COMPLEXITY AND ENDOGENEITY IN ECONOMIC MODELING
ABSTRACT
The concepts of complexity, endogeneity and circular causation (Myrdal’s (1957) term
was circular causation) are shown to be interrelated ones in configuring economic
modeling in the framework of systemic embedding and its empirical application. The
ensuing framework of economic modeling with complexity provides a controllable and
predictable overarching worldview. Anomie in the economic universe and its embedded
world-system is analytically rejected. This consequence is due to the epistemic nature of
modeling that combines complexity, endogeneity, and circular causation for attaining
predictability and controllability even in the face of complex systemic perturbations. The
epistemology of unity of knowledge contrasted with rationalism is treated as the
foundational worldview. An illustrative empirical work is given to convey the conceptual
model and its applied viability.
Keywords: embedded economic system; economic epistemology; economic and social
modeling.
Objective
Realism in economic and social theory requires the study of systemic dynamics and
change that explain inter-variable and inter-systemic causality. Economic theory is
devoid of the study of social processes of being and becoming (Prigogine, 1980).
Consequently, the problem of complexity in social and economic interrelations cannot be
explained by means of the underlying extensive causality that exists between the intercausal variables. Yet the complexity approach in economic modeling is essential to study
inter-causal relations among variables pertaining to a given problem.
In this paper we introduce a methodology for economic modeling that establishes
extensive inter-causal organic relations by evolutionary learning in the variables and their
embedded systems. Such inter-causal organic relations will be explained as being able to
analyze the system complexity by treating completely endogenous inter-relationships
between the variables.
The paper considers the nature of complexity in socio-scientific methodology
including economics. It introduces the meaning of pervasively endogenous inter-causal
relationships between the variables that arise from the complexity of their relations. We
then mesh up these two characteristics of social realism by the method of circular
causation. An empirical example is provided to explain the nature and role of circular
causation in evolutionary learning model of unity of knowledge as the underlying
episteme.
Complexity
The concept of complexity is explained in this paper as the semblance of
uncontrollability of interactions among variables in modeling that, defies predictability
1
and definitive solutions. By the nature of interactions between ever-increasing linkages of
causally related variables, complexity becomes a property of nonlinear systems.
Formally, complexity has been defined as follows (Bertuglia and Vaio, 2005, p.
269): “The fundamental characteristic of complexity is the fact that, in the study of the
evolution of dynamical systems that complexity deals with, the nature of the system in
question is usually irrelevant. In the vision proposed by complexity, we can identify
forms and evolutive characteristics common to all, or almost all, systems that are made
up of numerous elements, between which there are reciprocals, nonlinear interactions and
positive feedback mechanisms. These systems, precisely for this reason, are generally
called complex systems.”
In our model of evolutionary learning the complexity and endogenous system of
relations will be depicted by nonlinearity caused by continuous systems of bifurcations
creating diverse learning paths. Every point of such evolutionary learning bifurcated and
linked paths of organic relations has two-stages of its movement with the rest of the
interrelated points. Firstly, there are expectational convergences towards, but not attained,
dynamic equilibriums within given systems of relations. Secondly, there are similar forms
of evolutionary learning equilibriums between interrelated points across diverse systems.
Their intra- and inter- systemic organic relations are explained by circular causation
(Choudhury, 2011). The emergent circular causation relations represent the reciprocity,
nonlinearity, and feedback mechanisms that are pointed out by Bertuglia and Vaio.
Chan’s (1984) liewise Bertuglia and Vaio’s depiction of the system-view of
complexly interrelated variables to attain an objective criterion is shown by the following
system-model. This is an improvised formulation of the diagram given by Bertuglia and
Vaio (op cit) to explain the nature of nonlinearity, complexity, endogeneity, and circular
causation relations.
