TS sproj 0824090320262313
[NEAS: This candidate creates a time series of birth rates for 23 year old women. Time series analysis can be used for demographic data, including birth rates, mortality rates, and population movements (immigration, emigration, travel, pilgrimages). The NEAS project template gives guidance in forming your student project on birth rates and similar data.]
[NEAS: You may use births as a ratio to population, births as a ratio to women of child-bearing age, or births to women of a given age, such as 23 years old. The option is the least distorted by changes in age groups, such as more older women and fewer young women. By choosing 23 year old women, the birth rates are high enough that trends and cycles are more apparent.
Birth rates to 23 year old women have two potential distortions for projecting population growth.
~ Many women defer marriage and birth until they finish school. The number of women attending college has risen greatly over the twentieth century, and the average age at marriage has increased several years. An apparent decrease in the birth rate may really be a deferral of marriage.
~ Average family size for many nations and ethnic groups has decreased. Even if a women of age 23 is as likely to have a child in 2005 as in 1955, she may be more likely to stop having children after age 27 or 28.
These two items don’t invalidate your student project. We focus on your statistical work, not whether this time series is best for projecting population growth. But you may want to consider the inter-action of birth rates at age 23, family size, and age at marriage when choosing your time series.]
[NEAS: Figure 1.1 shows that birth rates are not a white noise process, a random walk, or a simple ARIMA process. One hears population forecasts for the twenty-first century in news-magazines and TV shows. Most of these forecasts are based on projections of future birth rates. We read about the decline of Russia or Japan, the Islamization of Europe, or the social security crises in many western nations.
Actuaries are experts on demographic changes, particularly as they affect pension plans, health costs, social security programs, and insurance costs. Many candidates use census data and demographic time series for this jobs. They sometimes wonder what they might use for their student projects, not realizing that they are working with extensive time series data. The data are publicly available figures. You are already familiar with the time series. Fit an ARIMA process to a time series for the student project.]
[NEAS: Figure 1.1 shows several items that influence birth rates.
Wars cause a decline in the birth rate, with a corresponding rise when the war ends. The sharp decline in 1943-1946 followed by the rise in 1947-1948 reflects World War II. The combined effect is a moving average process: if births are lower than expected one year, they are higher than expected the next year. The effects are greater when the war is domestic with high casualties, as has been true in several African nations in the past two decades.
Macroeconomic conditions affect birth rates. The decline in 1929-1935 reflects the Great Depression. If welfare payments are not made to single women with children, lower income may reduce birth rates. The economic prosperity of the 1950’s led to the Baby Boom generation. The stagflation of the 1970’s coincided with a decline in birth rates.
Economists studying economic growth say that long-term rising income may raise birth rates in under-developed countries but lowers birth rates in advanced countries. We consider the effects in advanced countries as cultural conditions.
Culture affects birth rates, but quantifying cultural conditions is not easy. The Baby Boom of the 1950’s is associated with the family values culture of that decade. The decline in birth rates during the 1960’s and 1970’s is associated with greater education and labor force participation of women and the sexual liberation of the 1960’s and subsequent years.
The NEAS project template on birth rates discusses other cultural conditions affecting birth rates. The ARIMA processes for birth rates differ by country. You may choose the nation or ethnic groups that most interests you.]
[NEAS: The candidate compares three ARIMA processes: AR(1), AR(2), and MA(1). All three can be fit to the first differences, though none forecasts that well. You may want to fit a structural model to birth rates and fit an ARIMA process to the residuals. See the NEAS project template for the types of analysis you might do.]