
scenario without any intervention. The increase in prices is the least rapid and of the smallest
magnitude for the intervention to reduce Y S mortality. The increases in prices may be
misinterpreted (or misrepresented) by policy makers as resulting from their policy actions rather
than from the underlying dynamics of demand growth and lags in production response.
15
Nicholson and Parsons
Dynamic Modeling of Sheep Sector Policy Options in Mexico
Table 2 Simulated Outcomes of Alternative Policy Options Under Three Demand Growth Scenarios
No Growth Constant Growth Slowing Growth
Outcome
: Reduced : Reduced A Reduced
Base Subsidy Mortality Base Subsidy Mortality Base Subsidy Mortality
Sheep Meat Price? ($/kg) 40.00 39.32 39.09 54.82 53.97 52.79 51.74 51.19 49.95
Diff from DE -0.68 -0.91 14.82 13.97 12.79 11.74 11.19 9.95
Diff from No Policy 0.68 0.91 -0.85 -2.03 -0.56 “1.79
Value of Sales ($ mil)’ 43,969 43,585 43,454 64,437 63,884 63,160 60,507 60,144 59,388
Diff from DE -384 -514 20,469 19,915 19,191 16,538 16,175 15,419
Diff from No Policy 384 “514 554 | -1,277 -362_ | -1,119
Producer Net Margin” ($ mil)
Yucatan, Commerical 22.7 24.0 23.7 46.2 52.9 49.5 40.1 43.9 43.5
Diff from DE 14 Ti 23.5 30.3 26.8 17.4 21.3 20.8
Diff from No Policy 14 11 6.8 33 3.9 35
Yucatan, Tras Patio 19.5 18.3 17.9 45.0 42.8 40.5 38.6 37.9 35.9
Diff from DE -1.2 -1.6 25.4 23.3 21.0 19.1 18.3 16.4
Diff from No Policy -1.2 -1.6 -2.2 4.5 -0.8 -2.7
Other, Commercial 2,851.3 2,996.0 3,003.5 4,825.9 5,166.9 5,212.9 4,484.4 4,619.8 4,803.1
Diff from DE 144.7 152.2 1,974.6 2,315.6 2,361.6 1,633.1 1,768.5 1,951.8
Diff from No Policy 144.7 152.2 341.0 387.0 135.4 318.7
Other, Tras Patio 2,309.6 2,214.5 2,177.0 4,328.6 4,228.6 4,068.6 3,944.3 3,881.9 3,706.6
Diff from DE -95.1 -132.6 2,019.0 1,919.0 1,759.0 1,634.7 1,572.3 1,397.1
Diff from No Policy -95.1 132.6 100.0 260.0 -62.5 -237.7
16
Nicholson and Parsons
Dynamic Modeling of Sheep Sector Policy Options in Mexico
No Growth Constant Growth Slowing Growth
Outcome
: Reduced : Reduced . Reduced
Base Subsidy Mortality Base Subsidy Mortality Base Subsidy Mortality
Regional Net Margin’ ($ mil)
Yucatan 42.2 42.4 41.7 91.1 95.8 90.0 78.7 81.8 79.4
Diff from DE 0.2 -0.5 49.0 53.6 47.8 36.5 39.6 37.2
Diff from No Policy 0.2 -0.5 4.6 -1.2 31 0.7
Other 5,160.9 5,210.5 5,180.5 9,154.5 9,395.5 9,281.5 8,428.7 8,501.7 8,509.8
Diff from DE 49.6 19.6 3,993.6 4,234.5 4,120.6 3,267.8 3,340.7 3,348.9
Diff from No Policy 49.6 19.6 241.0 127.0 72.9 81.0
Government Subsidy? ($ mil)
Yucatan 0.0 10.4 0.0 0.0 16.6 0.0 0.0 16.5 0.0
Diff from DE 10.4 0.0 0.0 16.6 0.0 0.0 16.5 0.0
Diff from No Policy 10.4 0.0 16.6 0.0 16.5 0.0
Other 0.0 723.3 0.0 0.0 1,100.4 0.0 0.0 1,066.6 0.0
Diff from DE 723:3 0.0 0.0 1,100.4 0.0 0.0 1,066.6 0.0
Diff from No Policy 723.3 0.0 1,100.4 0.0 1,066.6 0.0
' Mean value over 120-month simulation.
