Abstract
This paper analyses empirically the relationship between economic development and fertility. Through a new sample selection and quantile regression, it investigates whether there is an inverse J-shaped pattern between these two variables, and, if so, whether it depends on development and fertility levels. Our results confirm that the inverse J-shaped pattern exists, but only when a certain level of economic development is attained. Results also suggest an innovative finding: the J-shape depends not only on the development but also on the fertility level. The higher the fertility rate, the higher the GDP per capita needed to reverse fertility decline, and the faster the negative and positive segments of the J-shape fall and grow.
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Source: Developed by the authors
Source: Developed by the authors using estimates from Table 2
Source: Developed by the authors using estimates from Table 3
Source: Developed by the authors using estimates from Table 4
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Notes
Total Fertility Rate (TFR) indicates number of children that would be born to a woman if she were to live to the end of her childbearing years and bear children in accordance with current age-specific fertility rates (World Bank 2015).
Myrskylä et al. (2009) open a new debate on when reversal occurs. For them, 2005 is an important year for this reversal, but they also identify different years for different countries—such as 1976 in the USA, 1983 in Norway and 1994 in Italy—as well as some countries (e.g. Japan, Canada, South Korea) where decline in fertility does not reverse at all. The question of when the reversal occurs is beyond the scope of this paper.
Since one of our main objectives is to divide the sample by income level to study the relationship between fertility and income, it is preferable to use GDP pc as the main covariate for measuring this relationship. The HDI is a compounded score of 3 indicators: Education Index, Health Index and GDP pc (Malik 2014). According to Luci-Greulich and Thévenon (2014: 192), “as life expectancy and school enrolment are correlated with GDP per capita… it is unclear what elements behind human development drive the fertility rebound in highly developed countries”.
An empirical test—comparing regression coefficients between tertile groups (Allison 2009)—has been made to contrast whether a significantly differentiated effect of the J-shape relationship exists among the tertile groups considered in our analysis. The outcomes of this test—available upon request—prove the importance of considering a differentiated regression analysis for each tertile group to provide a better knowledge of the J-shape pattern, as this pattern is significantly different for each group.
Following Luci-Greulich and Thévenon (2014), we include 10-year-period effects to control for variables not observed in the model that influence variation in fertility rate by decade.
The CQR approach, developed by Koenker and Bassett (1978), provides rich characterization for using a regression model to analyse the effect of covariates on conditional distribution of the dependent variable. This new technique is an advance in econometrics that facilitates analysis of the full, conditional distributional properties of the dependent variable, considering a possible differentiated effect estimated between variables depending on the τth quantile considered in the analysis (Hao and Naiman 2007). In contrast to LRM, the CQR technique is quite useful when the conditional distribution of the dependent variable does not meet the normality assumption, as it improves the robustness of the estimates in the presence of outliers.
Although we do not consider the first and second tertiles of income group in this new analysis, we applied additional estimates to test for the linear relationship between fertility and income, and whether this relationship differs for different fertility levels, or quantiles. To do so, we applied a new CQR fixed-effects panel-data analysis (Canay 2011), estimating the following equation:
$${\text{TFR}}_{it} = \beta_{0} + \beta_{1} {\text{Log\_GDPpc}}_{it} + \alpha_{i} + \delta_{t} + \varepsilon_{it} .$$The outcomes obtained indicate a significant and negative relationship between fertility and income, where the slope estimated is greater for the higher levels of fertility (Q.75 and Q.90). Thus, countries with a higher number of children born per woman suffer a greater negative impact of a variation in GDP pc on their fertility level in both tertile groups. Results from this additional analysis are available upon request.
Estimations for first and second tertiles of GDP pc are not included in the paper because their results were not statistically significant in previous subsection. Nevertheless, they are available upon request.
The \({\text{Log\_GDPpc}}_{it}\) adopts different values in OECD and third tertile subsamples.
We repeated the same analysis with the whole sample to prove that the CQR results are not driven by the subsamples selected. This robustness check, available upon request, shows that the main qualitative findings still hold, although the threshold points are lower (US$ 4794.36 for the Q10 and US$ 5092.14 for the Q90). In this regard, we consider our tertile division CQR analysis adequate in order to calculate the threshold points, since the differentiated J-shape pattern by tertile of income is significant, something that is not considered when applying an analysis for the whole sample.
Since GDP per capita is only available from 1990 for some countries, we have also repeated the same analysis with a larger sample of 167 countries and a shorter time period (1990–2010) to confirm our results. This robustness check, available upon request, shows that, although the main qualitative findings still hold, the results for the third tertile of income show a positive and significant relationship between fertility and GDP pc. When reducing the time period in the new sample and including the most recent years and the most highly developed countries, we find the final positive segment of the J-shape curve. This result highlights the importance of considering the time period in fertility studies, as it conditions the results. Further research is needed to analyse this issue in greater depth.
The difference between our outcomes, obtained using the CQR approach, and those obtained by Furuoka (2009, 2013) using the threshold regression methodology (Hansen 2000), is that the later does not find any J-shape relationship, while we do. Our approach can perform a different analysis for the different levels of fertility, something not possible with Furuoka’s methodology. The threshold regression method determines a threshold value or breaking point in the fertility–development (defined by the HDI) relationship. Considering the different levels of fertility in the sample jointly, the threshold value is calculated by dividing the independent variable into two groups (this value is calculated by minimizing the concentrated sum of squared errors of the estimated single threshold equation), avoiding the need to differentiate the presence of several J-shaped patterns between the countries with high fertility levels from those of the lower ones.
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Appendices
Appendix 1
See Table 6.
Appendix 2
Appendix 3
Quantile regression for different models using the OECD sample (see Table 2). Vertical axes show coefficient estimates of \({\text{Log\_GDPpc}}_{it}\) and \({\text{Log\_GDPpc}}_{it}^{2}\) variables; horizontal axes depict the quantiles of the dependent variable. Quantile regression error bars correspond to bootstrapped 95 % confidence (400 bootstrap replications)
Quantile regression for different models using the third tertile of income sample (see Table 3). Vertical axes show coefficient estimates of \({\text{Log\_GDPpc}}_{it}\) and \({\text{Log\_GDPpc}}_{it}^{2}\) variables; horizontal axes depict the quantiles of the dependent variable). Quantile regression error bars correspond to bootstrapped 95 % confidence (400 bootstrap replications)
Appendix 4
The Wilcoxon Signed-rank test (W test) is a nonparametric test (which does not assume any probability distributions of the variables compared) useful for contrasting differences in the distribution of two variables (see Wilcoxon 1945). The null hypothesis is that both distributions are the same, which means that there are no differences in the behaviour of the variables compared, so there are no differences in the J-shape by fertility levels:
Table 10 presents the results of W test rejecting the null, thus confirming that the J-shape is different by levels of fertility.
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Lacalle-Calderon, M., Perez-Trujillo, M. & Neira, I. Fertility and Economic Development: Quantile Regression Evidence on the Inverse J-shaped Pattern. Eur J Population 33, 1–31 (2017). https://doi.org/10.1007/s10680-016-9382-4
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DOI: https://doi.org/10.1007/s10680-016-9382-4