Figure 1: Inter-causal evolutionary dynamics under complexity
and endogeneity of systems
circular causation: nonlinear reciprocity
A
process
B
C set of endogenous
variables intra- and
inter-evolutionary systems
Intra-systemic
Interaction leading
To its own dynamic
Evolutionary equilibriums:
Intra-systemic circular causation
D
inter-system
evolutionary
dynamics of
interrelations
and evolutionary
equilibriums of
endogenous variables
by circular causation
2
C’
functional
space of the
endogenous
variables,
explaining
circular
causation
A’
continuity
B’
similar to
B in the
functional
space
Complexity and endogeneity in the philosophy of science
The complexity doctrine of economic modeling can also be found in the continuous reemergence of incomplete systems of logical relations (Godel, 1965). In such models there
is no end to a plethora of evolving undecided logical relations. Consequently, the
evolutionary complexity of mathematical systems results in the absence of unique
solutions even within the realm of mathematical precision. Godel (See Smullyan, 1992)
refers to such mathematical systems of relations as ‘printable’ but yet ‘undecidable’. An
example is that of sentences printable by a computer, but having no meaning. The
sentences do not connect logically to form language to convey meaning.
Popper’s (1965) conjectures, refutations and falsifications are yet other ways of
stating the possibility of anomie in inductive testing of deductive premises (Blaug, 1993).
Logical problems of socio-scientific nature arise from Popper’s methodological anomie
(Popper, 2004). Firstly, it becomes impossible to establish sustainable predictability of
systems of ideas. Secondly, anomie leads to the absence of universality and uniqueness of
a convergent worldview.
Notwithstanding the reality of indeterminateness of dynamical systems in which
predictability, uncontrollability, indecisiveness and anomie abide, yet the probabilistic
nature of events remain entrenched in actualized observations. The future is thereby read
as complexity, though it is determined by the sequences of past events, despite being
probabilistic.
Complexity is indeed an unshakable nature of all multidimensional relations of
variables and systems defined by them. Yet the dynamic evolutionary learning nature of
systemic interactions needs to chart the history of the future to predict, guide and explain
reconstruction and change. Such attributes reveal inner consciousness that is embedded in
historical change. Indeed, history can be understood as a system-ensemble (Hegel trans.
Sibree, 1956; Hubner trans. Dixon & Dixon, 1985; North, 1981; Smith, 1992).
Consciousness wrapped up in system-ensemble gives the idea of historiography. This is
essential in the economic understanding of positivism followed by normative simulation
in economic models. Normative simulation presents the reconstructive lessons of the
future based on the conditions of the past and present from which recursively evolved
lessons are generated.
Endogeneity
Endogenous variables are systemic variables. In economic theory such variables arise
from interactions within the market exchange process. On the other hand, Exogenous
variables are determined independently of the market process.
Examples of exogenous variables are individual preferences; policy variables;
other extra-disciplinary variables outside the economic and market system, importantly
ethics and morality. Some variables are strongly exogenous, such as ethics and morality,
preferences and behavior as datum, and fiscal policy variable. Other variables, such as
population, technology, and monetary policies are of the weakly exogenous type.
Endogenous variables are inter-related in a circular way. Hence they cannot be
sustained as being weakly endogenous. For instance, while in mainstream economic
modeling monetary policy variables and fiscal policy variables (Blaug, 1993) remain
3
exogenous of each other; yet in terms of endogenous system-variables these are
considered to be relational. An example is the treatment of monetary and fiscal policy
complementarities in Schumpeterian growth model with innovation (Cantner et al.2009).
Endogeneity therefore is the character of systems that are embedded ones.
Market-variables are then interlaced with policy variables, preferences, technology, ethics
and economics, and social variables. The latter variables are consequently changed into
endogenous variables as well.
Endogeneity is thereby based on circular causality between the variables in
reinforcing the embedded effects of the variables and their embedded systems that lie in
the state of complex interrelations. However, by the methodological application of the
circular causation interrelations between the variables the degree of entangled complexity
is converted into solvability, predictability, and controllability over the evolutionary
learning processes. Endogeneity is thereby epistemologically driven by a normative
worldview to correct and reformulate a positivistic problem situation.