? Cumulative value over 120-month simulation.
Note: All monetary values are in pesos. The symbol ‘$” is used to denote this in Mexico. DE indicates dynamic equilibrium.
17
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
0 12 24 36 48 ~~ 60 72 84 96 108 120
— Growth — Subsidy — Reduce Mortality
Figure 6. Sheep Meat Price (Pesos/kg) for Initial Equilibrium and Two Intervention Alternatives,
$ 000 / mo
with Constant Demand Growth
1000
900
800
700
600
500
400
300 eee
200
0 12. 24 #36 48 60 72 84 96 108 12
— Growth — Subsidy — Reduce Mortality
Figure 7. Commercial Producer Net Margin, Y ucatan, for Initial Equilibrium
and Two Policy Alternatives, with C onstant Demand Growth
18
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
Despite the appearance of robust growth in sheep production and prices, sheep meat and animal
prices are in fact lower than they would have been in the absence of the interventions, again
consistent with outcomes observed for no growth case.
The impacts of the interventions on sheep producer net margin mirror those of the no growth
case. Commercial sheep producers see an initial dramatic increase in net margin upon
introduction of the subsidies (Figure 7, previous page), a period when net margin with the
subsidy is roughly equal to that without subsidies, then a period of increasing difference due to
the subsidy. In this case, the effects of growth over the long term dominate the initial response
of commercial producers to the subsidy, and net margins continue to rise over the 10-year period.
Net margins are initially larger than they would have been without interventions for tras patio
producers due to relative reduction in Y S sales by commercial producers and the associated more
rapid price increase (Figure 8). By two years after the introduction of the interventions,
however, net margins are smaller for tras patio producers because the decrease in prices is not
compensated by either a corresponding reduction in variable costs or increased sales.
In cumulative terms, constant demand growth without other interventions results in a 37%
increase in the mean sheep meat price over the model simulation time, a 46% increase in the
cumulative value of sheep meat sales (due to both price and quantity increases) and a 116%
increase in regional net margin for Y ucatan sheep producers (Table 2). The impacts of the
interventions generally are to decrease each of these values by a small amount. Commercial
sheep producers in Y ucatan benefit from interventions in the context of demand growth and tras
patio producers are made worse off. As for the case of no demand growth, increases in
cumulative net margin realized by both types of sheep producers are small compared to
government expenditures on subsidies, but the proportion of subsidy expenditures realized as net
margin gains by producers in Y ucatén increases from 0.5% to 27.8%. The effects of growth
dominate the effects of the interventions and the likely interpretation by policy makers is that
their interventions deserve much of the credit for sustained growth of the sheep sector.
19
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
$ 000 / mo
wu
c—)
6
0 12. 24 36 48 60 72 84 96 108 12¢
— Growth — Subsidy — Reduce Mortality
Figure 8. Tras Patio Producer Net Margin, Y ucatan, for Initial Equilibrium
and Two Policy Alternatives, with C onstant Demand Growth
Slowing Growth Scenarios
If demand growth were to slow to less than half its current annual rate after four years of model
simulation time, the results are qualitatively similar to those with constant growth, but somewhat
attenuated.'” Demand growth that slows over time still results in markedly increased sheep meat
prices, consumer expenditures on meat sales, and sheep producer net margins (Table 2). The
impacts of the interventions on prices and the value of sheep meat sales in the context of slowing
growth are qualitatively similar to the constant growth case, but the magnitude of the impacts is
somewhat reduced. This suggests that the magnitude of the policy impacts depends to a certain
extent on the rate of demand growth relative to the ability of the sheep production sector to
respond given the inherent biological delays and the assumed producer decision making
structure. Slowing growth does not alter the outcome that the principal beneficiaries of
interventions in the sheep production sector are higher-income consumers, that commercial
sheep producers benefit from the policy and that tras patio producers experience reductions in
1 Because the graphical results in particular are qualitatively similar to those for constant growth, only tabular
results are presented for these scenarios.
