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Fertility Decline and Background Independence - Shuichirou Ike


Year 2016

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PrefaceAcknowledgmentsChapter 1 Background Independence of Fertility Decline1.1 The Fallacies of Demographic Transition Theory1.1.1 A Decline of Mortality Is not the Cause of a Decline of Fertility1.1.1.1 Consistencies and Inconsistencies1.1.2 Industrialization1.1.2.1 Lack of Concrete Causality1.1.3 Urbanization1.1.4 Education1.1.4.1 Educated but with Many Children1.1.4.2 Japanese Public Education1.1.4.3 Mere Quasi Correlations1.1.5 Demographic Transition Is Only a Tale and not a Theory1.1.5.1 Enhanced Nutritional Status and Not Demographic Transition Theory Explains the Decline of Mortality: McKeown's Thesis1.2 The Early Stage of Diffusion Hypothesis and Its Limitations1.2.1 Carved Seals of Diffusion1.3 Household Economics—Not Even Wrong1.3.1 Is a Society's Formation Entirely the Result of our Clear and Conscious Choices?1.3.1.1 Alterations of Circumstances are Previous Given1.3.2 What Are the Causes of Alterations of Preferences?1.3.3 The Lack of Falsifiability1.3.4 Not Even Wrong1.4 Evidence of Background Independence1.4.1 Japan1.4.2 Normal Distribution in Hokaido1.5 The Rise of Neo-Diffusionism1.5.1 Mathematical Model of Neo-Diffusionism1.5.2 The Model of Rosero-Bixby and Casterline1.5.3 The Background-Dependent Simultaneous Differential Equation Model1.6 The True Impact of Diffusion Hypothesis: Background Independence1.6.1 A Preoccupation Which Governs Us1.7 What Diffusion Theory Should Propose1.7.1 Irreversibility1.7.2 Stability and SmoothingChapter 2 Reaction-Diffusion of the Number of Children2.1 What Is the Reaction-Diffusion System?2.2 Reaction-Diffusion of the Number of Children2.2.1 Diffusion of Low Fertility2.2.1.1 Not Imitation nor a Meme2.2.2 Reaction as Disintegration of the Balance of Stochastic Fluctuations2.2.3 Fertility Decline Difference Equation2.2.3.1 An Extreme Case of DESDC2.2.4 The Application of Fertility Decline Difference Equation2.2.4.1 One Dimensional Space2.2.4.2 Two Dimensional Space2.2.5 Differential Equation of Fertility Decline2.2.5.1 Variances of Fertility Decline Are Proportional to Time in Its Initial Stage2.2.5.2 Properties of Reaction-Diffusion Equation of Fertility Decline2.2.6 Progressive Wave2.2.6.1 The Velocity for One Dimensional Space2.2.6.2 The Velocity for Two Dimensional Space2.3 A Search for a Singularity-Origin of Fertility Decline in Europe2.3.1 The Date When a Singularity Appeared2.3.2 Where Is a Singularity?2.3.2.1 Lot-et-Garonne2.3.2.2 Why Lot-et-Garonne Not Paris?2.3.2.3 The Probability of Disintegration of the Balance2.4 Reaction-Diffusion from the Singularity of Lot-et-Garonne2.4.1 Features of Lot-et-Garonne2.5 Areas Around the Singularity: Aquitaine and Parts of the Midi-Pyrénées2.5.1 Background Independence of Fertility Decline2.5.1.1 Effects of Economic Development: Restraint Factors in Fertility Decline2.6 Districts Situated 600–500 km Away from the Singularity2.7 Districts Located Further than 600 km Away from the Singularity2.7.1 Advanced Industrial Development in Nord-Pas-de-Calais2.7.2 Low Fertility in Northern France2.7.3 The Reaction-Diffusion Process in Belgium2.8 ConclusionChapter 3 Marriage Function as an Integral Equation3.1 Introduction to Marriage Function3.2 Previous Marriage Functions3.2.1 Coale-McNeil Distribution: A Convolution Model3.2.2 Applications of Extreme Events3.3 How First Marriages Occur3.3.1 Hernes ' Func яtion3.3.2 Flaws of Hernes' Function3.3.3 The More Marriages That are Evident Within a Space, the Higher the ccurrences of Marriage3.3.3.1 A Monotonic Decreasing Element3.3.3.2 Monotonic Decrease in the Never Married Ratio3.3.4 Formulation of an Integral Equation3.3.4.1 Characteristics of SDSMF—Thicker Right Tail and Higher Kurtosis3.3.4.2 Background Independence of Marriage Occurrences3.3.5 The Fit of SDSMF with the Data3.3.5.1 The Inflection Point Method3.3.5.2 The Results of Estimation3.4 Decisive Evidence of SDSMF3.4.1 A Good Theory Can Predict Some Theoretical Values3.4.1.1 The Result of a Test3.4.2 Comparing SDSMF to the Coale-McNeil and Double Exponential Distributions3.4.2.1 The Decisive Discriminant Test3.4.2.2 The Ratio of the Ever Married Population for the 1960 Cohort3.5 Testing SDSMF in Other Countries3.5.1 Testing SDSMF Using Cohorts Within the Swiss Population3.5.1.1 Similarities to the Japanese Cases3.5.2 Marriage at Young Ages: The Second Decisive Discriminant Test3.5.2.1 How Often Do Marriages at Young Ages Occur?3.5.3 A Test Using Algeria Data3.6 ConclusionAppendix A Mathematical SupplementA.1 Transforming a Difference Equation into a Differential Equation using Taylor Expansion (one-dimensional)A.2 Deriving the Velocity of the Progressive Wave in Two-Dimensional Space as √2μαReferences
 
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