non-linear dynamic modelling for panel data in the social sciences
TRANSCRIPT
UPPSALA DISSERTATIONS IN MATHEMATICS
Non-linear dynamic modelling forpanel data in the social sciences
Shyam Ranganathan
Department of MathematicsUppsala University
UPPSALA 2015
91
Dissertation presented at Uppsala University to be publicly examined in Polhemsalen,Ångströmlaboratoriet, Lägerhyddsvägen 1, Uppsala, Friday, 6 November 2015 at 10:00 forthe degree of Doctor of Philosophy. The examination will be conducted in English. Facultyexaminer: Dr. Oliver Johnson.
AbstractRanganathan, S. 2015. Non-linear dynamic modelling for panel data in the social sciences.Uppsala Dissertations in Mathematics 91. 40 pp. Uppsala: Department of Mathematics.ISBN 978-91-506-2481-6.
Non-linearities and dynamic interactions between state variables are characteristic of complexsocial systems and processes. In this thesis, we present a new methodology to model these non-linearities and interactions from the large panel datasets available for some of these systems. Webuild macro-level statistical models that can verify theoretical predictions, and use polynomialbasis functions so that each term in the model represents a specific mechanism. This bridgesthe existing gap between macro-level theories supported by statistical models and micro-levelmechanistic models supported by behavioural evidence. We apply this methodology to twoimportant problems in the social sciences, the demographic transition and the transition todemocracy.
The demographic transition is an important problem for economists and developmentscientists. Research has shown that economic growth reduces mortality and fertility rates, whichreduction in turn results in faster economic growth. We build a non-linear dynamic modeland show how this data-driven model extends existing mechanistic models. We also showpolicy applications for our models, especially in setting development targets for the MillenniumDevelopment Goals or the Sustainable Development Goals.
The transition to democracy is an important problem for political scientists and sociologists.Research has shown that economic growth and overall human development transforms socio-cultural values and drives political institutions towards democracy. We model the interactionsbetween the state variables and find that changes in institutional freedoms precedes changes insocio-cultural values. We show applications of our models in studying development traps.
This thesis comprises the comprehensive summary and seven papers. Papers I and II describetwo similar but complementary methodologies to build non-linear dynamic models from paneldatasets. Papers III and IV deal with the demographic transition and policy applications.Papers V and VI describe the transition to democracy and applications. Paper VII describes anapplication to sustainable development.
Keywords: Dynamical systems, stochastic models, Bayesian, panel data, social sciences,development
Shyam Ranganathan, Applied Mathematics and Statistics, Box 480, Uppsala University,SE-75106 Uppsala, Sweden.
© Shyam Ranganathan 2015
ISSN 1401-2049ISBN 978-91-506-2481-6urn:nbn:se:uu:diva-261289 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-261289)
List of papers
This thesis is based on the following papers, which are referred to in the textby their Roman numerals.
I Shyam Ranganathan, Viktoria Spaiser, Richard P. Mann, and DavidJT Sumpter. "Bayesian dynamical systems modelling in the socialsciences." PLOS ONE 9(1): e86468, 2014.
II Shyam Ranganathan. "Parsimonious Dynamical Systems using theLASSO and the Bootstrap - a summary" manuscript.
III Shyam Ranganathan, Ranjula Bali Swain, and David JT Sumpter."The Demographic Transition and Economic Growth: Implications forDevelopment Policy." Palgrave Communications, 2015, accepted.
IV Shyam Ranganathan, Stamatios C. Nicolis, Ranjula Bali Swain, andDavid JT Sumpter. "Setting development goals using stochastic,dynamical system models." World Development. under review.
V Viktoria Spaiser, Shyam Ranganathan, Richard P. Mann, and DavidJT Sumpter. "The dynamics of democracy, development and culturalvalues." PLOS ONE 9(6): e97856, 2014.
VI Shyam Ranganathan, Stamatios C. Nicolis, Viktoria Spaiser, andDavid JT Sumpter. "Understanding Democracy and DevelopmentTraps Using a Data-Driven Approach." Big Data 3(1): 22-33, 2015.
VII Shyam Ranganathan, and Ranjula Bali Swain. "AnalysingMechanisms for Meeting Global Emissions Target - A DynamicalSystems Approach." manuscript.
The following papers were also written as part of the PhD but are notincluded in the current thesis.
1. Viktoria Spaiser, Peter Hedström, Shyam Ranganathan, KimJansson, Monica K Nordvik, and David JT Sumpter. Identifyingcomplex dynamics in social systems: The case of school segregation.Sociological Methods & Research, in press.
2. Viktoria Spaiser, Shyam Ranganathan, Ranjula Bali Swain, andDavid JT Sumpter. Building an index for sustainable developmentgoals using a data-science approach. Policy and Internet, special issue,2016, forthcoming.
3. Shyam Ranganathan, Stamatios C. Nicolis, and David JT Sumpter."Foreign aid effectiveness: An analysis of the linkages between donorand recipient countries using the Solow growth model." manuscript.
Reprints were made with permission from the publishers.
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Two transitions - I: The Demographic transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1 Demographic transition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Fertility choice model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3 Non-linear dynamic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 Two transitions - II: Transition to democracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.1 Transition to democracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2 Human Development Sequence theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.3 Non-linear dynamic model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4 Paper Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.2 Applications - Demographic transition, Millennium
Development Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.3 Applications - Transition to democracy, Development Traps . . . . . 324.4 Sustainable Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5 Summary in Swedish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
6 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
1. Introduction
Mathematical modeling is ubiquitous in the physical sciences. An electron ora chemical reaction equation, for instance, are both mathematical models thatare elegant, compressed representations of a mass of empirical observations.They allow us to make specific and verifiable predictions and hence enhanceour understanding of the complex systems of which they are parts.
In the social sciences, which had already been studied for centuries beforethe electron was conceived, mathematical models are less unequivocally em-braced. An important reason for this is the near impossibility of formulatinguniversally valid theories on most aspects of the behaviour of individuals as-sumed to be endowed with free will. In contrast to electrons or molecules thatsubmit themselves to anonymity and allow us to make representative state-ments about all similar entities based on experiments on a few, as the Bardsays, “we [humans] defy augury.”
The paucity of empirical observations has led to the proliferation of oftenmutually incompatible theories as to how the social, economic and politicalworlds operate without sufficient basis in data. Ideology has dictated the for-mulation of grand theories on the best economic or political organization ofpeople, for instance. But the successes of the scientific method and empiricismhave caused a major rethinking of the approach to these problems, primarilymotivated by the work of economists over the last century.
There are two main strands of economics-based models that have been ap-plied in the social sciences. The mechanistic modelling approach focuses onspecifying plausible mechanisms and shows how broad patterns in observa-tional data agree with the predictions of the models. The aim here is to under-stand the fundamental micro-level processes that build up to observed macro-level phenomena. But this strand of research can be criticised for axiomat-ically basing their models on unrealistic sets of conditions such as rationalagents, perfect information, a precisely specified objective function etc. Sci-entists working on this strand of research try to improve the specifications ofthe models and to align them with reality by validating theoretical assumptionsand the qualitative characteristics of the models.
On the other hand, the theoretical modelling approach focuses on specifyingan overarching system of relationships that characterise the particular prob-lem. The theory is then confirmed by identifying broad relationships betweenindicator variables through regression analysis. The aim here is to understandsystems qualitatively using reasonable theories and to use statistical models tosupport the already formulated theories. These methods can be criticised for
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ignoring complex interactions and non-linearities in the mechanics by whichthe systems work and for accepting correlational evidence as proof of causaltheory. Scientists working on this strand of research try to improve their ap-proach by formulating theories that are more specific in terms of observedindicator variables and hence more amenable to empirical testing.
