Change and prediction of income and fertility rates across countries

Abstract

This paper analyzes and predicts the changes of relationship between income and fertility rate of cross-countries using a bivariate mixture model and a latent change score model. This paper has shown that there is a negative relationship between income and fertility rate, which is presented in the form of inverted S-shaped curve which shows the three regimes of demographic transition. Some developed countries have completed their demographic transition in fertility rate, and in developing countries, the demographic transition in fertility rate is still in progress. This paper has also shown that the number of peaks of income distribution has increased in recent years comparing to 1960s and the number won’t decrease in the future. However, the number of peaks of fertility rate distribution hasn’t changed from 1960s to recent years but due to the shift, finally, the distribution will change to a uni-modal distribution in the future. The income will be applied to the conditional convergence and the fertility rate will be applied to the absolute convergence. The fertility gap among cross-countries will disappear, but the income gap won’t. Although the population conditions in developing countries will improve, income inequality in cross-country may not be improved after all.

Keywords:

• income distribution
• fertility rate
• mixture distribution
• latent change score model
• Bayesian estimation

AMS Subject classifications:

• J11
• J13
• O15

Public Interest Statement

This research analyzes and predicts the changes of relationship between income and fertility rate of cross countries. Income and fertility rate have a strong interrelationship. The changes of fertility rate itself have been studied long time ago in demography. However, the study on the changes of distribution is pretty new. Furthermore, this research analyzes the changes in the joint distribution of income and fertility rate. This research shows not only the negative relationship between income and fertility rate which is a well-known fact, but also change, convergence, and prediction of their distributions. The fertility gap among cross countries will disappear but the income gap will not. Even though the population conditions in developing countries will improve, income inequality in cross-country may not be improved after all. By playing animations, readers can observe the results visually.

Acknowledgements

I would like to thank the editor and anonymous referees for their very useful comments and suggestions.

Notes

Supplemental material for this article can be accessed here http://dx.doi.org/10.1080/23322039.2015.1119367

1 The three types in Thompson (1929), Landry (1934), and Notestein (1945) are closely parallel to each other. Kirk (1996), Weber (2010), and Galor (2011) surveyed on the demographic transition in detail.

2 Some researches (e.g. Doepke (2005), Murphy (2009), Fernández-Villaverde (2001), etc.) report that an increase in the income increases fertility.

3 This research, I believe, is the first one to consider and analyze the joint distribution of both variables at the same time using a bivariate mixture distribution model and a latent change score model in the framework of demographic transition.

4 In the data, there are unusual countries which are birth control countries, oil-producing countries, and negative growth countries. We have also analyzed the data, exclusive of 10 unusual countries. These countries are China (20), which carries out one-child policy, Iran (51) and Venezuela (104), which are two major oil-producing countries, and Central African Republic (17), Congo Dem. Rep. (23), Guinea (43), Haiti (45), Madagascar (61), Nicaragua (74), and Niger (75), which were poorer in 2010 than in 1960. These countries have lower GDP per capita in 2010 when compared to GDP per capita in 1960. The figures in parentheses are country numbers in Tables 1 and 2.

5 Many previous studies depict the demographic transition due to time flowing; however, Figure 1 is depicted by per capita income level. The horizontal axis shows GDP per capita, instead of time flowing.

6 The investigation of the results using other distributions instead of the normal distribution is left for further study.

7 In this analysis, the three-peaks start to appear from 1972.

8 In this analysis, the left peak starts to be higher than the right peak from 1990.

9 The names of classification in this research—low-income, lower middle-income, upper middle-income and high-income—are just for the sake of convenience. They differ from the classification of World Bank which is defined according to the GNI per capita, calculated using the World Bank Atlas method.

10 With the amendments in individual effects, this research assumes the distributions of priors for ${\mathit{\alpha }}_{y,i}$ and ${\mathit{\alpha }}_{f,i}$ as follows: ${\mathit{\alpha }}_{y,i}\sim N(m,s^2)$ and ${\mathit{\alpha }}_{f,i}\sim N(m,s^2)$ where $i=1,\cdots ,106$, $m=0$ and $s^2=10,000$.

11 We post the estimation results using 96 countries in Table 3 in Appendix. Excluding these 10 countries has no significant effect on the results.

12 Credible interval estimates the probability of being in that interval, but confidence interval does not predict that the true value of the parameter has a particular probability.

13 The 0.0000s in Table 7 mean very small positive numbers, not exact 0, because we have rounded to four decimal places.

14 We post the estimation results using 96 countries in Table 4 in Appendix. Except that the 95% credible interval of ${\mathit{\delta }}_{yf}$ includes 0, the results where we have used 96 countries are not so different from the results where we have used 106 countries. Excluding these 10 countries has no significant effect on the results.

15 Predicting ${\mathit{\alpha }}_{y,i}$ and ${\mathit{\alpha }}_{f,i}$ over 20 years, the fertility rates of Bangladesh (5) and Zimbabwe (106) are negative values which are unrealistic values. So, predicting over more years has been stopped.

16 It is considered that the result, the arrows at the lower right corner are slightly upward, is due to the recent rising trend in the birth rates in some developed countries, e.g. Sweden, the UK, Spain, Italy, and Finland.

Additional information

Funding

The author received no direct funding for this research.

Notes on contributors

Inyong Shin

The author is an economist and statistician. His main research fields are Economic Growth, Computational Economics, Bayesian statistics and Dynamics. His current research area includes demographic transition. Demographic transition has been studied by Economics as well as Demography, Sociology, Statistics, etc. Almost all of previous studies on demographic transition depict the demographic transition due to time flowing. However, he depicts the demographic transition by income per capita level in this research, that is, the demographic transition is analyzed from an aspect of Economics. The problems like gap between rich and poor, and raising population are great economic and political issues of our time to be solved.