The design of circular causation was rendered by Myrdal (1958), recently
summarized by Toner (1999), and also used by Schumpeter (see Gaffard, 2009) in
describing their complex social and economic development processes. In each of these
contributions the empirical functioning of the circular causation system of endogenous
relations between the variables to disentangle complexity (Maurer, 1999) is not shown.
Yet, the implication is that complexity can be disentangled by invoking strong
endogeneity between the otherwise exogenous policy variables in economic modeling.
An example in this regard is the ignored possibility of endogenous relationship
between monetary policy and fiscal policy by the evolutionary learning and technological
effects. Such endogenous effects can liberate the real output from the condition of its
neutrality to monetary and fiscal policies at the Keynesian full-employment level of real
output. Consequently, the innovation and entrepreneurial possibilities that follow from
the mix of evolutionary learning and technological change extends the elasticity of the
aggregate supply curve. Furthermore, macroeconomic general equilibrium theory gets
influenced by microeconomic foundations of dynamic changes in household and social
preferences; production menus; and regimes of economic development as by the adoption
of the basis needs approach.
Absence of pervasive endogeneity is entrenched in economic theory
Boland (1989) has shown in reference to Popper-Samuelson (Samuelson, 1963) lately
and Keynes’ earlier (see O’Donnell, 1989) epistemological viewpoint in economic
methodology that rationalism remains at the core of economic modeling. Rationalism is
understood as dichotomy between the Kantian type a priori reasoning and a posteriori
reasoning. This methodological dichotomy in logical reasoning is pointed out as the
problem of synthesis by Carnap (1966). In economic theory, such heteronomy reveals
itself as the differentiation between ethics and economics; social justice and economic
efficiency; and thereby between exogenous variables and endogenous variables of
economic modeling.
4
The central postulate of marginalism between allocative variables as independence of
relations: endogeneity versus exogeneity
In fact, all of economic theory is entrenched in marginal rate of substitution both in the
static sense and dynamic sense of optimal control theory. Dasgupta (1987) points out
marginalism to be the core axiom of entire economic theory. Marginalism denies the
entrance of knowledge in the resource allocation system. Consequently, it becomes
impossible to integrate a priori reasoning (deductive neoclassicism) with the a posteriori
reasoning (inductive reasoning). This is the problem of methodological demarcation that
is pointed out by Blaug (op cit, pp. ) in respect of Popper’s falsification model applied to
economic and social issues. In fact, separation between the deductive reasoning and
inductive reasoning abides permanently in socio-scientific reasoning. Any attempt to
establish a unique formalism of continuity that integrates the a priori and the a posteriori
reasoning is therefore lost. Thereby, the problem of a priori and a posteriori demarcation
in economic theorizing remains permanent.
Pervasive endogeneity in the economic literature
Desai (1989) points out the meaning of exogeneity and endogeneity in the following
relational way: Let there be three vectors of variables {x, y, z}. These are endogenously
related if there exist functionals like f 1 , f 2 , f 3 , such that, x = f 1 (y,z); y = f 2 (x,z); z =
f 3 (x,y). The existence of a series of functionals of the type {f 1 , f 2 , f 3 } also means circular
causation between the endogenous variables {x, y, z}.
This system of organic inter-relations proves the theorem that disentangling of
complexity, endogeneity of relations between the variables, and the circular causation
relations between them, are coterminous in economic modeling with extensive
endogeneity. Contrarily, if any of the system of functional relations fails to exist, then the
organic continuity of relations between the variables is disrupted. Consequently, both
endogeneity and the means of explaining embedded nature of interactive systems are lost.
Such is the case in policy-induced economic models where policies remain as exogenous
variables.
A formal expression for circular causation
A formal expression for circular causation is presented in Figure 2. In terms of the
episteme of unity of knowledge of the system-orientation to embedded social modeling,
the economic phenomena of circular causation between variables of diverse subsystems
exemplify pervasive complementarities between the variables. From this idea arises the
simulation of the objective criterion of wellbeing.