Ideally, these two strands of research should converge in an understandingof the social science problem of interest by providing us information aboutmechanisms underlying the systems and processes while remaining true toreality in terms of theoretical and qualitative specifications. However the ab-sence of sufficient empirical evidence on which to base either broad theoriesor fundamental mechanisms has largely stymied this convergence.
In recent years, the emergence of computational social science and ad-vances in cognitive science have helped mechanistic researchers understandsocial processes better and to incorporate accurate qualitative assumptions intotheir models based on experimental evidence. Large public datasets contain-ing macro-level data have also become available. But while these advancesgradually result in the development of universally accepted mechanistic mod-els, it is important in the meantime to develop new methodologies that allowus to integrate the available data in making efficient policy decisions.
In this thesis, we look at a methodology to build non-linear dynamic mod-els for panel data in the social sciences. Our methodology balances the twoapproaches described earlier. The models we build extend existing theoreticalmodels to include non-linearities and interactions between indicator variables.At the same time, each model can be identified with a set of specific mecha-nisms and hence selecting the best model is equivalent to identifying the mostplausible mechanisms that result in observed phenomena.
We test a large number of data-driven dynamical system models, and useBayesian statistics to select the best model that agrees with the data. In ourframework, we assume every mechanism is equally plausible but new knowl-edge on specific sets of mechanisms can be incorporated directly by modify-ing the prior probabilities appropriately. Using these quantitatively specificmodels, we show that empirically observed phenomena in different social sys-tems are characteristics of the phase spaces of these models. We also showthat these models can predict short-term changes accurately, and hence can beused efficiently for policymaking purposes. The modelling methodology andthe background are discussed in detail in Papers I and II.
Our work focuses on two specific problems in the social sciences. Thefirst, relating to human development, is a modern extension of the study ofthe factors of economic growth. We study the demographic transition withthe key indicator variables child mortality, fertility and economic growth andshow how economic growth causes reductions in child mortality, which re-sults in fertility decline, and which in turn spurs further economic growth. Weuse our models to evaluate global initiatives such as the Millennium Develop-ment Goals and we suggest that more feasible, country-specific policies can
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be constructed using our methodology. We discuss this in detail in Chapter 2in this thesis along with a mechanistic model from the existing literature forillustration.
Having built models that explain aspects of human development, in the sec-ond problem, we ask how human development affects the evolution of culturalvalues and political institutions. Specifically we test the statements of a mod-ernization theory called the Human Development Sequence which suggeststhat economic development leads to individual emancipation which in turnleads to institutional freedoms. We show that our methodology can be adaptedto evaluate existing theory and also to understand the socio-political systembetter by identifying the sparsest set of mechanisms that agree with availabledata. We discuss this in more detail in Chapter 3 in this thesis along with atheoretical model from the existing literature for illustration.
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2. Two transitions - I: The Demographictransition
Human development is a multi-dimensional problem. Economic growth is animportant aspect of it, but often it is used as the single variable indicator of hu-man development. In this chapter, we consider a broader definition of humandevelopment and discuss our work on modelling the demographic transitionwhich looks at interactions between child mortality, fertility rate and economicgrowth. We use this model as the basis for evaluating global policy initiativessuch as the Millennium Development Goals. We briefly discuss our work onsustainable development, the new paradigm which moves from anthropocen-tric development to include the environment as a key variable of interest.
2.1 Demographic transitionThe demographic transition is an important phenomenon observed in histor-ical data where countries move from a regime of high birth rates and highdeath rates to a regime of low death rates and low birth rates. The basic modelstates that as countries become industrialised and more “developed,” crudedeath rates fall (proportion of population dying each year in total population),followed by crude birth rates (proportion of population born per year in to-tal population), leading to a transition from a high death rate, high birth rateregime to a low death rate, low birth rate regime with five distinct stages (Fig.2.1).
Researchers have studied the causes of the demographic transition and havecome up with different theories to explain the process based on a similar pat-tern observed in the socio-economic indicator variables child mortality (de-fined as number of children lost before age 5 per 1,000 live births) and totalfertility rate (the average number of children borne per woman in the courseof the reproductive lifetime). Child mortality decline was a significant driverof reduction in crude death rates as living conditions and medical knowledgeimproved and this was followed by a decline in the total fertility rate. Fig. 2.2shows how a phenomenon similar to the demographic transition can be ob-served for different countries in the child mortality and fertility rate variables.
This observation relating mortality and fertility rates has provided the in-spiration for an economic model of the transition as a problem involving aquality-quantity tradeoff. The classic models, pioneered by Becker (1981) and
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Figure 2.1. The five stages of the demographic transition model. Countries movefrom high birth and death rates in the first stage to a declining death rate and highbirth rate in the second stage. In the third stage, birth rate also starts to decline andboth birth and death rates have low values in the fourth stage. In the first four stages,population keeps increasing (slow in the first stage and faster in subsequent stages)until it saturates and declines slightly in the fifth stage when birth rates reach close toreplacement levels and death rate (as a proportion of the total population) increasesslightly.
since extended by a number of researchers (Barro and Becker, 1989; Tamura,1996) modeled the demographic transition from the standpoint of the family(or the mother) making a fertility choice decision based on an economic im-perative.
The basic idea of the model is as follows: women choose to optimise ontheir consumption and child-bearing (and child-rearing) based on the goodsavailable. Investments of time in child-bearing and child-rearing bring aboutlong-term benefits for the survival of the family across future generations butcome at the cost of decreased general consumption at the present time. Whenwages (or the value of time) are low, investment in quantity or number of chil-dren is optimal in the long-run, whereas investment in quality or child-rearingis optimal as wages and the value of time increase due to higher opportunitycosts.
This idea has been tested out against empirical data and a wealth of litera-ture exists both confirming some basic hypotheses (Barro and Becker, 1989;Barro, 1991) and disputing others (Doepke, 2005; Haines, 1998). This has ledto a proliferation of models that improve the basic model or are variants of thesame basic idea (see Paper III for a detailed literature review).
We next discuss the model proposed in Kalemli-Ozcan (2002) as illustra-tive of the general set of theoretical models that deal with the quality-quantitytradeoff.
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Figure 2.2. The demographic transition as seen in terms of the indicator variables fer-tility rate and child mortality. The lines are timeseries data for the different countrieswith the right end of each line indicating 2008 levels. We can see a transition fromhigh fertility rate and high child mortality to low fertility rate and low child mortal-ity, with the figures indicating that child mortality decline tends to precede fertilitydecline.
2.2 Fertility choice modelConsider an economy with total output at time t given by
Yt = F(Ht ,X) = AHαt X1−α
This Cobb-Douglas production function (Acemoglu, 2008) is often used ineconomic growth literature and here Yt represents the output at time t, A repre-sents the productivity, Ht represents human capital at time t and X representsthe total amount of land, which is assumed to be fixed. α is the output elastic-ity of human capital, measured as the ratio of percentage change in output topercentage change in human capital.