20
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
net margin. Nor does the growth rate change modify the limited effectiveness of the subsidy
expenditures for increasing producer net margin. In fact, slowing growth reduces the proportion
of subsidy expenditures realized by commercial producers as net margin.
Conclusions and Implications
The foregoing analyses suggest that rapid growth in the demand for sheep meat in Mexico will
generate increased earnings for both commercial and tras patio sheep producers over the next
decade. The growth in demand dominates the effects of policies designed to assist the sheep
sector, whether through direct production subsidies or research to support technological
interventions that reduce animal mortality. The policies, in fact, have the impact of primarily
benefiting Mexican sheep meat consumers, many of whom tend to be higher-income urban
residents, and inevitably reduce net margins (relative to no interventions) for smaller, resource-
poor tras patio producers. Thus, as a strategy for rural development, the policies have decidedly
mixed results and the effectiveness of government expenditures—in terms of benefits for
producers—is quite limited. The Mexican sheep system thus exhibits two characteristics of
dynamically complex systems: unintended consequences (e.g., reduced cumulative net margins
for all sheep producers in some cases as a result of policy) and policy resistance—the ability of
the endogenous response of the system to various incentives to limit the ability of policy to
achieve specified objectives!!.
Although the principal results of the modeling effort discussed above are specific to the case of
sheep production in Mexico and the specific interventions analyzed, there are also a number of
broader implications. The first concerns the usefulness of an approach to modeling systems
evolution that addresses both policy and technology options as a part of the process. In this case,
the system evolution is driven externally by exogenous demand growth (i.e., the drivers of that
demand growth change are not modeled), but also internally by the stock-flow-feedback
structure and behavioral responses assumed to characterize the system. Although it is easy to
imagine extensions of this model to better represent the drivers of change and the evolution of
"' Ttis also worth noting that in conversations with numerous state government and research officials in Mexico that
they have not always clearly defined a set of consistent objectives for the livestock sector or agriculture and rural
development more generally.
21
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
production technologies, the above analyses illustrate in a relatively simple and stylized case the
practicability of system evolution analyses that include policy and technology factors.
Second, this application of a dynamic model highlights the usefulness of what has sometimes
been termed the “complex systems” approach to analysis of agricultural systems. As mentioned
in the introduction, some authors believe that most social, economic, biological and other natural
systems can be usefully conceived of as dynamically complex (Rosser, 1999; Sterman, 2000;
Allen and Strathern, 2005). Thus, these systems can generate a variety of behavioral modes and
outcomes that differ in the short and long term. The concepts and conclusions underlying this
general school of thought are not frequently applied in models of agricultural systems, but they
may prove useful for predicting future systems evolution with policy and technological
interventions. According to this school of thought, unexpected future developments may arise
due to the nonlinear characteristics of the system, past behaviors (and therefore statistical
relationships or correlations) may not be a good guide to the future, and simplification through
aggregation may ignore essential elements of system structure and undesirable elimination of
potential behavioral modes. This perspective on modeling extends also to model evaluation,
suggesting that neither parsimony nor independent verification are always possible when the
production system of interest may display dynamically complex behavior. The use of a systems
approach that emphasizes the development of both conceptual and empirical causal models often
will be most appropriate for these systems.