Wellbeing is treated as the conceptual objective criterion for ‘estimation’
followed by normative ‘simulation’ of the estimated results. The simulation of the
estimated results represents the degree to which there ought to exist complementarities
between the selected variables. Pervasive complementarities between the variables in the
normative sense of the positivistic estimated results are derived from the epistemology of
unity of knowledge in the problem under study between the selected variables. Because
5
of the principle of complementarities representing the measured degree of unity of
knowledge between the variables, such variables get knowledge-induced.
We write the circular causation system as follows:
Simulate
Subject to,
W(X(θ)); X(θ) = {x 1 , x 2 , …, x n }[θ]
x i (θ) = f i (x j (θ),θ);
where x j (θ) = {X(θ)} j≠i i,j = 1,2,..,n
θ = F(X(θ)) ≡ W(X(θ))
(1)
(2)
(3)
While W(X(θ)) is the conceptual objective of wellbeing, θ = F(X(θ)) is the measured
functional that is identical to W(X(θ)). While leaving out the technical details here, the
above (n+1)x(n+1) dimensional system of equations and variables is uniquely solvable
for the variables. All the technical applications of estimation followed by simulation by
changes in the estimated coefficients and in predictor values of the simulated variables
reproduce their own simulacra of reiterated results.
The pervasive complementarities between variables in circular causation relations
explain the extensive endogeneity between them. The simulated dynamic nature of the
coefficients of the circular causation system explains perturbations as complexity in the
system. The ‘estimation’ (positivistic) of the circular causation relations followed by their
‘simulation’ (normative) and predictor-values in repeated simulations (simulacra) across
evolutionary learning processes explains the absence of anomie in the circular causation
relations. Thus the circular causation system integrates complexity, endogeneity,
predictability, and controllability altogether.
The empirical work shown in the Appendix illustrates one-process estimation by
circular causation method and its results. The entire simulation exercise with evolutionary
θ-values moving across evolutionary learning processes is a detailed computer-generated
exercise. It is not shown except for an illustration on simulation of the type by choice of
coefficients using the Spatial Domain Analysis (SDA).
A methodology of disentangling complexity by endogenous relations in economic
modeling
Desai’s circular causation system of endogenous functional relations between the
variables defines endogeneity and exogeneity. Yet this does not establish the possibility
of existence of pervasive endogeneity in economic modeling. This latter problem is of an
epistemological nature. We have argued above that the presence of rationalism at the core
of heteronomy between the a priori and a posteriori reasoning makes it impossible to
disentangle complexity by pervasive endogeneity. This again is based on circular
causation relations between variables. Consequently, as long as this sort of
epistemological impediment remains in economic reasoning, as in Kantian type
heteronomy, it is impossible to model embedded systems of relations. Yet such
overarching embedding forms the true picture of socio-scientific cybernetic worldview.
Economic modeling needs to comprehend such systemic inter-causality.
Such a project of continuity in scientific reasoning would break down the walls of
heteronomy as in rationalism. The revolutionary scientific change would then be to
include inter-causal embedding in economic modeling. The emergent discipline of
6
economic modeling can then enable the study of methodological convergence of varied
disciplines towards an explanatory wholeness. Such a convergence of systemic
embedding establishing interrelations means pervasiveness of endogeneity that
disentangles complexity by means of the circular causation interrelations.
The new epistemic methodology for attaining such integration must therefore be
premised on systemic unity of knowledge. The order of systemic differentiation reflected
in the prevalent nature of economic modeling -- arising from the epistemology of
rationalism -- is replaced by the episteme of unity of knowledge intra- and inter- systems.
The resulting theory of economic modeling causes every variable to be endogenously
interrelated with other variables.
In such extensively endogenous systems of circular causal relations there is only
one exogenous variable. Upon this the whole evolutionary learning system of overarching
system variables is premised. This is the initializing of know-ing on the basis of the
epistemic nature of oneness of knowledge treated as super-topology (Rucker, 1982). The
evolution of knowledge based on the core of epistemic oneness is regenerated across
continuums of knowledge, space and time dimensions as learning processes continue.