The output per worker is given by
yt = Ahαt x1−α
t
where yt = Yt/Lt , ht = Ht/Lt and xt = X/Lt , Lt being the number of workersat time t. Assuming the absence of rent on land, and assuming market clearingconditions, the return to human capital (wage per unit of human capital) attime t is given by
wt = FH(H,L) = Aα(xt/ht)1−α
Now, assume a population of individuals in this economy with identicalpreferences and living through two distinct periods during their lifetimes. Timeis divided into discrete periods and denoted by t. For the generation that livesas adults in time t, in their non-adult period (t − 1), individuals consume aconstant fraction of their parents’ time endowment (we assume time is thecurrency of interest in all these computations). In the second period for thisgeneration (time t), the individuals consume a certain amount of their time Ctfor themselves and spend the remaining in child-bearing (at a constant cost
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v ∈ (0,1) of their total income wtht per child) and child-rearing (at a cost etfor their education). A total of nt children are assumed to be born in the adultphase, where nt is a random number chosen by optimising expected utility.A fraction of these children qtnt survive to adulthood and we assume initallythat the survival probability for each child qt is uniform and exogenously spec-ified. The education is assumed to benefit the child’s human capital accordingto ht+1 = eβ
t ht so that the child’s human capital is proportional to the parent’sht and the time spent by the parent on education (0 ≤ β ≤ 1). Note that thecost of education is distributed across all children whereas in an analysis ofmortality, there could be a quantitative difference due to investments beingmade only on surviving children.
The budget constraint on the parent’s time endowment is then given by
Ct +wtht(v+ et)nt = wtht (2.1)
Using standard assumptions on the utility function with a Cobb-Douglasfunctional form again, the rational individuals at time t maximise the functiongiven by
Ut = γ ln(Ct)+(1− γ)Et [ln(Ntwt+1ht+1)] (2.2)
The first term is the consumption of the individual at time t, and the secondterm is the expectation at time t of the total income of all the surviving childrenat t +1, with Nt children surviving into their adulthood. The constant γ is theelasticity of consumption.
In Kalemli-Ozcan (2003), the author shows a benchmark where survivalprobability is exogenous and precisely specified so that exactly a fraction qof children survive. Thus Nt = ntq. In this case, the optimisation problem ofchoosing the optimum number of children and the optimum level of educationfor each child given by
{n∗t ,e∗t }= argmaxnt ,et
{γ ln(wtht(1− (v+ et)nt)+(1− γ)[ln(ntqwt+1ht+1)]},
(2.3)subject to n∗t ,e
∗t ≥ 0
The first order conditions in this case are given by
n∗t =1− γ
v+ e∗t(2.4)
and
e∗t =β (1− γ)
(β (1− γ)+ γ)
1− vn∗tn∗t
(2.5)
solving which we get the optimum number of children and optimum time spenton education as
n∗t =1− γ
v(1−β ) (2.6)
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e∗t =β
1−βv (2.7)
Kalemli-Ozcan (2002) explores the more complicated case where there isuncertainty as to the number of children who would survive in each generation.Given nt children are born at time t and assuming each child has a uniformprobability qt of surviving to adulthood, the total number of children survivingper individual is modeled as a random variable drawn from Bin(nt ,qt) so thatprobability of Nt children surviving is given by
f (Nt ;nt ,qt) =
(nt
Nt
)qt
Nt (1−qt)nt−Nt , Nt = 0,1...,nt
In this case, the optimization problem and the first order conditions aregiven by
{n∗t ,e∗t }= argmaxnt ,et
nt
∑Nt=0{γ ln(Ct)+(1− γ)[ln(Ntwt+1ht+1)]} f (Nt ;nt ,qt),
(2.8)
e∗t =β (1− γ)
(β (1− γ)+ γ)
1− vn∗tn∗t
(2.9)
− γ(v+ e∗t )1− (v+ e∗t )n∗t
+1− γ
n∗t+
(1− γ)(1−qt)
2qtn∗2t= 0 (2.10)
Assuming constant qt over time allows us to solve for the optimal et andnt and Kalemli-Ozcan (2002) shows that the model shown above supportsimportant stylized facts of the demographic transition, viz., 1) given exoge-nous decrease in child mortality, parents have fewer children and spend moretime on education, 2) growth rate of population increases as child mortalityincreases and population growth rate is negative as child mortality tends to 0(survival probability q→ 1).
The next step to understand the demographic transition and its linkages witheconomic growth is to endogenize child mortality by connecting the survivalprobability qt to the economic output yt . In Kalemli-Ozcan (2002), the authorachieves this by calibrating a survival function qt = q(yt) = a0(1− e(−a1yt))based on empirical data. The paper also shows the reasonably close agreementof the model to historical datasets.
2.3 Non-linear dynamic modelMechanistic models such as the one discussed above help us understand thesystem in terms of micro-level mechanisms and explain a significant portion
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of observed data. But it is not clear if these are the best models that fit the data.Also, their use in policymaking is limited as they do not necessarily containinformation on dynamic changes in the macro-level state variables, as theyfocus on micro-mechanisms.
On the other hand, macro-level models of changes in state variables are nat-urally suited to modelling problems where we are interested in the time evolu-tion of system variables. The dynamical system representations help validatethe models in terms of observed macro-level phenomena such as fixed points,tipping points etc. There are a number of techniques in the econometric andstatistics literature for specification and estimation of dynamic models and Pa-per II provides a more detailed overview. Here we will only briefly discuss theidea of using non-linear dynamic models with a simple illustration.
The use of dynamic models using differential equations or difference equa-tions is not new to demographic literature. Indeed one of the most commonlyused examples of dynamical system models - the logistic growth equation -comes from the study of demographics in ecology. Here the evolution of thepopulation (P) is modeled as
dPdt
= rP(1−P/K)
where r is the rate of population growth and K is the carrying capacity. Forthis model to be useful in empirical analysis, we should be able to infer theparameters in the model (r and K) from data. This can be done by discretisingtime in the model equation and using regression analysis with an additionalstochastic error term, which is often assumed to be normally distributed. Forinstance, the estimating equation for the logistic growth model can be writtenas
∆P(t) = P(t +1)−P(t) = rP(t)(1−P(t)/K)+ ε(t)
where P(t) is the population at discrete time t, ε(t) are identically distributednormal random variables independent across time t. Note that this model al-lows instantaneous P(t) < 0 for large negative values of the noise variable,which is physically impossible, and hence needs to be specified more pre-cisely but we ignore that here. Once we have an estimating equation in thisform, we can perform regression analysis to obtain the best estimates of theparameters from the available data.
While the logistic growth model is a simple example, the same procedureis used to fit more complex dynamic models. First, we specify a differentialor difference equation model, then write out the estimating equation with astochastic error term to represent observational noise and then estimate theparameters of the models. Such dynamic models provide phase portrait repre-sentations which show the relationships between the state variables. As theydirectly model changes in the variables, they can be integrated forward to un-derstand the time evolution of the system.
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For instance, Fig. 2.3a shows the phase portrait visualisation of the changesin child mortality and log GDP per capita based on historical data with differ-ent country trajectories superimposed. We can see that child mortality tendsto decrease and GDP tends to increase over time and that the relationship be-tween these state variables is non-linear. Fig. 2.3b shows the phase portraitfor a non-linear dynamic model that fits the data and captures the essentialfeatures of the data phase portrait. The difference equation model is given bythe equations
∆C =C(t +1)−C(t) = −0.0028C(t)(1.6G(t)−0.02C(t)) (2.11)
∆G = G(t +1)−G(t) =2.5
C(t)G(t)(10.9−G(t)) (2.12)
We briefly discuss below the methodology by which we obtain similar modelsfor the demographic transition. A more detailed description can be found inPapers I and III.
Childmortality
Gross domestic product (log)
ChinaUSA
SwedenIndia
BrazilKenya
6 9 126 9 12
0
200
400
0
200
400
Figure 2.3. Data and Model Phase portraits for child mortality and GDP. a) Lines anddots represent the development states and average yearly changes based on historicaldata. The dark, continuous lines represent trajectories for different countries from1960−2009. b) Lines and dots represent the development states and predicted yearlychanges based on models. The dark, continuous lines represent predicted trajectoriesfor different countries starting from 1960 values.