Finally, this process of undertaking this research has underscored the benefits of interdisciplinary
collaboration to assess technology and policy options. A simplified version of this model has
been used as a pedagogical tool for high-level agricultural researchers in INIFAP. Because they
had not previously been exposed in any detail to economic concepts, they did not realize the
importance that a parameter such as the demand elasticity could play in the determination of
outcomes related to their principal mission of developing technologies to benefit agricultural
producers in Mexico. Conversely, however, there is often a benefit to economic analyses of
more detailed representation of the stock-flow- feedback dynamics found in all agricultural
production and market systems. Applied biological scientists working collaboratively with
economists to develop more appropriate systems- oriented models often can provide both better
policy answers and more robust learning processes.
22
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
References
Allen, Peter M. and Mark Strathem. 2005. Models, Knowledge Creation and Their Limits.
Futures, 37:729-744.
Batty, M. and P. M. Torrens. 2005. Modelling and Prediction in a Complex World. Futures,
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Costanza, R., L. Wagner, C. Folke and K.-G. Maler. 1993. Modelling Complex Ecological
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Delgado C, Rosegrant M, Steinfeld H, Ehui S, Courbois C. 1999. Livestock to 2020: The Next
Food Revolution. Washington (DC): Intemational Food Policy Research Institute, Food and
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Fell, M. 2005. Personal communication regarding MSc thesis on sheep marketing channels in
central Mexico, Humboldt-Universitat zu Berlin.
Food and A griculture Organization. 2006. FAOSTAT data for sheep numbers, offtake, and
production, 2000-2005. http://faostat.fao.org/site/340/default.aspx (site accessed March 20,
2006)
Meadows, D. L. 1970. Dynamics of Commodity Production Cycles. Cambridge, MA: Wright-
Allen Press.
Nicholson, C. F. 2007. Review of Methods for Modelling Systems Evolution. International
Livestock Research Institute (ILRI), Nairobi, Kenya. [Discussion Paper No. 3 Targeting and
Innovation]
Nicholson, C. F., L. O. Tedeschi, and A. C. G. Lellis Vieira. 2011. The Application of System
Dynamics Modeling to Enhance Profitability and Sustainability in Latin American Livestock
Systems. (A plicacion de Modelos en el Estudio de Sistemas Dinamicos para Mejorar
la Rentabilidad y Sostenibilidad de los Sistemas de la Produccién Ganadera en
América Latina) Paper presented at the II Simposio Internacional Genomica y Modelacion en
los Nuevos Escenarios de la Ganaderia Bovina Tropical, June 22-25, 2011, Palmira,
Colombia.
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AGLINK-COSIMO Model. Unclassified report presented for discussion to the Working
Party on Agricultural Policies and Markets under item 8 of the draft agenda of the 41*
session, 23-25 October 2006. Paris: Directorate for Food Agriculture and Fisheries,
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Parsons D., A. Calderon-Quintal, C. F. Nicholson, R. W. Blake, C. Lopez-Cervantes, F. Torres-
Acosta, R. Caémara-Sarmiento, and G. Rios-Arjona. 2006. Diagnostico y necesidades de
investigacion en los sistemas de producci6n ovinos en Y ucatan. Universidad Autonoma de
Yucatan.
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Parsons, D., C. F. Nicholson, R. W. Blake, Q. M. Ketterings, L. Ramirez-Aviles, D. G. Fox, L.0.
Tedeschi, and J. H. Cherney. 2011. Development and evaluation of an integrated simulation
model for assessing smallholder crop-livestock production in Y ucatan, Mexico. Agricultural
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Rosegrant, M. W., C. Ringler, S. Msangi, S. A. Cline, and T. B. Sulser. 2005. International
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Model Description. Washington, DC: Intemational Food Policy Research Institute [mimeo]
Rosser, J. Barkley. 1999. On the Complexities of Complex Economic Dynamics. Journal of
Economic Perspectives, 13(4):169-192.
Sterman, John. 2000. Business Dynamics: Systems Thinking and Modelling for a Complex
World. Boston: Irwin/McGraw Hill.