The emergent analysis of economic problems in the resulting economic modeling with its
epistemological roots is thus carried out over the dimensions of knowledge, space and
time.
The characterization of events in knowledge, space, time dimensions is shown by
the spanning set:
Event: {θ, X(θ),t}, with θ∈(Ω,S)
X(θ) = (x 1 , x 2 , …,x n )[θ]
(4)
We can now express the total phenomenology of the evolutionary learning system
as the unique and universal methodology of all systems by virtue of the episteme of unity
of knowledge as follows (Figure 2):
Process 1: time period 1
Process 2: time period 2
[Ω→ S ≡(Ω,S)] →
{θ}→ X(θ)
(5)
↓
{θ,X(θ),t}→ W(X(θ);t)
Simulate by circular causation
x i = f i (x j (θ;t), θ), i≠j = 1,2,..,n
θ = F(X(θ);t) → → continuity across
evolutionary learning
epistemic recalling
processes of simulacra.
Figure 2: The phenomenological model of unity of knowledge in ‘everything’: Economics as
embedded evolutionary learning system in unity of knowledge across systems with
endogenously knowledge induced variables in knowledge, space and time dimensions
An overarching dialectical system model of the above type is given by Sztompka
(1991) and Resnick and Wolff (1987). But the epistemic recalling in their model of social
7
becoming remains to be rationalism. Hence inter-systemic and process-oriented
continuity of unity of knowledge – hence evolutionary learning -- remains questioned in
these other systems.
Illustrative example
An empirical exercise in circular causation with one-process learning in evolutionary
learning phases is presented below. The diagrams show the substantively different form
of spread between real growth rate (G) and poverty rate (P) across time and knowledge
flows. Knowledge-flows are computed as ranks assigned to θ in terms of the appropriate
trends in the socioeconomic variables corresponding to the episteme of oneness shown by
degrees of complementarities between the selected variables. It is expected that θ↑as P↓;
θ↑as G↑ in the assignment of such θ values. The individual θ values are then averaged to
yield the final knowledge ranks between the trends in (G,P).
Conclusion
While complexity is the indispensable part and parcel of embedded social systems, in
which economics ought to be a participatory candidate, yet such systems are not totally
chaotic. Order out of chaos prevails to restore a reasonable degree of predictability and
controllability of the multi-dimensional system-variables that enter the large evolutionary
learning class of economic and social modeling (Rosser Jr. 2004). Such classes of
overarching systemic models form social wholes of simulacra between the variables
(Fitzpatrick, 2003).
The invoking of ontological and epistemological consideration underlying the
immanent modeling of such evolutionary learning behavior becomes harbinger to a new
domain in socio-scientific venture. At this juncture of smart computers the study of large
embedded social, scientific, and economic sub-systems is becoming increasingly
possible. Economic modeling would thus be more meaningful, rather than a luxury of
unrealism, in studying evolutionary learning and embedded systems.
Indeed, the grandest failures of economic modeling are caused by its failure in
predicting and controlling some of the worst kinds of financial crises that have occurred
in recent times and continue on. In the extensive form of embedded economic model the
presence of factors such as Greed, Trust, Values and Ethics in consumption and
investment behavior would be subtle components of the new modeling enterprise. They
will be endogenous behavioral variables in explaining the comprehensive picture of
financial perturbations.
The indelible need for premising the ethically reconstructive future of change on
the episteme of unity of knowledge is to incorporate the dynamics of endogenous factors
in modeling both positive and normative transformation. In the emergent mind-matter
epistemological system the functional nature of extensive forms of economic, social, and
scientific factors will abide. This will cause ethical endogeneity through the emergent
evolutionary learning systems. The same cannot be explained otherwise in modeling with
the rationality qua rationalism as axiom.
This paper has considered such vaster domains of inclusiveness that prevailing
economic modeling with its rationalistic epistemological basis and exogeneity of human
8
values cannot incorporate. Instead, the new genre of smart computers would be able to
extend the domains of economic modeling. The result would be a further revision of the
bounded rationality axiom of Simon’ Models of Man (1957) and the like.