In our non-linear dynamic model of the demographic transition, the changesin the state variables (child mortality, fertility rate, and log GDP) are (possibly)non-linear functions of the current states. We approximate these relationshipsusing polynomial basis functions, with each polynomial term representing afeasible mechanism. When we restrict our analysis to only linear and quadraticterms in the variables and their inverses along with all possible 2-variable and
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3-variable interaction terms, there are 33 possible polynomial terms in the fullmodel specification and hence 233− 1 possible sub-models. We choose thebest among these using a two-stage algorithm where we first rank models witha given number of terms using log-likelihood values and then choose the bestamong these pre-selected models using a Bayes factor metric (detailed de-scription of methods in Paper I). There are specific issues related to robustnessof models - multicollinearity, endogeneity etc - that we discuss in Paper III.
Our non-linear dynamic model specified in terms of difference equations inthe key variables of interest child mortality (C), fertility rate (A) and log GDPper capita (G) is given by
∆C = −0.0028C(t)(1.6G(t)−0.02C(t))+ εC(t) (2.13)
∆G =0.043A(t)
(16−G(t)− 51G(t)
)+ εG(t) (2.14)
∆A = −0.0007A(t)(100−0.11C(t)−9A(t)− 130A(t)
)+ εA(t) (2.15)
Here, εC,εG and εA are independent and normally distributed with zeromean and variance estimated from the data. The other constants in the equa-tions are also estimated from the cross-country data.
Interestingly, we find that our model agrees with many of the propositionsmade in the mechanistic model in Kalemli-Ozcan (2002) although we made nocausative assumptions before selecting the model. For instance, we show thatthe data supports the existence of a development cycle where child mortalityand fertility declines are powered in a cycle of positive feedback by economicgrowth (Fig. 2.4).
Also, we find that child mortality is the key variable of interest rather thaneconomic growth for studying fertility decline and the model suggests a mech-anism whereby women might have fewer children if child mortality levels arelow. Similarly, we find that our model confirms the endogenous survival prob-ability function based on output per capita specified in Kalemli-Ozcan (2002)as qt(yt) = a0(1− e−a1yt ) when we ignore second order effects (we obtain∆C = −0.00448C(t)G(t) when we ignore the second-order C(t)2 term). Wealso discuss how a lagged effects analysis of our model suggests that adultmortality is also an important variable to consider for the demographic transi-tion (Paper III).
2.4 ApplicationsThe Millennium Development Goals (MDG) programme has provided an ex-cellent platform for a global approach to tackling development problems, but ithas been criticised for setting infeasible targets for developing countries, espe-cially for sub-Saharan Africa by Easterly (2009) (Paper IV provides a detailed
17
Figure 2.4. The Development Cycle as seen in the data for the three indicator vari-ables. GDP drives changes in child mortality which drives changes in fertility ratewhich in turn drives changes in GDP. The arrow widths indicate the confidence in themodel. source: Paper III
review of the literature). Using our methodology and only data up to 2000,we can evaluate the MDGs by estimating the probability of the developmenttargets being achieved.
As Fig. 2.5 shows, based on our Monte Carlo simulations, most countrieshad less than a 20% chance of achieving the MDG target on child mortality.This implies that the MDG targets for different countries were not just ambi-tious, they were largely infeasible. While providing a methodology to evaluatethe MDGs, we also provide a flexible statistical tool for policy-makers to pre-dict future development trajectories in a country-specific manner and proposemore feasible country-specific targets based on our dynamic model. In PaperIV we show how both conservative and ambitious targets can be set for coun-tries based on the historical trajectories and quantitative deviations from thebusiness-as-usual scenario rather than in ad hoc fashion.
We use similar models, but based on the so-called Green Solow model(Brock and Taylor, 2010), to come up with a model-based protocol of emis-sion cuts for different countries based on their economic output and emissionslevels (Paper VII). Our models show that achieving the 44 Gigatonne CO2equivalent emissions reductions by 2020 is extremely infeasible without vol-untary emission cuts. Improvements in technology alone cannot account forsuch steep reductions and we analyse possible mechanisms to share the bur-dens in the emission cuts.
18
Probability of reaching target0−0.2 0.2−0.4 0.4−0.6 0.6−0.8 0.8−1
Figure 2.5. Probability (in 2000) of reaching the MDG target for child mortality by2015 for different countries. Red indicates that a country had less than 20% chanceof achieving the MDG target based on historical data. A few countries like Brazil,Mexico, Turkey and Egypt actually had a very good probability of reaching the MDGtarget and our models show that the MDG target was unambitious with respect to thesecountries. source: Paper IV
2.5 DiscussionWe need to note that the data-driven models that we propose are not intendedto replace a theory-based understanding of the socio-economic problems fac-ing the world. Instead, they are intended to supplement such an understandingin the context of policy-making. Where consensus exists on theoretical mech-anisms by which certain processes occur, our methods provide an extension totheory, accounting for non-linearities and interactions between the variablesof interest and hence provide a sharper quantitative picture. Where no suchconsensus exists, our methods provide a tool with which the policy-maker andthe scientist can make useful short-term predictions.
In the Bayesian framework, any new knowledge on fundamental mecha-nisms can be incorporated into our methodology in the form of a modifiedprior distribution on the model space. Similarly, additional variables that ex-plain any particular process can be added directly into the regressions frame-work to improve the model specification. The model space increases exponen-tially in size and it is impossible to perform a full search as more variables areadded to the system. There are techniques proposed in the literature to avoid afull search (George and McCulloch, 1996). However, in Paper II, we proposea shrinkage parameter based method which can perform reasonably close tofull subset search for suitable meta-parameter values while being flexible tothe addition of new variables.
Finally, a more important question is whether our fundamental assumptionthat all countries in the world behave similarly is valid. Clearly every country
19
attempts to decrease child mortality and increase GDP, but they do so withoften fundamentally different mechanisms. In fact we see that if we look atdifferent subsamples of data that isolate only sub-Saharan African countriesor only middle income countries, the models that fit the data best are verydifferent from the overall model though they provide the same phase spacerepresentation for the subsample considered. An approach that would allow usto specify different sub-models for different groups of countries is not difficultto visualize.
However, in the absence of universally accepted mechanistic models, Oc-cam’s razor would suggest that we use the minimum number of models that ad-equately explain the data. In our case, the global model performs a pretty goodjob and improvements due to sub-model specifications are not large enough towarrant their use. The full model explains the full phase space better than anyof the sub-models while explaining each of the smaller phase spaces reason-ably well. Further, even if micro-mechanisms are different, it is very plausiblethat they could lead to the same observations at the macro-level and we retainour methodology until we find contradicting evidence.
20
3. Two transitions - II: Transition todemocracy
If mathematical modeling of human development poses a tricky problem toscientists, the study of socio-political systems and processes poses an eventrickier problem. A long sequence of political thought and historical acci-dent has established democracy as “the worst form of government except allthe others that have been tried” (Churchill). However, democracy can be acatch-all term - the United States, a federal constitutional republic, the UnitedKingdom, a unitary constitutional monarchy and Switzerland, in many aspectsa direct democracy, are all “democracies” because of the similarities in theirsocio-political institutions. Also, any individual-level understanding of themechanisms by which political processes are shaped has to account for the ex-tremely diffuse idea of social and cultural values. In the following chapter, theemphasis will be on studying the processes of democratic change in terms ofsocio-political and cultural indicator variables that represent these underlyingideas.
