Education differentials and Population Growth on Pension Systems

死亡率预测的准确性影响着政府的支出决策。例如，对未来死亡率的高估会影响财政账户，因为更多的人要活下去，可能需要获得医疗服务和公共非缴费养老金。对生育率的低估可能会扭曲儿童抚养比率和计划的教育支出。因此，需要更好的预测来做出明智的决策。本文首先考虑调和人口学中的两种学派，即不同教育程度的死亡率学派，以及使用Lee-Carter模型预测死亡率的方法。其次，计算预测对公共卫生和养老金支出的影响。在传统的性别和年龄变量之外加上教育程度的差异，将有助于改进预测，因为教育水平与死亡率和生育率的变化密切相关。我们可以定义与人口变化组成部分有关的三种风险：死亡率、生育率和移徙。死亡风险已被广泛研究。Lee和Carter（1992）提出了一个用于预测死亡率的统计模型。尽管在预测死亡率方面应用最广泛，但该模型受到了批评，并提出了许多改进意见（例如Bergeron-Boucher等人，2017;Pascariu, Canudas-Romo, and Vaupel, 2018）。该建议指出了另外三个缺点：对序列长度的敏感性、建模假设和包含辅助变量。也就是说，如果没有长时间序列，模型就不能很好地预测，如果使用短时间序列，结果可能对附加数据敏感。这是一项挑战，因为许多国家没有足够长的系列，或者现有系列存在测量问题。该模型还对死亡率的年龄模式提出了强有力的假设（Girosi和King 2008）。最后，还没有测试社会经济和教育差异在多大程度上可以改善预测（Lutz和Samir 2013）。生育风险和移民风险是长期风险，没有像死亡率那样被广泛探讨。文献通常使用重叠代模型关注生育风险，其中孩子的数量是确定的，能力是随机的，而两者都取决于背景和教育（Cremer, Gahvari, and Pestieau 2011）。此外，家庭的生育决定影响人口增长率，从而影响养恤金制度的可持续性。另一方面，（p<e:2> nzaru 2015）显示了罗马尼亚的移民如何成为劳动力市场赤字的唯一解决方案。最后，在我的初步分析中，我已经证明，通过添加社会经济差异等变量，这些模型显示出死亡率和生育率预测的改善。在提议的研究中，我将进一步测试相关的和可用的变量，如教育和支出（作为财富的代理）来预测死亡率，生育率和移民，以进一步研究它们对养老金的影响。我的工作的初步结果表明，死亡率随着教育的变化而变化。

The accuracy of mortality forecasts shapes the government decisions on expenditures. For instance, overestimation of future mortality affects fiscal accounts because more people staying alive may require access to health services and public non-contributing pensions. Underestimation of fertility may distort the child dependency ratios and planned expenditures on education. Therefore, better projections are required for informed policymaking. This proposal considers, first, reconcile two schools in Demography, the school of various mortality outcomes depending on educational attainment, with the approaches of forecasting mortality using Lee-Carter model. Second, calculate the impact of the forecast on public health and pension expenses. The inclusion of educational differentials on top of the traditional variables of sex and age will lead to improved projections because the level of education is closely associated with changes in mortality and fertility. We can define three types of risks related to the components of population change: mortality, fertility and migration. The mortality risk has been widely studied. Lee and Carter (1992) proposed a statistical model used to forecast mortality. Despite being the most widely used in forecasting mortality, the model has been criticised and many improvements have been proposed (e.g. Bergeron-Boucher et al. 2017; Pascariu, Canudas-Romo, and Vaupel 2018). This proposal identified three further shortcomings: sensitivity to the length of series, modelling assumptions and inclusion of auxiliary variables. That is, the model does not forecast well without long time series and the results can be sensitive to additional data if short series are used. This is challenging as many countries do not have sufficiently long series, or the existing series have measurement problems. The model also imposes strong assumptions about the age patterns of mortality (Girosi and King 2008). Finally, it has not been tested to what extent the inclusion of socio-economic and educational differentials may improve the forecasts (Lutz and Samir 2013). Fertility risk and migration risk are a long-term risks not as widely explored as mortality. Literature typically focuses on fertility risk using an overlapping generation model, in which the number of children is deterministic, and abilities are stochastic, while both depend of background and education, (Cremer, Gahvari, and Pestieau 2011). Also, household's fertility decisions affect the rates of population growth and, thus, the sustainability of the pension system. On the other hand, (Pânzaru 2015) shows how migration in Romania becomes the only solution for labor market deficit. Finally, in my preliminary analysis, I have demonstrated that the models show improvements in mortality and fertility forecasts by adding variables like socioeconomic differentials. In the proposed research, I will test further the relevant and available variables such as education and expenditure (as a proxy for wealth) to forecast mortality, fertility and migration, to further study their effects on pensions. A preliminary result of my work suggests that there are changes in mortality rates according to education changes.