9
STATISTICAL APPENDIX
The empirical work presented below is for a one-process learning model for the case of
growth-poverty interrelations in Indonesia. The actual case of the relationship is
statistically estimated over time. The normative case of knowledge-induced change over
knowledge, space and time dimensions is implied in the framework of unity of
knowledge. This normatively points out the need for economic, social and policy change
that can establish coterminous relationship between increasing real growth rate (G↑) and
decreasing poverty rate (P↓), and thereby, to define the wellbeing index in its positivistic
and normative forms in terms of θ as a function of (G,P).
The conclusion gained from the empirical results is this: Reading the relationship
between growth rate and poverty rate in the normative scale reveals the internal dynamics
of ought-against-is state of such relations. The endogenous formulation of such normative
changes in the perspective of unity of knowledge, as explained earlier, while revealing
such internal ought-to-be relations between G and P as read out by the θ-ranks of
knowledge variable over the prescribed time-period, shows different statistical spread in
the predictor values between the knowledge-induced values and the time-dependent
values of (G,P). Knowledge-induced predictors form endogenous policy directions of
change. These are termed as Events. Time-dependent values present states of the
predictors as they are by observation.
Yet in all these relations of causality and differences between the two forms of
predictor values, the outlier ‘Black Swan’ point remains identical. This singular
observation can be explained by the fact that uncontrollability and lack of predictability
are rejected in the knowledge-induced case of the circular causation results. All
endogenous variables are thus interrelated. Exogenous variables do not comprise the
variables in the circular causation relations. θ-values corresponding to (G,P)-values over
a one-process ethical learning under unity of knowledge are thus attained by rejecting the
outlier as a non-learning entity in respect of its absence of inter-causal dynamic
complementarities.
An outlier is therefore an exogenous case in both the θ-dependent and t-dependent
systems. But in the latter, it can be a case of exogenous policy variable that remains
devoid of a functional relationship with the (G,P)-variables. An example of this case is
the fiscal policy variable of charity of the Indonesian Government for poverty alleviation.
Yet charity in this case does not generate productivity in the recipients to influence
economic growth.
On the other hand, the circular causation system of inter-relations necessarily
requires complementary relations between all the endogenous variables. Their inner
dynamics combined with evolutionary learning across processes over time explain the
nature of complexity in the embedded system modeling – growth, poverty, and
wellbeing.
10
Figure A1: 3-Dimensional representation of the scatter relationship between lon[Real
Economic Growth Rate (G)], ln[Poverty Rate (P)] over time.
10
0
G
-10
2020
2010
2000
14
TIME
11
22 24
20
16 18
P
26
Figure A2: Representation of ln[Real Growth Rate (G) and ln[Poverty Rate, P1] over
THETA (learning) = values (@) corresponding to Time Points
1.0
.8
.6
.4
growth
.2
-.0
-.2
-.4
10
8
1.4
6
4
@
1.3
1.2
2
P1
Statistical Results
lnG = -2.632 + 1.564lnP + 1.737lnTHETA
t-stats: -7.735 6.554
(A1)
24.362
R2 = 0.986
lnP = 1.618 + 0.482lnG – 0.895lnTHETA
t-stats 44.109 6.554
(A2)
-8.615
R2 = 0.904
lnTHETA = 1.573 + 0.562lnG -0.940lnP
(A3)
t-stats: 10.860 24.362 -8.615
R2 = 0.991
12
Table 1: Time (t), θ, lnθ, lnG and lnP values, Indonesia.