3.1 Transition to democracyAs an antithesis to Marx’s idea of capitalism digging its own grave and com-munism becoming the final form of political organisation, Francis Fukuyamapredicted the “End of History” (Fukuyama, 2006) and a convergence of worldpolitics towards a final form of Western liberal democracy with the fall of theBerlin Wall and the collapse of the Soviet Union. The global economic turmoiland political realignments of the last two decades have dampened enthusiasmfor such final theories. However, these last two decades have also providedsupport to the allied modernization theory, which predicts that countries andpeoples, as they begin to prosper economically, will move towards more lib-eral socio-cultural values and this, in turn, will affect the structure of politicalinstitutions making them more democratic.
Lipset (1959) provided some of the earliest empirical evidence for mod-ernization theory and later studies have confirmed similar relations betweeneconomic development and a transition to political democratisation (Barro,1999b; Wucherpfennig and Deutsch, 2009; Przeworski and Limongi, 1997;Krieckhaus, 2003). It is known that socio-economic factors such as educationand health and cultural values, provide favourable conditions for democratisa-tion (Barro, 1999b; Wucherpfennig and Deutsch, 2009), but the exact relationsare not known for certain (Barro, 1999a; Przeworski et al., 2000).
21
In this context, the Human Development Sequence (HDS) developed byWelzel and Inglehart (2005) suggests that economic (or generally human) de-velopment results in democratisation by changing individual socio-culturalvalues. To support this theory, the authors have been involved in the mas-sive World Values Survey (WVS) project where data is collected in regularwaves from across the world (Inglehart, 1997; Welzel, 2013), thus providinga large set of empirical data and testable theories. We discuss the HumanDevelopment Sequence in the next section.
3.2 Human Development Sequence theoryThe HDS theory, derived as it is from modernization theory, suggests a re-lation between the forces of economic development and democratisation, butas mediated by a change in socio-cultural values (Welzel and Inglehart, 2005;Inglehart and Welzel, 2005; Welzel et al., 2003; Welzel, 2013). The theorysuggests the existence of a linear relation where economic progress enableschanges in socio-cultural values which then leads to democratisation. Eco-nomic development provides the opportunities and means for a self-expressiveand emancipated life and the desire to shape one’s own life provides a motiva-tion to change the rules by which people are governed, with people demandingmore democracy.
To test this theory, Inglehart and Welzel (2005) define a set of indicatorvariables and predict the relationships between these variables based on thetheory. Economic development is measured at the individual level by incomeand at the country level by GDP (or GNI) per capita. Human developmentis measured in aggregate terms by the HDI and by its components GNI percapita, life expectancy and average years of schooling. Socio-cultural val-ues such as self-expression and emancipation are measured based on surveydata collected by the World Values Survey (Inglehart, 1997). Emancipativevalues provides an aggregate indicator of socio-cultural values that measures“decision-making freedom of the individual human being and the equality ofall human beings in this decision-making freedom” (see Welzel (2013) for afuller description of the variables). The analysis of WVS data shows interest-ing patterns. For instance, Fig. 3.1 shows a culture map of the world in termsof two socio-cultural indicator variables defined based on survey data. Thismap clearly shows the division of the world into distinct geo-cultural regions,and it has been shown to be persistent over multiple waves of data collection.
For the democracy variable, two measures that have been used are the hu-man rights-weighted democracy index which includes civil liberties, politicaland human rights indices published in the Freedom House and Cingranelliand Richards data project (Cingranelli and Richards, 2010), and the effectivedemocracy index which is based on the Freedom House indices but weightedby a rule of law index (Welzel, 2013; Alexander and Welzel, 2011; Alexander
22
Figure 3.1. A cultural map of the world based on WVS surveys on two socio-culturalindicator variables. The horizontal axis measures survival vs self-expression values,where a high positive number indicates prioritisation of values such as environmentalprotection, quality of life, social trust, respondent’s self-satisfaction etc. The verticalaxis measures traditional vs secular-rational values, with a high positive value indicat-ing toleration of alternative lifestyles, minorities, secular beliefs etc. In most waves ofthe WVS, a similar cultural map is generated by the plotting of these variables againsteach other with Protestant Europe scoring high in both indices. source: World ValuesSurvey.
et al., 2012). Table 3.1 briefly describes the ten socio-economic, democraticand cultural value indicator variables. These indicators are available for manyof the world’s countries over the last 30 years.
23
Tabl
e3.
1.In
dica
tors
used
inth
ean
alys
is(f
rom
Pape
rV
)In
dica
tors
Ran
geC
ompo
nent
sSo
urce
Year
sC
ount
ries
Soci
o-ec
onom
icin
dica
tors
log
GD
Ppe
rcap
ita(Y
)5
to12
-W
orld
-Ban
k(h
ttp://
data
.wor
ldba
nk.o
rg)
1800
-200
921
3
Hum
anD
evel
opm
ent
Inde
xH
DI(
H)
0to
1U
Ned
ucat
ion
inde
x,lif
eex
pect
ancy
,G
NI
perc
apita
UN
DP
(http
://da
ta.u
n.or
g)19
80-2
012
193
log
GN
Iper
capi
ta(G
)5
to12
-W
orld
-Ban
k(h
ttp://
data
.wor
ldba
nk.o
rg)
1980
-201
221
3
UN
educ
atio
nin
dex
(I)
0to
1m
ean
year
sof
scho
ol-
ing,
expe
cted
year
sof
scho
olin
g
UN
DP
(http
://da
ta.u
n.or
g)19
80-2
012
193
Lif
eex
pect
ancy
(L)
42to
83-
Wor
ld-B
ank
(http
://da
ta.w
orld
bank
.org
)19
60-2
008
213
Fem
ale
educ
atio
n(F
)0
to13
-B
arro
-Lee
Edu
catio
nal
Atta
inm
ent
Dat
aset
(http
://ba
rrol
ee.c
om)
Bar
roan
dL
ee(2
010)
1960
-200
414
6
Dem
ocra
cyin
dica
tors
Hum
an-r
ight
sdem
ocra
cy(D
)0
to1
polit
ical
righ
tssc
ore,
civi
llib
ertie
ssc
ore,
hum
an-r
ight
spe
rfor
-m
ance
scor
e
Free
dom
Hou
seFr
eedo
m-
Hou
se(2
008,
2010
),C
in-
gran
elli
&R
icha
rds
Hum
anR
ight
sD
ata
Proj
ect
(CIR
I)C
ingr
anel
lian
dR
icha
rds
(199
9,20
10)
1980
-200
618
7
Eff
ectiv
ede
moc
racy
(D’)
0to
100
polit
ical
righ
tssc
ore,
civi
llib
ertie
ssc
ore,
corr
uptio
nsc
ore
Free
dom
Hou
seFr
ee-
dom
Hou
se(2
008,
2010
),W
orld
Ban
k(W
orld
wid
eG
over
nanc
eIn
dica
tors
(WG
I)da
ta)
Kau
fman
net
al.(
2006
)
1996
-200
615
0
Cul
tura
lVal
uesi
ndic
ator
sE
man
cipa
tive
valu
es(E
)0
to1
-W
orld
Val
ueSu
rvey
(http
://w
ww
.wvs
evsd
b.co
m)
1981
-201
165
Self
-exp
ress
i ve
valu
es(S
)-2
to2
-W
orld
Val
ueSu
rvey
(http
://w
ww
.wvs
evsd
b.co
m)
1981
-201
165
24
The analysis of the empirical data for different countries, has shown evi-dence for the Human Development Sequence across different countries andover time (Welzel, 2013). This has been extended by the work of Abdollahianet al. (2012) who propose a set of non-linear differential equations to modelthe changes in the indicator variables. The model equations, based on thecausal path diagram for the HDS (Fig. 3.2) are given by:
dRdt
= [α1Y −α2(R−Y )]R(1−R) (3.1)
dSdt
= β1Y S(1−S) (3.2)
dD′
dt= [γ1S(S−D′)+ γ2D′](1−D′) (3.3)
dYdt
= λ1(1−Y )+λ2D′ (3.4)
where R is rational-secular values, S is self-expression values, D′ is effec-tive democracy, Y is economic progress measured as GDP per capita. Thedefinitions for these variables are given in the paper. The first two stand forsocio-cultural values, the third represents political institutional freedoms andthe fourth is the economic variable. All the variables except R are tabulated inTable 3.1. The model parameters α1,α2, ...,λ2 are estimated from the data.