Stout, J. and D. Abler. 2004. ERS/Penn State Trade Model Documentation. August 2003,
updated October 2004. [unpublished document available at http://trade.aers.psu.edu/]
Tedeschi, L. O., C. F. Nicholson and E. Rich. 2010. Using the System Dynamics modelling
approach to develop management tools for animal production with emphasis on small
ruminants. Small Ruminant Research, 98:102-110.
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Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
APPENDIX: Model Equation Specification
BS and YS Dynamics
BS,,, = |(Replacements,, + Adjustments,,, —Culls,, )+ BS,,. ?
pt
This equation indicates that the number of breeding stock is the integral of replacements for
culled animals, adjustments based on desired increases in the number of BS held less the number
of animals culled. In this and subsequent expressions, r indicates region (Y ucatan or Other), p
indicates producer type, and t is the time subscript.
d(BS 2)
( ar ) = Replacements, + Adjustments,,, —Culls.,,
This is the equivalent differential equation for the integral equation shown in (1).
YS. = {(Births,,, + Mortality,,, + Maturation, )+YS.,, 8
This is the integral equation for Y S, which indicates that births increase Y S numbers whereas
mortality and maturation (to the age for sale or use as a BS replacement animal) reduce YS
numbers.
alys 3)
al = Births,,, — Mortality,,, - Maturation,,,
This is the equivalent differential equation expression for (3).
Births,, = DELAY[Breeding,,, ,Gestation Time,,, ] 6)
This indicates that the birth rate is a fixed delay of the rate at which animals are bred, where the
delay duration is the gestation time.
LPL, \”
U,
The breeding rate is equal to the number of BS times the Lambs per Lambing (LPL) divided by
the Lambing Interval (LI).
Mortality, =DELAY(Births,,, ie", MatTime,,, 1)
pt
Breeding,,, = BS.,, {
Mortality is a fixed delay of births times a proportional mortality rate, with the delay equal to a
time required for maturation. Note that this is one of two commonly used formulations for
mortality in aging-chain and population models (Sterman, 2000). The other formulation assumes
a first order delay process rather than removing all mortality (and maturing animals; see below)
when cohort members exit.
Maturation,, =DELAY(Births,,, f1- cae ), MatTime,,, \®)
Arpt rpt
Maturation is a fixed delay of births times one minus a proportional mortality rate, with the delay
equal to a time required for maturation.
25
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
on", MatTime,,,, LI, = f (FeedBiomass,,, ,BS,,, +YS., )
The mortality rate, the maturation time and the lambing interval are nonlinear functions
decreasing in the relative availability of feed.
(10)
tpt? pt?
Maturation, = Sales}; + Replacements,,,
This condition implies that all maturing (female) animals at time t are either sold or retained as
BS replacements.
Replacements,,, < Maturation,,, a Fene(L1)
The number of replacements available must be less than or equal to the number of Y S reaching
maturation age time the proportion of the YS that is female.
; (12)
Slaughter, = DCulls,, -Yield** + ¥ Sales’ -Yield"®
7? 1p
The slaughter rate (in terms of kg of sheep meat per month) is the number of BS animals culled
times the carcass yield for BS plus sales of Y S times the carcass yield for Y S.
Feed Resource Dynamics
Feed,,, =/(Production,, + Losses,, +Consumption,,, )+ Feed,,, a
Feed resources available are the integral of feed production, losses (feed not consumed that
becomes senescent and decays) and feed consumed by animals.
d(Feed . a!
{Feed} = Production,,, — Losses,,, -C onsumption,,,
dt
This is the differential equation representation of (16).
FeedPerLand,, = f(FeedBiomass,,,, MaxBiomass,,, , Rain, yes
Feed produced per unit land is a decreasing nonlinear function of current forage or browse
biomass relative to the maximum possible biomass and current month rainfall.