Year
1994.00
1995.00
1996.00
1997.00
1998.00
1999.00
2000.00
2001.00
2002.00
2003.00
2004.00
2005.00
2006.00
2007.00
2008.00
2009.00
2010.00
2011.00
θ
6.65
6.92
7.93
8.52
6.05
1.12
5.64
4.89
6.07
6.44
6.99
7.20
5.69
7.43
8.16
7.84
9.25
8.24
lnθ
0.82
0.84
0.90
0.93
0.78
0.05
0.75
0.69
0.78
0.81
0.84
0.86
0.76
0.87
0.91
0.89
0.97
0.92
lnG
.76
.80
.87
.88
.63
-.40
.67
.57
.68
.71
.74
.77
.77
.71
.79
.80
.71
.80
lnP
1.26
1.26
1.22
.37
.92
.98
1.49
1.28
1.27
1.23
1.23
1.21
1.21
1.22
1.46
1.13
1.13
1.17
Source: Bank Indonesia databank.
13
Indicative simulation using Spatial Domain Analysis (SDA)
Figure A3: Interaction of Theta with Poverty Rate and Growth Rate
lnTheta = 1.573 + 0.562lnG -0.940lnP
The range of simulated values of the coefficients presently shown as ‘estimated’
coefficient values based on actual data, lies between the region dividing the three variables as
shown by their differently colored regions. The SDA-contours are the results of computation of
continuous sequences of values of possible simulation of coefficients in the divided regions.
Thus, if a value of the coefficient of lnP can be chosen in the divided region (lighter green) this
would imply a better relationship for (G↑,P↓), and thereby, better coefficient values to represent
corrected (i.e. normatively changed) relationship for (G↑,P↓,THETA↑).
Such simulated choices of coefficient values that are generated in SDA-fields involve
resource allocation questions. These in turn give rise to policy questions to be endogenously
determined by institutional discourse and formal simulation. Consider the following implication :
In Figure A3 we note the simulated possibilities:
Simulated THETA Elasticity of G > 0.562 ;
Simulated THETA Elasticity of P > - 0.940 (up to positive values)
That is, [%change in (THETA)/%change in G]/ [%change in (THETA)/%change in P] =
[%change in P / %change in G] = in the neighborhood of - 0.562/0.940 = -0.5978.
(A4)
14
Therefore, a one percent increase in the growth rate will decrease the poverty rate in the
neighborhood of 0.5978%. For this better development situation to be realized, appropriate
relations must be maintained between the G and P variables that are induced by THETA-ranks.
Such inter-variable relations for simulation purposes are implied by the results in (A5) and (A6).
Figure A4 : Interaction of Poverty Rate with Growth Rate and Theta
lnP = 1.618 + 0.482lnG – 0.895lnTHETA
By the method of SDA implications as explained in Figure A3, the simulation
implications of Figure A4 can be drawn up. The calculation in this case is the following :
Simulated P Elasticity of G < 0.482 (ought-to-be on normative policy scale to a negative value);
Simulated P Elasticity of THETA < -0.895 (up to positive values on a normative policy scale)
That is, [%change in (P)/%change in G]/ [%change in (P)/%change in THETA] ought to be
simulated to take values in the neighborhood of a positive simulated value.
[%change in THETA / %change in G] = in the neighborhood of around -0.482/0.895 = -0.5385.
That is a simulated value should be affixed in the neighborhood of +0.5385 to indicate an
increase in THETA by this percentage for a 1 percent increase in G.
(A5)
Therefore, a one percent increase in the growth rate will improve wellbeing by a value in
the positive neighborhood of +0.5385 per cent in order to affect a decrease in poverty rate in the
neighborhood of 0.5978% (expression A4). For this to be realized appropriate relations must be
maintained between the G and P variables and THETA-ranks.
15
Figure A5 : Interaction of Growth Rate with Poverty Rate and Theta
lnG = -2.632 + 1.564lnP + 1.737lnTHETA
In the same way as expressions (A4) and (A5) we obtain :
[%change in THETA / %change in P] = in the neighborhood of -1.564/1.737 = -0.9004
A6)
Therefore, a one percent decrease in P will improve wellbeing by a value in the
neighborhood of 0.9004 per cent in order to affect an increase in G and THETA (wellbeing)
relationship as indicated in expressions (A4) and (A5).
16
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