The authors use the empirical data to fit the equations for model parame-ters and show the implications of these model equations on country behaviourand socio-political evolution. Abdollahian et al. (2013) extends this model bybuilding an agent-based model of the individual-level dynamics and calibratethis against empirical data.
3.3 Non-linear dynamic modelThe models built by Abdollahian et al. (2012, 2013) are an important first stepin understanding modernization theory from a quantitative basis. By focusingon the dynamics and the interactions between the indicator variables, thesepapers provide direct testing of the theory. However, the main weakness of themodels is their ad hoc nature. Eqs. 3.1-3.4 only represent one plausible modelthat fits observations and agrees with theory and it is possible that alternativemodels might explain the data better.
We use the methodology described in Paper I and apply it to the variablesdescribed in Table 3.1 to test the models for the Human Development Se-quence theory. In Paper V, we show that alternative explanations have moresupport in the data, shifting the emphasis from personal freedoms driving in-stitutional change to the other way round (Fig. 3.3). The data also suggeststhat the virtuous cycle driving countries towards prosperity and development,implied in the theory, may not be feasible and that there are limits to growth
25
Figure 3.2. Human Development Sequence showing the linear relation of the eco-nomic, cultural and institutional dimensions with positive feedback from institutionalfreedoms to economic progress. source: Abdollahian et al. (2012)
especially as it is impacted by expanding social and political consciousness.Increasing democracy drives increased emancipation, which in turn has a pos-itive impact on the life expectancy and education components of HDI, but anegative impact on GNI per capita. The model equations are given in Table3.2.
Table 3.2. Set of equations describing relations in Fig. 3.3 (source: Paper V)
Equation RelationdDdt = 0.071H2−0.066D HDI→ Democracy
dDdt = 0.11D(IG−1.08D)+0.025G2
dEdt = 0.028D(L−0.585) Democracy→ Emancipative Values
Life expectancy→ Emancipative ValuesdLdt = 0.028E
(1− 0.887
L
)+ 0.004
L Emancipative Values→ Life expectancydGdt = 0.002 G
E Emancipative Values→ GNI per capitadFdt = 0.0088 E
F Emancipative Values→ Female educationdDdt = 0.016+0.041FG−0.048 D
G Female education→ Democracy
We use similar but different indicators from those used by Abdollahian et al.(2012). Instead of the self-expressive values, we use emancipative values (E)and we use human rights democracy (D) instead of the effective democracyvariable. Also, we use HDI apart from just the economic indicator GNI percapita (G). The reasons for using this slightly different set of variables areexplained in Paper V.
26
Figure 3.3. Modified Human Development Sequence. source: Paper V
3.4 ApplicationsThe methodology we use in developing our models provides an important toolfor testing theories. Since the quantitative exploration of the problem is still ina nascent stage compared to the demographic transition problem, for instance,this already aids us in understanding the problem better.
We use our models to quantify the long-observed phenomenon of povertytraps (or more generally development traps) where countries can be stuck ina low prosperity regime. We show that, quite apart from institutional andcountry-specific factors, such development traps could be the result of non-linear interaction effects between variables (Paper VI).
Recently, Spaiser and Sumpter (2014) built a micro-level model that showshow individual behaviour according to a simple set of rules can result in themacro-level transitions described in Paper V. This helps in bridging the gapbetween micro-level mechanistic understanding of the processes and the the-oretical approach used by Welzel (2013).
3.5 DiscussionThere are criticisms against HDS theory from a theoretical standpoint (Duchand Taylor, 1993; Hadenius and Teorell, 2005; Teorell and Hadenius, 2006;Teorell, 2010), and it remains an open question to what extent it can explaincommonalities in the development of very different countries. There are alsoquestions raised as to the nature of the problem posed itself, as it equatesdevelopment with a Eurocentric idea of socio-cultural values. For instance,the cultural map in Fig. 3.1 may be taken to indicate, merely tautologically,that Europe scores highly in European values.
It is also important to note that, as with any survey data, there are issueswith the WVS data. For instance, not all surveys in the different countries
27
have the same set of questions due to political restrictions. There are alsoissues with studying countries such as China and Luxembourg on an equalfooting given the vast complexities in the one and the negligible size of theother. The surveys are taken infrequently and this may not be sufficient tocapture rapid transitions in cultural values. Other surveys such as the EuropeanSocial Survey (ESS) have been instituted to address many of the questions butthe WVS is more global and remains one of the most important sources ofinformation about a diverse group of countries and so we use the data fromthis survey.
At the same time, we note that modelling the World Values Survey data,and testing the Human Development Sequence theory are only the first stepsin understanding the processes of political change and their interactions witheconomic and socio-cultural processes from a quantitative perspective. Re-finements to data collection methods and the availability of more reliable datawill help in the construction of more specific theories and lead to a deeperunderstanding of the underlying system.
In this context, our methodology presents a useful exploratory tool to iden-tify the best model that explains the available data. By providing specific pre-dictions that explain global observations of phenomena such as developmenttraps, these models justify their use in policymaking.
28
4. Paper Summary
4.1 MethodologyThe social sciences are characterised by extremely complex systems compris-ing a number of non-linearly interacting variables. The use of simple mathe-matical models that explain underlying social mechanisms often results in ourmissing important emergent phenomena such as tipping points. At the sametime, machine learning-inspired models that are mechanism-agnostic do notprovide us information that could be useful for, say, policy analysis. Thesecontradictory problems have resulted in a situation where different competingtheories each based on specific data subsets exist. Each theory explains the so-cial system of interest and predicts particular features of the system but thereis no consensus on whether any one theory is right or wrong.
Paper IShyam Ranganathan, Viktoria Spaiser, Richard P. Mann, and David JT Sumpter."Bayesian dynamical systems modelling in the social sciences." PLOS ONE9(1): e86468, 2014.
In Paper I, we describe our data-driven methodology that uses panel or lon-gitudinal data to construct a dynamical system model. We model the changesin a set of state variables as polynomial functions of the different variables withinteraction terms. Without making theoretical assumptions on which variableshave an effect on others, we use a Bayesian methodology that searches throughthe space of feasible models to provide us the model that best fits the avail-able data. We use this methodology to find a model that links democracy toeconomic growth and show that our model agrees closely with the data.
The dynamical system model captures the fundamental aspect of the socialsystem being studied - its yearly change - as a function of its current state.While we make an expert decision on our choice of explanatory variables, weallow for a wide range of models that capture different possible non-linearitiesand a variety of interesting complex phenomena and let the data speak for it-self. In this way, we balance the need to explain social phenomena in termsuseful for policy-makers while keeping ideological or theoretical biases awayfrom the data analysis. Since we use a Bayesian methodology we also allow
29
for prior knowledge to be incorporated in the choice of models based on the-oretical considerations where necessary. We provide a toolbox in R (availableas the R package bdynsys) so that augmented methods may be developed toaddress specific questions.
