Statistics and Other Calculations¶

Statistics¶

Case Shiller Home Price Index¶

The S&P Cotality Case-Shiller U.S. National Home Price Index tracks home prices in the United States. The time-series data taken from FRED is seasonally adjusted but not adjusted for inflation.

Case Shiller Home Price Index Inflation-Adjusted¶

The S&P Cotality Case-Shiller U.S. National Home Price Index tracks home prices in the United States. The time-series data taken from FRED is seasonally adjusted but not adjusted for inflation. The utility.adjust_for_inflation function is therefore used to adjust this data for inflation so that the values of the index can be compared over time.

CPI¶

The Consumer Price Index (CPI) tracks inflation in the United States. The time-series data taken from FRED is seasonally adjusted.

Cumulative Single-Family Units Completed¶

Cumulative single-family units completed is the number of single-family housing units that have been built since the start year. Given a function \(f(x)\) that returns the number of single-family housing units built in a given year \(x\) (where the start year is \(x = 1\)), the cumulative single-family units completed by year \(x\), \(h(x)\), is:

Time-series data for the number of single-family housing units built in a given year is taken from FRED.

Cumulative Single-Family Units Completed per Person¶

Cumulative single-family units completed per person is the number of single-family housing units that have been built since the start year divided by the population size in that year. Given a function \(f(x)\) that returns the number of single-family housing units built in a given year \(x\) (where the start year is \(x = 1\)) and a function \(g(x)\) that returns the population size in year \(x\), the cumulative single-family units completed per person by year \(x\), \(h(x)\), is:

Time-series data for the number of single-family housing units built in a given year and the U.S. population in a given year are taken from FRED.

Homeownership Rate by Age¶

Time-series data on homeownership rate by age is taken from FRED and has the following series IDs for each age range:

Mean Annual Hours Worked¶

Mean annual hours worked is obtained from FRED and represents all workers in the United States.

Nominal Median Income Male by Age¶

Time-series data for nominal median income for males by age is obtained from the U.S. Census Bureau Current Population Survey Annual Social and Economic Supplements, Table P-8.

Population¶

Time-series U.S. population data is taken from FRED.

Real Median Income Male by Age¶

Time-series data for nominal median income for males by age is obtained from the U.S. Census Bureau Current Population Survey Annual Social and Economic Supplements, Table P-8. This data is then adjusted for inflation by the function utility.adjust_for_inflation.

Real Median Income Male to Real Home Price Index by Age¶

Real median income for males to the real home price index is calculated for each age group for a given year \(x\) using the following formula:

where \(r(x)\) is the real median income for males and \(h(x)\) is the real home price index.

Real Median Income Male to Unit Output by Age¶

Real median income per unit output is calculated for each age group of males in the following manner. Let \(t(x)\) be the mean time, in hours, a worker works in a given year \(x\) and \(p(x)\) be the total factor productivity during that year. Then, let output \(u(x)\) be defined as:

Now let \(r(x)\) be real median income in year \(x\). Then, real median income per unit output for year \(x\), \(f(x)\), is then:

Time series data for total factor productivity and mean annual hours worked is taken from FRED, while nominal median income data is taken from the U.S. Census Bureau Current Population Survey Annual Social and Economic Supplements, Table P-8 and then adjusted for inflation using utility.adjust_for_inflation.

Real Net Worth per Household by Age¶

Time-series data for real net worth per age group and number of households headed by each age group is taken from the U.S. Federal Reserve Distributional Financial Accounts data. For more information, see the U.S. Federal Reserve's Distributional Financial Accounts overview.

Real net worth per household for a given year \(x\) is calculated using the following formula:

where \(w(x)\) is the real net worth of the age group during year \(x\) and \(h(x)\) is the number of households headed by members of the age group during year \(x\).

Single-Family Units Completed¶

Time-series data on the number of single-family housing units completed in the United States each year is taken from FRED.

Single-Family Units Completed per Person¶

Time-series data on the number of single-family housing units completed in the United States each year is taken from FRED. Time-series U.S. population data is taken from FRED.

Total Factor Productivity¶

Time-series data for total factor productivity is taken from FRED.

Other Calculations¶

Adjustment for Inflation¶

Adjustment for inflation is performed by the utility.adjust_for_inflation function (see the API documentation).

An inner join is performed on the year column of the nominal and cpi DataFrames prior to further operations.

Then, the CPI values provided in the cpi DataFrame are rebased to the last year provided in the column. Given a vector of CPI values \(\vec{c} = [c_1, c_2, ... , c_n]\) corresponding to years \(y_1, y_2, ... , y_n\) with base year \(y_i\) (that is, \(c_i = 1\)), the index can be rebased to a year \(y_j\) using the following equation:

Finally, the nominal values provided in the nominal DataFrame are adjusted for inflation using the rebased CPI values. Given a vector of nominal values \(\vec{v} = [v_1, v_2, ... , v_m]\) and a vector \(\vec{d}\) consisting of the reciprocals of the rebased CPI values, \(\vec{v}\) can be adjusted for inflation using the following equation:

A Note on Real Median Income¶

Real median income data for males is heavily utilized here because it allows for better comparison of real median wages over the long term without taking into account the rapid labor force and educational changes undergone by women during the past century. Though it has decreased substantially during the past century, the male labor force participation rate still exceeds the female labor force participation rate at nearly 70%. More consequentially, the percentage of male workers who work full-time has increased modestly from 65% in 1950 to 76% in 2022, while the percentage of female workers who work full-time has more rapidly increased from 37% in 1950 to 68% in 2022. Moreover, the percentage of bachelor's (as well as master's and doctoral) degrees awarded to women has similarly rapidly increased from 24% in 1950 to 59% in 2022, and the percentage of workers in STEM fields who are women has increased from 8% in 1970 to 27% in 2019.

The large increases in full-time female employment, the percentage of post-secondary degrees awarded to women, and the percentage of the relatively high-paying STEM workforce made up of women would be expected to drastically increase the real median income of female workers, obfuscating any potential negative economic factors experienced by the female workforce at different points in time. While the male labor force participation rate, the percentage of post-secondary degrees awarded to men, and the percentage of STEM workers who are men have all declined substantially over the past century, the modest increase in the percentage of male workers employed full-time and the modestly declining majority of STEM workers who are men permit a better comparison of real median wages over time. Therefore, the real median wages of males are used in the calculations of the majority of the statistics under observation here.

Even though young men's declining real median income and other economic statistics are signals of decreasing health for young men, young women's increasing real median income, full-time employment, educational attainment, and STEM workforce participation over the past century are signals of increasing health for young women. That said, all of the available signals must be taken into consideration when accounting for changes in male, female, and total youth health over time, as even these positive economic signals for young women may be outweighed by other signals of decreasing health for young women.