1. E-StItRoS:Inflation Expectations in Poor Rural Contexts
Umberto Perna†‡
& Pierre-Andr´e N¨oel‡
†University of Florence, Italy; ‡University of Califonia - Davis, USA.
Abstract
The spread of inflation expectations in fi-
nite closed communities can be modeled
through the use of a stochastic edge-based
epidemic model. This approach is to be
applied to the rural developing world.
Objectives
Network Information Spread models for:
• complex and/or dynamic contact pat-
terns in clustered communities;
• stochastic external shocks;
• guiding policy action.
Background
Compartmental models in mathematical epi-
demiology divide a population into com-
partments; two individuals in the same com-
partment are considered indiscernible.
I RS
In a SIR model, individuals may be Sus-
ceptible, Infectious or Removed. More
transmission routes are added for mecha-
nisms not characterized by a pathogen.
In our case individual are either Steady,
Inquiring or Revised with respect to
the inflation expectations and depending
on their available information. The state I
is ‘unstable’, agents pass through this stage
only in case they receive new data from
their bonds.
E
Shock
N
News about (dis)inflationary shocks arrive
from the external Environment (E), and
they reach a single node that spreads them
around the village N. If a certain thresh-
old, R, is reached than the message gets
sent to other villages (Na, Nb, Nc and so
forth). This mixture of internal dynam-
ics and external factors provides the name
for the model: E-StItRoS (Environmental -
Stable two-way Inquiring two-way Revised
one-way Stable).
Background - cont’d
Away from the powergrid, agents receive in-
formation almost exclusively in an infor-
mal, irregular manner through interpersonal
contacts (see [2]). This is particularly rel-
evant in the context of small farmers in
terms of their anticipated increases in the
price of fertilizers, and the crops that they
produce and eat.
Geospatial dataset
of existing electricity grid
Voltage [kV]
Distance from the grid [km]
0 - 50
100 - 200
50 - 100
200 - 500
500 - 1300
0 - 22
23 - 110
111 - 220
221 - 800
Availability of electricity and distance from mainline in
selected African countries (from [5]).
The network is Heterogeneous: Stable, peo-
ple who have not changed their opinion re-
cently and are less likely to do so if new
info pours in; and Revised, for whom the
converse is true. Furthermore, connectivity
varies, some agents see to be more socially
active than other, but clustering is gener-
ally high (see [4]). In order to model the
village network, we have considered one-
hundred nodes, and they entertain connec-
tions on average with a relevant fraction
(roughly one fifth) of the local population.
Inflation expectations have been a very de-
bated and researched topic in the economics
literature, but only very recently epidemi-
ological argumentation have been put for-
ward, helping to explain their stickiness
and imperfect rationality.
A Village-like Network Configuration
Methods
Following the methodology adopted in [1],
which is in turns based on [3], we consider
an undirected, bitype network, where the
system is characterized by:
• Pi
the Stochastic Connectivity matrix for
types i = S, R;
• T the Transmission matrix;
• σ the State Change vector.
Such setting will allow us to specify and
analyze the behavioral component of the
agents.
pi
k,l ∈ Pi
defines the probability of node
type i connected to k S-neighbors and l R-
neighbors. Such coefficients have been gen-
erated by a Bivariate Poisson Distribution
function, taking different values for λ0 =
1, λ1 = λ2 = {3, 8}.
Distribution for MP(1, 3, 3).
Distribution for MP(1, 8, 8).
The Transmission matrix includes four en-
tries for the probability that each type will
communicate with any other type, discrim-
inating in this way the different attitudes in
the sharing of information for Stable and
Revised agents. The latter group is ex-
pected a priori to be more willing to com-
municate new information. The change of
state vector assigns a probability for the
two types to stay the same the next period.
Results
For illustrative purposes, we provide differ-
ent scenario analysis with variation in the
behavioral terms. The average connectiv-
ity degree, λ takes the values of 4 and 9.
The elements of σ are first considered as
symmetric for both types (0.5 each), and
asymmetric (0.4 for S and 0.9 for R) subse-
quently. Three levels of Transmission like-
lihood are also shown here (where the effect
on R has been made steeper than on S).
As for the probability of becoming inquir-
ing depending on the state at the begin-
ning of any given period, we notice that
the effect is on average more pronounced
for agents of the R type, since they have
been subjected to higher transmission rates
than S.
Conclusions
The development of the E-StItRoS model
has shown the possibility of modeling to
a sensible level of complexity the response
to an external informational shock, with a
handful of parameters. The results here
presented are preliminary, since the model
is still in its prototype stage, but the ap-
proach is promising, as it allows for a flex-
ible approach. The ability to adapt this
framework to the local idiosyncrasies is one
of the requirements for its effectiveness, as
in underdeveloped economic context local
social customs drive also the way agents
process information. A better understand
of these processes will provide guide to pol-
icy action in preventing unfunded rumors
about the current or future state of the
economy to spread beyond control.
Extensions
More types can be accounted for, modeling
the different behavioral responses of men
and women with respect to saving/spending.
The connectivity structure can be made hi-
erarchical to take into account the differ-
ent weight in the opinion reputation of the
community members.
Noise and simultaneous contradicting in-
formation coming for the environment (per-
sonal ties vs. traditional media) can better
model the real-life scenarios.
Interesting interplay of receiving vs. send-
ing of information can be analyzed when
the R threshold is exceeded in more than
one village at any given time.
Selected References
[1] Allard, A. et al., Heterogeneous bond percolation on multitype network with an
application to epidemic dynamics. PRE 036113, 2009.
[2] Babu, S. C. et al., Farmers’ information needs and search behaviors: case study
in Tamil Nadu, India. IFPRI DP 01165, 2012
[3] Newmanm M.E.J., Spread of epidemic disease on networks. PRE 016128, 2002.
[4] Rahman, M. A. et al., Social networks in rural situation: a case study in My-
mensingh district of Bangladesh, The Agriculturist 9, 2011.
[5] Szab´o, S. et al., Energy solutions in rural Africa: mapping electrification costs
of distributed solar and diesel generation versus grid extension, Environ. Res. Lett.
034002, 2009.
Acknowledgments
U.P.’s visiting position at UC Davis is founded 3-DSRDTRA
Research Grant awarded to Prof. Raissa D’Souza.