Contribution: I worked on the methodology, analysed the data and wasresponsible for writing the paper.
Paper IIShyam Ranganathan. "Parsimonious Dynamical Systems using the LASSOand the Bootstrap - a summary" manuscript.
The underlying mathematical basis for the modelling methodology and testson different synthetic datasets was looked at as part of Masters thesis work byRoss Linscott and Tilo Wiklund under the supervision of the author of thisthesis. This work is available on the DiVA portal. In the current dissertation,a summary of some key findings of the work has been written up as Paper II.
In Paper I, we used the number of terms in the model as a complexity pa-rameter. Each polynomial term represents a particular mechanism in the socialsystem (main effects, interaction effects and non-linearities) and hence our ob-jective is to find a sparse model in terms of mechanisms. However model se-lection algorithms run into problems with the huge model space and hence themethodology becomes infeasible for systems with more than four state vari-ables. In this paper, we select models based on LASSO regressions, whichmeasure complexity based on the total absolute weight of coefficients in themodel terms and evaluate this against a shrinkage parameter. This methodconverges to the best subset selection method for an appropriate shrinkage pa-rameter value. In Paper II, we test an adaptive LASSO algorithm with stabilityselection which uses bootstrapping techniques to search through the parameterspace efficiently.
The theoretical background for the methodology used in Paper I and sub-sequent papers in this thesis was also investigated. Specifically, we found thatthere are precedents in the literature for looking at time series data as havingbeen obtained from an underlying continuous time process and inferring theparameters of the underlying system based on the discrete data. However, us-ing synthetic and benchmark datasets from the Lorenz system and the systemof equations derived in Paper V, we find that low sampling rates, high levelsof noise and high non-linearities can significantly affect the correct detectionof underlying models.
The R code is available for download from github from github.com/rossklin.Ross Linscott also has an online application where the modelling algorithms
30
can be tested (rossklin.shinyapps.io).
Contribution: I discussed the methods in the paper with the students andsupervised the analysis and results for the Masters thesis. I wrote the summarypaper, selecting relevant material from the thesis report.
4.2 Applications - Demographic transition, MillenniumDevelopment Goals
We applied our methodology developed in Paper I to specific problems of in-terest to different social scientists. The applications to human developmentand specifically to the demographic transition and the Millennium Develop-ment Goals are described in the next two papers.
Paper IIIShyam Ranganathan, Ranjula Bali Swain, and David JT Sumpter. "The De-mographic Transition and Economic Growth: Implications for DevelopmentPolicy." Palgrave Communications, 2015, accepted.
Different postulates exist as to the causative mechanisms for the demo-graphic transition and understanding this problem is crucial for policymakersworking on human development in less developed countries.
We use our methodology to create a model of the demographic transition ascharacterised by the child mortality and total fertility rate indicator variablesinteracting with GDP. The model shows that fertility rate is decreased by de-crease in child mortality, which in turn decreases when GDP increases. GDPitself increases when fertility rate decreases resulting in a virtuous cycle thatcharacterises the economic history studied by demographers. As a useful toolfor policymakers, we analyse the effect of female education on fertility rateto see if initiatives in developing countries to educate women to have fewerchildren have a basis in the available data. We show that, while there are first-order effects, it is more effective in these countries to reduce child mortalityto encourage reductions in fertility rates. We also show that our model, up tofirst order effects, agrees with the mechanistic model built by Kalemli-Ozcan(2002) in many important aspects.
Contribution: I developed the model, analysed the data and was responsiblefor writing the paper.
31
Paper IVShyam Ranganathan, Stamatios C. Nicolis, Ranjula Bali Swain, and DavidJT Sumpter. "Setting development goals using stochastic, dynamical systemmodels." World Development. under review.
The Millennium Development Goals (MDG) was an ambitious global ini-tiative started in 2000 that attempted to pool the world’s resources to elim-inate (or reduce) pressing problems in developing countries such as hungerand extreme poverty. Set to expire in 2015, the MDG initiative has helped anumber of countries with their problems. But it has also faced criticism fromeconomists for various reasons including the setting of arbitrary goals and thewasting of resources.
In our paper, we develop a stochastic version of our previous model and useit to predict the development trajectories of different countries. Our resultsshow that the MDG target on child mortality was too ambitious in the caseof many countries and it was fundamentally flawed because of a one-size-fits-all approach. We show that realistic targets could have been set for differentcountries using our methodology. This in turn would have resulted in a usefulallocation of global resources based on feasibility.
Contribution: I developed the methods, analysed the data and was respon-sible for writing the paper.
4.3 Applications - Transition to democracy,Development Traps
Applications to problems in political science are discussed in the next two pa-pers. Paper V studies the Human Development Sequence, a theory developedby political scientists that captures similarities between countries as they tran-sition towards democratic institutions and the linkages with economic growthand human development. Paper VI explores development traps, where coun-tries may get stuck in low levels of development due to the interaction effectsbetween different socio-economic and political variables.
Paper VViktoria Spaiser, Shyam Ranganathan, Richard P. Mann, and David JT Sumpter."The dynamics of democracy, development and cultural values." PLOS ONE9(6): e97856, 2014.
The Human Development Sequence (HDS) is an influential theory explain-ing how democratisation works in different countries. Based on regularly
32
undertaken World Values Surveys, the developers of this theory argue thatdemocratisation takes place in countries when the socio-cultural values (mea-sured as the indicator variable emancipative values based on the survey data)cross a certain threshold. The emancipative values themselves are shown toincrease with increase in economic status of the citizens.
While this theory has evidence in the World Values Survey data and has afeasible underlying micro-level mechanism, it is not clear if cross-country datasupports the theory. An earlier paper (Abdollahian et al., 2012) constructeddifferential equation models that showed agreement between the theory andthe data but it was not clear if alternative explanations were better. We usedour methodology to construct a dynamical system model based on these ex-planatory variables. The model showed that economic prosperity (and moregenerally the Human Development Index, which includes economic prosper-ity, health and education) has a direct effect on democracy levels which thenaffects the emancipative values, suggesting that institutional factors might bemore important in creating an emancipated citizenry than the other way round.
Contribution: I worked on the methodology and participated in writing thepaper.
Paper VIShyam Ranganathan, Stamatios C. Nicolis, Viktoria Spaiser, and David JTSumpter. "Understanding Democracy and Development Traps Using a Data-Driven Approach." Big Data 3(1): 22-33, 2015.
In spite of enormous amounts of resources spent on under-developed coun-tries, they are often seen to be stuck in what is called a “poverty trap.” Coun-tries caught in these traps seem unable to progess economically because ofsystemic effects and economists have been suggesting a number of ideas tohelp move these countries out of these trap regions.
Using our models developed in Paper V, we show that the development trapsare a natural characteristic of the dynamical system models. They representa period of slow growth due to the interactions of the various state variables.Apart from the economic trap we identify democracy and emancipation trapswhich do not allow countries to democratise or emancipate its citizens easily.For policymakers, we identify the key aspects of the traps in terms of the ex-planatory variables, indicating the most meaningful allocation of resources ifa country is to escape a trap region. At the global level we also identify coun-tries that are close to the trap regions and hence are at danger of falling intothe trap region because of noise in the system. This analysis can also help inthe formulation of global initiatives to help under-developed countries.
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Contribution: I developed the methods, analysed the data and was respon-sible for writing the paper.