Ai Loss (16)
Losses,,, = Biomass,,, - 0,
Losses of feed are a constant proportion of current forage or browse biomass.
Consumption,,, = BS,,, -FeedPerBS.,, +YS,,, - FeedPerYS,,,°”
Feed consumption equals feed consumed by BS and by YS, where consumption by each of those
animal types is equal to the number of current animals times the amount of feed consumed per
animal per month.
FeedPerBS,,,, FeedPerYS.,, = f (Biomass,,,BS.,, +YS,,)
Feed consumed per animal per month is a function of the relative availability of feed, which is in
tum a function of the current forage or browse biomass and the numbers of BS and Y S.
mt?
26
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
Inventory and Price Dynamics
(19)
se = Slaughter, — Sales, + Imports,
Sheep meat inventories are increased by the slaughter rate and imports and decreased by sales.
(20)
pye
Imports, = Imports ** (gm=|
Sheep meat imports are an increasing function of Mexican sheep meat prices, formulated as a
reference level of imports times current sheep meat price relative to a reference meat price value
with an import demand elasticity ¢ > 0. Note that there are few trade barriers for sheep meat
entering Mexico.
Meat nl)
Sales, = Sales;** (jm
p RePMeat
Sheep meat sales are a decreasing function of Mexican sheep meat prices, formulated as a time-
dependent reference level of sales times current sheep meat price relative to a reference meat
price value with own-price demand elasticity y <0. Growth in demand for policy scenarios is
effected through increases in the value of “reference” sales over time.
Pw = Pp™™=. f (Inventories, , Sales, )
Sheep meat prices are determined in response to a smoothed value of inventory coverage
(inventories at time t divided by sales at time t, which has units of the number of months for
which inventories are sufficient to cover the current rate of sales). Prices are a nonlinear
decreasing function of inventory coverage.
pis = (Px = Costs iss )-Yield 3s (23)
Prices per BS animal received by sheep producers are equal to the sheep meat price less meat
marketing costs (which differ by producer type and region) adjusted by the yield in kg per
animal.
pss = (Pu 7 Costs’ ) Yield ys(24)
Prices per Y S animal received by sheep producers are equal to the sheep meat price less meat
marketing costs (which differ by producer type and region) adjusted by the yield in kg per
animal.
Producer Decision Dynamics
BS;, =BS,,- (Net Margin, }”
The desired (aggregated by producer group and region) level of breeding stock is equal to the
current number of BS times a nonlinear increasing function of expected long-run net margin (an
exponential smooth of past net margin values) relative to a reference net margin value. The
27
Nicholson and Parsons Dynamic Modeling of Sheep Sector Policy Options in Mexico
functional form is constant elasticity, with an elasticity of BS* with respect to long-run net
margin of € > 0. Note that this uses an anchoring and adjustment heuristic that Sterman (2000)
argues is commonly used in capacity decisions.
BS" (26)
MTBS,, = f] —"
" BS...
The mean time an animal is retained in the BS stock is a nonlinear increasing function of the
ratio of desired to current breeding stock.
* (27.
BS 27)
mt
MTBS,,
The number of animals to be replaced is a first-order expression involving the number of desired
BS animals and the mean time animals are retained as BS (MTBS).
Replacements, =
* (28)
-BS,
Adjustments, = aT
Adjustments are animals added to the BS in response to changes in the desired level of BS
holdings. They are expressed as a first-order expression of the difference between current and
desired levels of BS holdings, modified by a parameter representing the time required to adjust
BS holdings (BSAT).
(29)
Animals are culled at a fractional rate of animals currently held as BS. This fractional rate
equals (1/MTBS).
YSSales,,, = Maturation, - (Replacements,,, + Adjustments,,, yo
Sales of YS by the sheep producer are limited by the maturation rate. Animals not needed for
replacements or adjustments due to changes in the desired breeding stock are assumed to be sold.
28