4.4 Sustainable DevelopmentPaper VIIShyam Ranganathan and Ranjula Bali Swain."Analysing Mechanisms for Meet-ing Global Emissions Target - A Dynamical Systems Approach." manuscript.
Sustainable development is an important consideration for modern policyplanners. Balancing the environment with material and social goals is oftentricky, especially with issues relating to climate change. The United Nationshas assembled a task force on sustainable development and is promulgatinga set of Sustainable Development Goals on which countries should focus inthe coming years. But, in the absence of explicit mathematical models, theformulation of arbitrary goals can be a problem as evidenced by the problemswith the MDGs.
In our paper, we look at a narrow aspect of sustainable development - the in-teraction between greenhouse gas emissions and economic growth. We showhow different countries progress on the phase plane defined by these two vari-ables and how emissions can be predicted to grow on a business-as-usual basis.Our model is based on three parameters that countries can tweak to achievedifferent levels of emission control - the policy control parameter, the tech-nology parameter and the preferences parameter. We show tradeoffs betweeninvesting in each of these parameters based on the recommendations made bythe Inter-governmental Panel on Climate Change (IPCC).
Contribution: I developed the methods, analysed the data and was respon-sible for writing the paper.
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5. Summary in Swedish
Ickelinjär och dynamisk växelverkan mellan tillståndsvariabler är en karakter-istisk egenskap hos komplexa sociala system och processer. Med grund i storapaneldata presenterar vi i denna avhandling en ny metodik för att modellerasådana tillståndsvariabler samt deras ickelinjära växelverkan. Vi konstruerarstatistiska modeller på makronivå vilka kan verifiera teoretiska förutsägelser,och använder polynomiella basfunktioner där varje term i modellen represen-terar en särskild mekanism. Detta överbryggar den klyfta som finns mellanmakroteorier, som baserar sig på statistiska modeller, och mikroteorier, somstödjer sig på beteendebaserade evidens. Vi tillämpar denna metodiken påtvå viktiga forskningområden inom samhällsvetenskapen, nämligen den de-mografiska transitionen samt transitionen till demokrati.
Den demografiska transitionen är ett viktigt område inom ekonomisk forskn-ing och utvecklingsforskning. Man har påvisat att ekonomisk tillväxt minskardödlighet och födelsetal, vilket i sin tur resulterar i ökad ekonomisk tillväxt.Vi konstruerar en ickelinjär dynamisk modell och visar hur denna datadrivnamodell utvidgar befintliga mekanistiska modeller. Vi demonstrerar också hurvåra modeller kan användas inom policyutformning, i synnerhet när det gälleratt sätta utvecklingsmål för Milleniemålen eller för de globala målen för håll-bar utveckling.
Transitionen till demokrati studeras av statsvetare och sociologer. Forskn-ing visar att ekonomisk tillväxt och övergripande mänsklig utveckling förän-drar sociokulturella värden och driver politiska institutioner mot demokrati. Vimodellerar samspelet mellan tillståndsvariablerna och finner att förändringar iinstitutionella rättigheter föregås av förändringar i sociokulturella värden. Vibeskriver också tillämpningar av våra modeller i studien av utvecklingsfällor.
Avhandlingen består av en sammanfattning och sju artiklar. Artikel I ochII beskriver två liknande men komplementära metoder för att konstruera ick-elinjära dynamiska modeller från paneldata. Artikel III och IV behandlar dendemografiska transitionen och tillämpningar inom policyutformning. ArtikelV och VI beskriver transitionen till demokrati samt tillämpningar. Artikel VIIbeskriver en tillämpning inom hållbar utveckling.
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6. Acknowledgements
The infinite monkey theorem has always held a special place among my wak-ing nightmares. If I am less frightened of it now than I was about five yearsago when I started this PhD, it is because I have been around a lot of peoplewho have helped me realise that there are more efficient mechanisms to gen-erate Shakespeare than monkey sweatshops. And probably that is what thisthesis is all about.
This thesis and my academic development owes a lot, of course, to DavidSumpter, my supervisor. He has been a big part of the five adventurous yearsof collaborating with economists, sociologists, and political scientists trying tomake sense of the large tangles of information out there. Five years of learningbookended by two long conversations at the same table at Sven Dufva. Thefirst, I remember, featured Hume, Popper and the point of “scientific” socialscience, and in the second, the machines were on the verge of taking over. Allthe other conversations in the intervening period must have been stages alonglife’s way in some cosmic pattern. I hope I have imbibed enough optimismand love of doing new things from him.
Ranjula Bali Swain, my second supervisor, has been patient through muchof the five years with my tendency to go off on tangents rambling about Indianpolitics or obscure technical issues. I hope I have learnt from all her cheerfulhospitality and sound practical advice on getting things done.
Peter Hedström and the other researchers (including Viktoria who latercame to Uppsala) at the Institute for Futures Studies at Stockholm deservethanks for the help they provided me in the initial stages of my PhD, espe-cially with the Social Mechanism seminars. Ronald Inglehart and ChristianWelzel were generous with the World Values Survey data and parts of thisthesis would not have been possible without that.
The Sumpter lab, with its extremely diverse set of international scholars -there have been people from every ‘continent’ but Antarctica - has been a won-derful place to work at. Stam has been there through every long ramble as thewise elder brother. Richard, I wish I could juggle projects half as well as youdo. Viktoria, your work ethic and sincerity are inspiring. Daniel, Boris andQi, the three musketeers when I landed here, thanks for doing it in all your dif-ferent styles. Natasha and Arianna, I guess we were supposed to be the sequelto the three musketeers. Teddy, your biology fun facts and extreme politenessnever cease to amaze. Alex, thanks for the support during the long, dark tea-time of the soul. Line, thanks for the wonderful cakes and French lessons onstochastic processes. Hongli, your forthrightness is refreshing. Ernest, I hopeyou retain your earnestness. Maksym, you are the definition of solid.
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Anja, your enthusiasm is infectious and thanks for trying to teach me toswim. Erik, I have learnt a lot about chess and ‘lagom’ness from you. Marta,thanks for all the boardgame (and non-boardgame) fun. Lotta and Ty, all ourfikas and outings have helped keep me sane over these years. Dylan, our longchess-politics sessions have been awesome. There have been a number offriends from before my time in Sweden without whom all this would not havebeen possible and I will leave them nameless here even if I hope they know Iam grateful for all their support.
I have to thank Ross Linscott and Tilo Wiklund who did their Master’sthesis under my supervision. Their hard work helped clarify a lot of things forme and I learnt quite a bit in our interactions.
The Centre for Inter-Disciplinary Mathematics (CIM) has made this PhDpossible with its generous funding. It has also been instrumental in my aca-demic growth by funding interesting courses and opportunities for interactionswith other researchers. I thank the director Elisabeth Larsson and other CIMscholars for their support.
I also thank all the other PhD students, faculty and staff at the Mathematicsdepartment for the collegial atmosphere they have provided. Uppsala and theUniversity has been a wonderful base of operations and I will cherish my timehere.
Finally, at home, Divya, and back home in India, my parents, have alwaysbeen there for me. Divya has had to wear the triple crown of having to supportme as partner, parent of my child and patterner of data (the alliteration did notpan out too well but I know Divya will bear this too with patience). She hasabsolutely insisted that I state that she is the “love of my life” and I acknowl-edge that freely. My parents, sister and extended family have all supported methrough the ups and downs of a quite checquered life, even if I say so myself,and I thank them for their support and patience. To say much more about thesepeople would still be grossly insufficient so I would rather say just this little.
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